Statistics of the Minimum Value Set Order Instructions: Please , you have to write the questions, just answer the 5 problems.
Statistics of the Minimum Value Set
just one page. is actually due by the 12, so I will make a payment on that pretty soon.
Statistics of the Minimum Value Set Sample Answer
The minimum value is the least observation in a set (Larson, 2012). For instance, the minimum value list is 2.
The lower quartile or first quartile, in this case, will be computed as follows:
N = number of observations = 15
1st quartile = 0.25*15 = the 3.75 observations
The first quartile will be the average of the 3rd and the 4th observation.
1st quartile = (3 + 4) /2 = 7/2 = 3.5
The median is defined simply as the central or middle observation when all values are arranged in descending or ascending order (Larson, 2012). In this case, when the observations are arranged in ascending order, and the middle value considered the median is 5.
The upper quartile or 3rd quartile is calculated as follows;
3rd quartile = 0.75*15 = 11.25 observations
This implies that the 3rd quartile is the average of the 10th and 11th observations.
3rd quartile = (11 + 11) /2 = 22/2 = 11
Maximum value is the largest observed value = 20
Inter-quartile range = 3rd quartile – 1st quartile
= 11 – 3.5
= 7.5
Standard deviation =
= =
=
=
= 14.14213562373095
= 14.14
Z-score = = = 1.2
The sample standard deviation can be derived from the population standard deviation using the following formulae (Larson, 2012).
= = 5 / √25 = 5 / 5
= 1
Thus, the sample standard deviation is 1.00.
:
:
n = 30, NY mean = 2.00 and NY sd. Dev. = 0.05
n = 30 NJ mean = 2.02, and NJ Sd. Dev. = 0.05
t =
=
=
=
DF =
=
= 58
t (.05, 58) = T.INV.2T(0.05,58) = 2.0017
Since the |t calculated| = 3.8730 > t (.05, 58) = 2.0017 reject (Larson, 2012). This means that the two means are not equal, NJ and NY gas prices is not equal.
Assignment requested deadline July 26 by 8pm. Please read below for information concerning assignment. Support responses with examples and use APA formatting in the paper. You may access the school’s website by logging into: https://mycampus.southuniversity.edu/portal/server.pt
Please note that when you log into the website you must click launch class, and on the next screen click syllabus to view this week’s readings (week 1) and Academic Resources to access the school’s library.
To support work, use the course and text readings and also use outside sources. As in all assignments, cite your sources in your work and provide references for the citations in APA format.
Deliverables:
In a 2- to 3-page Microsoft Word document, submit the following:
• Citing research from a variety of sources, including the company’s website, social media sites, company blogs, industry and trade sources, and other sources, provide a description of the organization, including the organization’s products or services, customer or client base, areas of operation or distribution, history, main competition, and the corporation’s current situation.
• Discuss the mission, vision, and ethics policy of this corporation. What led you to select it?
• Discuss the ethical principles under which the organization works.
Provide your references in APA format.
Note: Your instructor will assign final companies based on student selections. Please note that you may receive your second or third choice in order to avoid overlapping among students.
Submission Details:
• Name the document SU_BUS3001_W1_A3_LastName_FirstInitial.doc.
• Submit the document to the W1 Assignment 3 Dropbox by Tuesday, July 26, 2016.
Assignment 3 Grading Criteria Maximum Points
Provided a description of the organization, citing research from a variety of sources. 10
Discussed the corporation’s mission, vision, and ethics policy and your reason behind selecting the corporation. 20
Discussed the ethical principles of the organization. 10
Wrote in a clear, concise, and organized manner; demonstrated ethical scholarship in the accurate representation and attribution of sources (i.e., in APA format); and displayed accurate spelling, grammar, and punctuation. 10
Total: 50
The 2 companies that I submitted are as follows:
1) General Motors
2) Ford Motor
SAMPLE ANSWER
Deliverables
This essay provides a description of General Motors including the company’s products, customer base, areas of operation, history, main competition, and the company’s current situation. It also gives a discussion of the mission, vision, and ethics policy of the company and gives reasons as to why this writer selected it. The paper additionally provides a discussion of the ethical principles under which General Motors works.
General Motors is a global car manufacturer that has its headquarters in Detroit, Michigan. The company was founded in 1908 by William C. Durant. According to Alfred P. Sloan (2015), the products General Motors offers include automobile models such as Chevrolet, Oldsmobile, Buick, Cadillac, and GMC Truck & Coach (p. 12). The organization also produces a high number of locomotives, gas-turbine, and diesel engines as well as appliances for domestic use. The company’s customer base is mainly the section of the population that does not have too much money to spend on cars but are seeking fuel-efficient automobiles (Thomas A. Crumm 2010). General Motor’s main areas of operations are the production and selling of motor vehicles and their parts as well as the sale of financial services. Currently, the company’s situation is such that it has 215,000 employees, serves six continents, and it is making high sales having sold 9.8 million vehicles globally in 2015 (General Motors 2016).
According to Ovidijus Jurevicius (2013), General Motors does not have an official mission statement. However, the company states on its website that the Corporation is committed to delivering outstanding cars and works towards giving the buyers of their products a positive ownership experience. The vision of the company is to be the global leader in transport products and associated services. The company also desires to earn the enthusiasm of its customers through continuous improvement motivated by reliability, cooperation, and invention (General Motors Vision Statement, 2016). The values enshrined in the ethics policy of General Motors are creating lifetime customers, continuous improvement, prioritizing safety and quality, delivering products that offer long-term value and making a progressive transformation (General Motors Vision Statement, 2016).
The ethical principles that General Motors works under may be discussed as follows. Safety and quality are crucial in automobile products and so General Motors focus on it is commendable. Creating lifelong customers is also vital because the organization needs customers to remain in business. Continuous improvement is critical because new technologies are making cars and other products that the company produces more fuel-efficient and environmentally friendly. The company’s commitment to long-term value is also essential because buyers are assured that they will get value for money and that the firm will offer the necessary support services from the company as they continue to use their products. Making a positive difference is also crucial both to buyers and other citizens of the world because the company does not only offer goods and services to its customers but also engages in corporate service responsibility activities that improve the quality of life of people who are in need in one way or another.
From the foregoing explanations and discussions, it is clear that General Motors is one of the most prominent companies that produce automobiles and household appliances. The current standing of the company among its competitors is an indication that its products are likely to continue being used by customers into the future.
References
Crumm, T. A (2010). What is good for general motors?: Solving America’s industrial conundrum New York: Algora Publishing
General Motors (2016) Our Company General Motors Retrieved from
Statistics and the Sample Standard Deviation Sample Answers
The sample standard deviation can be computed from the population standard deviation. In fact, the sample standard deviation is calculated using the following formula:
=
=
= 1.00
Hence, the standard deviation of 100 people is 1.00.
A mode is an ideal measure of central tendency when dealing with nominal data. It is, mostly, used to determine the most common category. However, it has a limitation that it is not unique. For instance, when there are two or more, highest frequencies (Lucy, 2013). Thus, it leaves the researcher with the problem, especially in the situation when there are more categories with high equal frequencies.
Mean = 65, std. dev. = 2
The z-score of a group of 36 with a mean of 66 will be as follows:
First, we need to obtain the sample standard deviation of the 36 people.
=
=
Notably, the μ sample = μ population = 65
z-score =
Thus, the z-score of a group of 36 is 3.00 (Lucy, 2013).
Since the interval does not contain the claimed mean of 100, there is no sufficient evidence to claim that the mean is 100 (Lucy, 2013).
The critical values at the 95% level of significance is as follows:
= = 1.96.
Statistics and the Sample Standard Deviation References
Lucy, D. (2013). Introduction to statistics for forensic scientists. John Wiley & Sons. From https://books.google.com/books?hl=en&lr=&id=WCo9nLhTDzsC&oi=fnd&pg=PT9&dq=introduction+to+statistics&ots=wunSXou94x&sig=-7y17S27TxgNEBeaErQdxBUDYG0
Imagine that you are a contracts officer for the Internal Revenue Service (IRS), and that your supervisor has tasked you with the procurement of a new software system for processing tax returns.
Use the Internet to research one (1) scandal related to government procurement that has occurred within the past four (4) years.
Write a two to three (2-3) page paper in which you:
Analyze the Federal Acquisition Regulation (FAR), and conclude whether or not these regulations overall offer adequate protection of the collective buying power of the American people. Prepare an argument in support of your position.
Based on the scandal that you have researched, determine whether or not the executive branch is the proper branch to effectuate change that would provide checks and balances for the purchase of good and services for the United States government. Provide a rationale for your answer.
Use at least three (3) quality academic resources in this assignment. Note: Wikipedia and similar websites do not qualify as quality academic resources.
Format your assignment according to the following formatting requirements:
Typed, double spaced, using Times New Roman font (size 12), with one-inch margins on all sides.
Include a cover page containing the title of the assignment, your name, your professor’s name, the course title, and the date. The cover page is not included in the required page length.
Include a reference page. Citations and references must follow APA format. The reference page is not included in the required page length.
The specific course learning outcomes associated with this assignment are:
Describe the legal and administrative framework and economic considerations of the federal procurement process.
Distinguish between the various types of contracts and considerations for use.
Use technology and information resources to research issues in procurement and contract law.
Write clearly and concisely about procurement and contract law using correct grammar and mechanics.
SAMPLE ANSWER
Introduction
The federal government is one huge institution whose operations are regulated. In order to ensure smooth operations within government, there are certain rules and regulations that must be followed. Just like every other organization, the government also has a procurement department whose mandate is to make purchases on behalf of the government. Government procurement is slightly different from ordinary procurement process. This is mainly due to the nature of contracts as most involve huge amounts of money. To ensure that due process is followed when it comes to government procurement, the Federal Acquisition Regulations (FAR) were established. With these rules, government procurement has been standardized and this has enhanced consistency (Oyer, 2015). Further, FAR ensures that there is impartiality and fairness. Even with the stringent regulations that have been put in place, scandals in government procurement still happen from time to time. The aim of this discussion is to critically analyze the Federal Acquisition Regulations with the aim of establishing their effectiveness. The discussion has in particular sought to establish whether the regulations offer adequate protection of the collective buying power of the American people. In order to properly put into context the effectiveness of FAR, the paper has analyzed one of the recent scandals in government procurement namely ‘The Fat Leonard Scandal’.
Analysis of FAR
As aforementioned, government procurement is somewhat complex compared to the normal procurement procedure for businesses. The process of procurement is different and so is the nature of contracts awarded. Fully aware of the mischief presented therein, it became necessary to have specific laws that govern the procurement process within various government departments. The aim was among other issues to protect the collective bargaining power of the American people adequately. Unfortunately, as seen from the Fat Leonard Scandal below, the FAR is not yet strict enough to offer the protection required.
The Fat Leonard Scandal
In this scandal, Glenn Defense Marine was appointed to provide logistic services to the United States Navy. Glenn Francis, the leader of the company is however accused of flouting government procurement rules by bribing officers in the navy. According to a report released recently, (Manuel, 2015) Glen Francis, together with members of his company plotted a scheme that would see the cost of husbanding logistic services provided to the Navy hiked. The scheme was collusion between Glenn’s company and some insiders from the Navy who, together, would work to see inflation of prices of the services provided. When the scandal was unearthed sometime in mid-2014, the services of Glenn Defense Marine were suspended immediately and some officers from the Navy were relived off their duties.
In the year 2009, the American Navy made a request as required by the procurement procedures. In the request out, the requirement was for a company that has the capability to husbanding services in logistics. Husbanding services is a common term that is used in the maritime field to refer to support services offered to the navy including protection of the ships and transporting the members of each ship. These services also include provision of basics such as water and food, removal of sewage and trash and any form of logistical service that the Navy may require. Usually, each request will clearly outline the nature of husbanding services that the Navy is seeking. The scandal would go on undetected until some in 2013 when discrepancies were noticed and immediate action taken.
Loopholes in Public Procurement
The Federal Acquisition Regulation has been cited as one of the most effective and efficient. It has seen a watertight process that ensures that the procedure is followed to the letter. However, even with such strict measures, it is evident that some loopholes still exist (Manuel, 2015). With the Fat Leonard Scandal, it is clear that there are areas that the federal government must step in to tighten the ropes. Although investigations into the Fat Leonard Scandal are still ongoing, it is becomes clear that there are major gaps within the system. In this particular case, how is it that the members of the Navy got too involved in the procurement process that they had a chance to negotiate a deal with the service providers. The standard requirement is that the team involved in procurement should not be the ones directly benefiting from the services to avoid conflict of interest. In this case, it appears that those involved in the process of procurement were also directly benefiting hence the corruption.
Another area of the Federal Acquisition Regulation that must be carefully relooked and evaluated is on the selection of the bidders (Thai, 2012). Besides selecting the lowest bidder, other criteria must be used. For instance, a background check would help to establish the history of the company. In this case, there is a possibility that Glenn Defense Marine could have been involved in other shady dealings in the past. With such a revelation, this company would not have been selected to provide services to the navy.
Eliminating the Loopholes
From the above case, it is clear that Federal government must step in to ensure that all the loopholes are sealed. In particular, the executive arm of the government is best placed to put checks and balances that will see an effective FAR. It will also be necessary that the government is more proactive than reactive, dealing with symptoms way before hand.
Conclusion
Public procurement is an essential part of the government allowing the federal government to provide the public with jobs. However, it is unique from normal procurement because it often involves contracts of large sums of money. As such, it is of extreme importance that stringent measures are put in place and that all loopholes are eliminated. The federal government has worked tirelessly to ensure that any existing loopholes are sealed. Still, there is need to reassess and re-evaluate the entire public procurement procedure. This will help point out the areas of weaknesses and thereby identify possible solutions.
References
Manuel, K. (2015).Responsibility Determinations under the Federal Acquisition Regulation: Legal Standards and Procedure. London: Diane Publishing
Oyer, D. (2015). Accounting for Government Contracts: Federal Acquisition Regulation. New York: Lexis Nexis.
Thai, K. (2012). International Handbook of Public Procurement. California: CRC Press.
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The author of the article has duly defined the factors that favor incompetence that occurs in the care of patients with diabetes type 2. The article’s primary focus is the provision of care to patients with diabetes type 2, which has been shown to be a task that is faced with more challenges than not. For instance, the article has well described the attitude towards the care African American men get for the condition. The fact that the medicines offered affect the masculinity of some of the patients has led to the patients deciding not to undertake such medication (Hooker et al., 2012). The fact is the drugs affects one’s self-esteem. However, the author has achieved a sense of making the patients rethink their previous decisions. This sense can or could be delivered in a perfect way through a patient education in spite of the stressed workforce that offer health care. Thus, the evidence illustrated by the author has justified the key point of the article in their appending nature.
Article 2
The article talks about vaccination. The need for it and the importance of it. The author has succeeded in showing the impending need for the education of generations to come. After all one cannot see the need for a vaccine unless there is worry of contraction of the disease after a major outbreak. However, as mentioned by the author, it is possible that the process of vaccination of rather the practice of it saves lives apart from being cost effective. The cost-effectiveness comes in the concerning the hospital bills incurred for treating a disease that would rather have been prevented by a vaccine. Other than that, the particular instances that cause parents to refuse vaccination for their children are rather alarming (Healy et al., 2014). Due to these facts mentioned in the article. The author has achieved a given significance in educating people on the importance of getting vaccinated and all about the different vaccines that exist.
Article 3
Education makes people aware of terms and information that would rather have been oblivious to them. In such sense, it is essential to monitor a given education program by evaluating the effectiveness of the system used to implement such informative programs. For one to know what he or she is teaching has an audience that is attentive, and keen ton is learning the details of what is being taught. You have to give tests. Simple tests are suitable for such awareness programs. The tests only need to capture the factual information and the context in which the one being examined understood the subject. Such tests would be the probable effectiveness measuring tool. However, in any education program, feedback is critical (Tones et al., 2013). Not alone important but also significant. If the students don’t come back with feedback. Either in the form of seeking clarification, mere curiosity or fact-seeking questions. The system of delivering the program would not have been effective at all. Therefore, any feedback should be appreciated as it shows concern and interest in the subject being taught.
References
Healy, C. M., Montesinos, D. P., & Middleman, A. B. (2014). Parent and provider perspectives on immunization: are providers overestimating parental concerns?. Vaccine, 32(5), 579-584.
Hooker, S. P., Wilcox, S., Burroughs, E. L., Rheaume, C. E., & Courtenay, W. (2012). The potential influence of masculine identity on health-improving behavior in midlife and older African American men. Journal of men’s health, 9(2), 79-88.
Kim, J., Kwon, Y., & Cho, D. (2011). Investigating factors that influence social presence and learning outcomes in distance higher education. Computers & Education, 57(2), 1512-1520.
Sherman, L. D., McKyer, E. L. J., Singer, J. N., Larke, A., & Guidry, J. J. (2014). Understanding the essence and lived experience of self-care management among African-American men living with type 2 diabetes. Journal of Social Health and Diabetes, 2(2), 96.
Tones, K., Robinson, Y. K., & Tilford, S. (2013). Health education: effectiveness and efficiency. Springer.
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Descriptive Statistics Variables in the Dataset Order Instructions: Module 2 – SLP
DESCRIPTIVE STATISTICS
Using the provided dataset in Excel, calculate the appropriate descriptive statistics for each of the variables in the dataset.
Descriptive Statistics Variables in the Dataset
Include a 2-3 page description of the descriptive statistics including tables of the summarized data, similar to a “Results” section in a published manuscript or journal article.
SLP Assignment Expectations
Length: SLP assignments should be at least 2 pages (500 words) in length.
References: At least two references must be included from academic sources (e.g. peer-reviewed journal articles). Required readings are included. Quoted material should not exceed 10% of the total paper (since the focus of these assignments is critical thinking). Use your own words and build on the ideas of others. When material is copied verbatim from external sources, it MUST be enclosed in quotes.
Descriptive Statistics Variables in the Dataset Essay Paper Format
The references should be cited within the text and also listed at the end of the assignment in the References section (APA format recommended).
Organization: Subheadings should be used to organize your paper according to question
Format: APA format is recommended for this assignment. See Syllabus page for more information on APA format.
Grammar and Spelling: While no points are deducted for minor errors, assignments are expected to adhere to standards guidelines of grammar, spelling, punctuation, and sentence syntax. Points may be deducted if grammar and spelling impact clarity.
The following items will be assessed in particular:
• Achievement of learning outcomes for SLP assignment.
• Relevance—all content is connected to the question.
• Precision—specific question is addressed; statements, facts, and statistics are specific and accurate.
• Depth of discussion—points that lead to deeper issues are presented and integrated.
• Breadth—multiple perspectives and references, multiple issues/factors considered/
• Evidence—points are well-supported with facts, statistics, and references.
• Logic—presented discussion makes sense; conclusions are logically supported by premises, statements, or factual information.
• Clarity—writing is concise, understandable, and contains sufficient detail or examples.
• Objectivity—use of first person and subjective bias are avoided.
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Module 2 – Background
DESCRIPTIVE STATISTICS
Descriptive Statistics Variables in the Dataset Required Reading
Module Overview
• SLP
o Demonstrate proficiency in calculating descriptive statistics including proportions and mean.
Data are most often presented using descriptive statistics. Categorical variables are introduced using proportions (%) and sample sizes (n). Continuous variables are most often described with mean and standard deviation (although a range can also be used in lieu of a SD). An example of a results table is shown below:
Descriptive Statistics for Entire Study Population:
StatTrek: One-Way Tables in Statistics. Retrieved from http://stattrek.com/statistics/one-way-table.aspx?Tutorial=Stat
Descriptive Statistics for Subpopulations (e.g. Study Population Divided by Gender or Disease Status)
StatTrek: Two-Way Tables in Statistics. Retrieved from http://stattrek.com/statistics/two-way-table.aspx?Tutorial=Stat
Mean, Median, Modes, and Standard Deviation
Australian Bureau of Statistics. Statistical Language – Measures of Central Tendency. Retrieved from http://www.abs.gov.au/websitedbs/a3121120.nsf/home/statistical+language+-+measures+of+central+tendency
Lake Tahoe Community College. Mean, Mode, Median, and Standard Deviation. Retrieved from http://www.ltcconline.net/greenl/courses/201/descstat/mean.htm
The Michigan Chemical Process Dynamics and Controls Open Text Book. Basic statistics: mean, median, average, standard deviation, z-score, and p-value. Retrieved from https://controls.engin.umich.edu/wiki/index.php/
Basic_statistics:_mean,_median,_average,_standard_deviation,_z-scores,_and_p-value
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Descriptive Statistics Variables in the Dataset Sample Answer
The frequency distribution of the race is as summarized in Table 1.
Table 1:
Race
Frequency
Percent
Valid Percent
Cumulative Percent
Valid
White
164
54.7
54.7
54.7
Hispanic
55
18.3
18.3
73.0
African-American
35
11.7
11.7
84.7
Native-American
9
3.0
3.0
87.7
Asian-American
21
7.0
7.0
94.7
Other
16
5.3
5.3
100.0
Total
300
100.0
100.0
The results indicate that the sample population consists of 54.7% of White peoples, 18.3% of Hispanic, 11.7% of African-American, 7.0% Asian-American, 3.0% Native-American, and 5.3% Others. This is a clear indication that this variable was asymmetric with a long tail to the left. In particular, the variable is positively skewed.
The gender distribution is as summarized in Table 2.
Table2:
Gender
Frequency
Percent
Valid Percent
Cumulative Percent
Valid
Male
141
47.0
47.0
47.0
Female
159
53.0
53.0
100.0
Total
300
100.0
100.0
The composition of the whole sample is 47% whereas the female proportion is 53%. Notably, the distribution is uniformly distributed.
The sample education distribution is as illustrated in Table3.
Table 3:
Education
Frequency
Percent
Valid Percent
Cumulative Percent
Valid
high school
46
15.3
15.3
15.3
College
101
33.7
33.7
49.0
Masters
90
30.0
30.0
79.0
Professional
63
21.0
21.0
100.0
Total
300
100.0
100.0
The sample has a large population of people with college education qualification (33.7%), followed by Masters qualified with a proportion of 30%, followed by professional with a percentage of 21%; the smallest percentage is of those with high school qualifications 15.3%.
The frequency distribution of those with a history of diabetes is as summarized in Table 4.
Table 4:
Diabetes
Frequency
Percent
Valid Percent
Cumulative Percent
Valid
No
191
63.7
63.7
63.7
Yes
109
36.3
36.3
100.0
Total
300
100.0
100.0
A larger proportion of 63.7% in the sample population has no record of being sick of diabetes while as only 36.3 percent has a suffered from this disease.
The frequency distribution of those with a history of allergies is as summarized in Table 5.
Table 5:
Allergies
Frequency
Percent
Valid Percent
Cumulative Percent
Valid
No
120
40.0
40.0
40.0
Yes
180
60.0
60.0
100.0
Total
300
100.0
100.0
In the sample, 60% has suffered from allergies, whereas 40% has not.
The proportion of families that have diabetes is as summarized in Table 6.
Table 6:
Family has diabetes
Frequency
Percent
Valid Percent
Cumulative Percent
Valid
No
188
62.7
62.7
62.7
Yes
112
37.3
37.3
100.0
Total
300
100.0
100.0
The results indicate that 62.7% of the sample population has no history of family members with diabetes whereas 37.3% has a history of a family member with diabetes.
The proportion of families that have allergies is as summarized in Table 7.
Table7:
Family has allergies
Frequency
Percent
Valid Percent
Cumulative Percent
Valid
No
152
50.7
50.7
50.7
Yes
148
49.3
49.3
100.0
Total
300
100.0
100.0
The results illustrate that in the sample 50.7% of the respondent had family members that have not suffered from allergies. On the other hand, 49.3% of the sample had members that have suffered from allergies.
The distribution of sample population depression during winter is as summarized in Table 8.
To feel depressed during the winter
Frequency
Percent
Valid Percent
Cumulative Percent
Valid
1.00
38
12.7
12.7
12.7
2.00
75
25.0
25.0
37.7
3.00
75
25.0
25.0
62.7
4.00
75
25.0
25.0
87.7
5.00
37
12.3
12.3
100.0
Total
300
100.0
100.0
These results deduce that the distribution of people feeling being depressed during winter is normally distributed, with a plot that is symmetrical (skewedness is 0.002 which is close to zero).
The distribution of how people behave (overreact) when stressed is as illustrated in Table 9.
Table 9:
To overreact when stressed out
Frequency
Percent
Valid Percent
Cumulative Percent
Valid
1
67
22.3
22.3
22.3
2
67
22.3
22.3
44.7
3
67
22.3
22.3
67.0
4
66
22.0
22.0
89.0
5
33
11.0
11.0
100.0
Total
300
100.0
100.0
These results deduce that the sample population has a positive skewedness in regard to how they overreact when stressed, in other words, the high proportion is on the lower values. Thus, the data has a positive skewness.
The distribution of preference of exercise during summer is tabulated below.
Table 10:
To exercise during the summer
Frequency
Percent
Valid Percent
Cumulative Percent
Valid
1
27
9.0
9.0
9.0
2
54
18.0
18.0
27.0
3
54
18.0
18.0
45.0
4
110
36.7
36.7
81.7
5
55
18.3
18.3
100.0
Total
300
100.0
100.0
This data shows that the sample population preference of exercise during summer is negatively skewed (more people on the higher values).
The summary table 11 shows the distribution of continuous variables.
Statistics
Age
Salary
weight
height
BMI
N
Valid
300
300
300
300
300
Missing
0
0
0
0
0
Mean
50.46
54498.02
159.1133
66.9833
24.6387
Median
50.00
50012.00
161.0000
67.0000
25.0000
Mode
18
15000a
145.00a
65.00a
25.40
Std. Deviation
20.020
28923.783
31.66517
3.75010
2.23138
Variance
400.797
836585198.715
1002.683
14.063
4.979
Skewness
.085
.407
.495
-.060
.583
Std. Error of Skewness
.141
.141
.141
.141
.141
Kurtosis
-1.133
-.913
.112
-.743
.653
Std. Error of Kurtosis
.281
.281
.281
.281
.281
Minimum
18
10123
110.00
60.00
21.30
Maximum
91
117878
235.00
74.00
30.20
a. Multiple modes exist. The smallest value is shown
The table illustrates that on average the sample population has a mean of 50.46, with a standard deviation of 20.020. Nevertheless, the minimum age of the participants is 18, and the maximum age is 91 years. The most repeated frequency in the sample is 18, and the median is 50 years.
On average the sample population has a salary of 54498.02 with the maximum receiving $ 117,878 and the minimum is $10,123. The salary data has a positive skewedness, implying that most of the people in the sample receive the lower values.
The average weight of the sample population is 159.1133, with a standard deviation of 31.66517. The minimum weight in the sample data is 110 and the maximum 235, further the data has a positive skewness.
The mean height of the sample is 66.9833, and notably, the median of the height is 67. The height variable has a standard deviation of 3.75010, and the minimum height is 60, and the maximum is 74.
The average BMI of the sample population is 24.6387, with a mode of 25.4 and the median 25. The standard deviation of BMI data is 2.23138. The minimum BMI is 21.3, and the maximum BMI is 30.2.
• A manager at a small organization is interested in determining the impact of the recent company outing to Camp Feel-Good on job satisfaction. She would like to compare those who attended and completed the individual and team building exercises during the weekend event to those who did not attend, without making any assumptions regarding which group will have higher job satisfaction. A job satisfaction survey is administered 1 month after the event to 40 employees (20 who attended and 20 who did not attend). The survey is a 10 item Liker scale measure (scale: 1=”Very Dissatisfied” to 5=”Very Satisfied”) with a range of total scores from 10-50, where the higher the score, the greater the level of job satisfaction.
SAMPLE ANSWER
Research statistic
The small organization’s manager wanted to determine the effects the company outing to the Camp Feel-Good had on job satisfaction. Some people attended and completed some team building and individual exercises as the weekend event was going on, while others never attended. The two groups were compared in the absence of assumptions about the group likely to have the highest job satisfaction. Forty employees engaged in this research, where half had attended while the other half had not. A likert scale measure with ten items was during and the total score was to be ten to fifty, where a higher score meant a greater job satisfaction level (Conference Board, 2013).
Definitely, the twenty employees who participated in the outing are likely to report higher job satisfaction levels using the likert scale. This is based on the fact that the employees in a company are among the most vital assets. Therefore, managing them appropriately can make them happy and productive. In the first place, the outing is an indication of organizational support, recognition as vital components of the company, and using the likert scale after the outing is an indication that the company wants to get feedback from the employees. These are vital aspects that make the employees highly motivated (Conference Board, 2013). The outing would also need the employees to be flexible as most are conducted during work days, and this indicates that the management believes in the employees. In addition, an outing is a good way for the life-work balance, which highly motivates the employees (Conference Board, 2013). Attending the event is also a good opportunity for the employees to socialize and converse with the colleagues they might not have interacted with, which promotes the positive, intended impact on employee job satisfaction.
Reference
Conference Board. (2013). Determinants of Job Satisfaction. New York: The Conference Board, Inc.
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This week spend time discussing the similarities and differences between correlation and regression, and why one would use correlation instead of regression. Consider how often there are bivariate relationships and whether a bivariate relationship will be meaningful for your DBA doctoral study as compared to a regression, which examines relationships differently.
As a researcher, you will become familiar and comfortable with the measures and scales others in choose to measure data. Understanding study measurement methods can help clarify how you might employ these measurement instruments. In this paper, you will find an example of a test and a scale used in your discipline’s literature, analyze its use in the study, and analyze the relationships among these instruments, populations, and the concepts of reliability and validity.
To prepare for this paper
• Review Lesson 38, “Item Analysis Using Reliability Procedure” In Salkind and Green. Review in particular how to report psychometric properties, including correlation coefficients (pp. 345-347)
• Search for an example of a test and an example of a scale. For each example, determine the typical population and the reliability and validity.
To search for pre-existing measures that are available in the public domain do the following:
1. Note that most measurement development is conducted in the field of psychology. Make sure that you select peer-reviewed and full-text articles. You will also want to conduct an advanced search as multiple terms will be searched.
2. In the first box type in your construct (depression, leadership, etc.)
3. In the second box type in the word “psychometric”.
4. In the third box type in one of the following words (you may have to try a few different ones) “measure” “instrument” “scale” or “survey”.
Note: Using a public measure allows you the opportunity to view the measure without purchasing it such as the Buros Institute of Mental Measurements http://www.unl.edu/buros/bimm/html/00testscomplete.html
· What considerations need to be made to ensure that the scale and test examples are reliable and valid for another population
Tools of Psychometric Measures and Scales Resources
• Websites
Trochim, W. (2006). Web center for social research methods: Selecting statistics. Retrieved from http://www.socialresearchmethods.net/
This site is an online textbook that addresses the topics of a typical graduate course in social research methods, including sampling, measurement, validity, types of designs, and analysis. Learners can navigate the textbook using a graphical research road map or simple table of contents. The textbook addresses the entire research process as well as the statistical aspects of research and is not software-specific. From the main page, click on the ” Selecting Statistics” link.
Tools of Psychometric Measures and Scales Sample Answer
The soundness of any research should use tools of measurement that psychometrically correct and sound. After that, confirmation of the validity and reliability of the tools helps one in assuring the trueness of the findings of the study. A great problem encountered is knowing the kind of psychometric property to look into (Friman, et al.,(2013). These may include the evidence that will be sufficient for the study and what statistical is used to test mean. The support for of instruments can be assessed by testing the content of the analysis, the construct, and the related concepts. Validity is the ability of the instruments to measure the different factors of the area under study. On the other hand, reliability in psychometrics is the ability of the test to measure the area or phenomenon under study in a consistent manner (Bejar, et al.,(2012).
When reporting the psychometric properties, it is important to learn the influences of other factors such as personal and environmental factors relating to a phenomenon. Instruments used to measure the outcome can be used in evaluating the perceived performance level of the analysis (Allison, et al.,(2011). These instruments present themselves either generically or specifically to the population. The quality of the output of the analysis depends on its properties from the psychometric test. For example, in a prosthetics psychometric analysis, the effect of the outcome can be classified according to test levels. The levels of outcome are four.
Nominal data that are produced when the people are arranged in categories like people amputated can be put in one category and the right-hand amputees on another. The ordinal level data involves the categories that are mutually exclusive but exhaustive. The categories tend to be ordered but not equal in intervals. An example is people who can move with a stick, those who are not able to move with the help of a stick and those who can move without a stick. The interval level data encompasses order and an equal hiatus amid units of dimension without an exact zero (Friman, et al.,(2013). An example is the temperature zero in a thermometer which does not represent that there is no temperature. The ratio level data involves array and same intervals flanked by units of measurement but with a real zero. An example is height measurement where zero represents the absence of height.
Reliability test
When the required presentation should be routine based, a rater’s input is required. The forms of reliability can be in several forms. Test-retest reliability shows the consistency in the test results. An example is an individual taking a prosthetic fit survey and repeats it a day later. The result should be the same because no change is expected. In internal consistency, the reliability is preserved for the measures in the outcome that are intended to test only one concept and assess the extent to which other concepts in the phenomenon affect this concept. An example is a depression scale where consistency is not required for stuff such as SF-36 that addresses extra concepts. Intra-rater reliability shows the consistency of a rater in administering outcome measure and scores (Allison, et al.,(2011). An example is a video where rating and re-scoring later should give consistent results. Inter-rater reliability implies that two raters agree on how to administer the outcome or result. An example is two skilled raters of a videotape whose rated result should be similar.
Validity
It is an essential but not adequate feature of an outcome measure. Validity is determined only by a question pertaining to a certain population or phenomenon. The various kinds of validities and examples are discussed below. Face validity refers to the degree to which a test appears to gauge its intention. The experiment is slanted, and an example is a clinician advocating for a universal clinical practice. Its intention should measure exactly what the clinicians need. In content validity, the test should include all the contents present in the testing phenomenon (Bejar, et al.,(2012). An example is an instrument measuring athletes that should measure jumping, running and walking. Criterion validity is assessed when the outcome can be measured against a set normal. It is a rarely used criterion. Construct validity shows the ability of the test to measure the subject of the analyzer. An example is measuring the importance of day walk to the elderly on their mobility. There is difference recorded between those who work as village volunteers daily and those already in an elderly care centers.
Considerations for reliability and validity of test and scale
For reliability, temporal stability should be considered to ensure that test and scale examples are reliable and valid for another population. One should ensure that in the same test is utilized for more than one experiment. The result should not emerge from the adaptively of the researcher hence not biased. Form equivalence should be consistent and can be used by different examinees. There should also be an internal consistency of figures (Friman, et al.,(2013). The consistency in results should form a pattern. There should be uniformity in results hence; subsequent tests should bring the same outcome.
Validity should have face validity meaning that it takes the face value. Modifications can be sought from experts in the field. Content validity is a major consideration whereby the representative of the entire population should represent the other population. The criterion should be drawn from a presumption in test scores and performance. The prediction and explanation should be consistent (Bejar, et al.,(2012). The construct validation should be uniform.
Tools of Psychometric Measures and Scales Bibliography
Bejar, I.I., Chaffin, R. and Embretson, S., (2012). Cognitive and psychometric analysis of analogical problem solving. Springer Science & Business Media.
Allison, C., Baron-Cohen, S., Wheelwright, S.J., Stone, M.H. and Muncer, S.J., (2011). Psychometric analysis of the Empathy Quotient (EQ). Personality and Individual Differences, 51(7), pp.829-835.
Friman, M., Fujii, S., Ettema, D., Gärling, T. and Olsson, L.E., (2013). Psychometric analysis of the satisfaction with travel scale. Transportation Research Part A: Policy and Practice, 48, pp.132-145.
Using the provided dataset in Excel, calculate the appropriate descriptive statistics for the following variables comparing diabetes with no diabetes status: gender, race, salary, education, height, weight, BMI, allergies, family history diabetes, family history allergies. For chi-square tests, report the chi-square value and the p-value (if p-value < 0.05, then the test is significant). For t-tests, report the t-test value and the p-value. Include a 2-3 page description of the descriptive statistics including tables of the summarized data, similar to a “Results” section in a published manuscript or journal article. Use the following online calculators to obtain the results for this analysis.
Chi-Square for Categorical Data: http://www.vassarstats.net/ (Choose “Frequency Data” from the far left, then “Chi-Square, Cramer’s V, and Lambda” from the middle of the page)
Enter in the number of people in each category (e.g. number of women who have diabetes, number of men with diabetes, etc.). Example of a table below:
Diabetes No Diabetes
Female 86 214
Male 36 264
Choose a 2 x 2 table and where A1 = 86, A2 = 36; B1 = 214; B2 = 264
Report the percent of people in each category and the chi-square and p-value. A possible sentence to interpret the results could be:
There are significantly more women (64%) who have diabetes than men (36%).
T-Tests for Continuous Data: http://www.vassarstats.net/ (Choose “t-Tests & Procedure” from the far left, then “Two-Sample t-Test” then click “Independent Samples” under Setup)
Copy and Paste the values for those with diabetes into Sample A and those without diabetes into Sample B, then click Calculate. For instance, copy and paste all of the ages of those with diabetes into Sample A and all of the ages of those without diabetes into Sample B. From the Data Summary window, report the Mean of those with Diabetes (Sample A) and those without Diabetes (Sample B); also report the “t” from the Results box, as well as the two-tailed p-value. A “P” that is <0.05 suggests the result is statistically significant. One way to report such a finding would be to use the following language:
The average age of those with diabetes is __ years and for those without diabetes is ___ years. Those with diabetes were significantly older/younger (p<0.05).
SLP Assignment Expectations
Length: SLP assignments should be at least 2 pages (500 words) in length.
References: At least two references must be included from academic sources (e.g. peer-reviewed journal articles). Required readings are included. Quoted material should not exceed 10% of the total paper (since the focus of these assignments is critical thinking). Use your own words and build on the ideas of others. When material is copied verbatim from external sources, it MUST be enclosed in quotes. The references should be cited within the text and also listed at the end of the assignment in the References section (APA format recommended).
Organization: Subheadings should be used to organize your paper according to question
Format: APA format is recommended for this assignment. See Syllabus page for more information on APA format.
Grammar and Spelling: While no points are deducted for minor errors, assignments are expected to adhere to standards guidelines of grammar, spelling, punctuation, and sentence syntax. Points may be deducted if grammar and spelling impact clarity.
The following items will be assessed in particular:
•Achievement of learning outcomes for SLP assignment.
•Relevance—all content is connected to the question.
•Precision—specific question is addressed; statements, facts, and statistics are specific and accurate.
•Depth of discussion—points that lead to deeper issues are presented and integrated.
•Breadth—multiple perspectives and references, multiple issues/factors considered/
•Evidence—points are well-supported with facts, statistics, and references.
•Logic—presented discussion makes sense; conclusions are logically supported by premises, statements, or factual information.
•Clarity—writing is concise, understandable, and contains sufficient detail or examples.
•Objectivity—use of first person and subjective bias are avoided.
I can send the provided assignment excel dataset download if you provide where to send to. Thanks
SAMPLE ANSWER
Descriptive Statistics
Using the provided dataset in Excel, descriptive statistics that are appropriate for variables concerning to diabetes including gender, race, salary, height, weight, as well as BMI. The descriptive statistics calculated using the provided dataset specifically include mean, standard deviation, variance as well as media. These descriptive statistics are mainly concerned with analysis of measurement of central tendency i.e. mean and median as well as measurement of variation i.e. standard deviation and variance.
Table 1: Descriptive Statistics
Age
Salary
Height
Weight
BMI
To feel depressed during the winter
To exercise during the summer
To overeat when stressed out
Mean
50
$54,498
66.98333
159.1133
24.63867
2.993333
3.373333
2.77
Standard Deviation
20
28923.783
3.750102
31.66517
2.231375
1.226773
1.227046
1.315116638
Variance
401
836585199
14.06327
1002.683
4.979035
1.504972
1.505641
1.729531773
Median
50
$50,012
67
161
25
3
4
3
In particular, this SLP assignment will be analyzed the provided dataset using chi-square tests and t-test. For the chi-square tests apart from the descriptive statistics, the report will also include chi-square value as well as the p-value. On the other hand, for the t-tests the report will include the t-test value as well as the p-value.
In addition, the specific numbers of people in the provided the dataset within their specific category i.e. diabetes and no diabetes are determined in order to enable the data analysis to be carried out. A summary of those statistics is presented in the table shown below:
Table 2: Data Summary
Diabetes
No Diabetes
Total
Percentages
Female
56
103
159
53%
Male
53
88
141
47%
Total
109
191
300
Percentages
36.3%
63.7%
100%
Based on the statistics presented in the above table concerning the chi-square obtained from the VassarStats website which is used for statistical computation, particularly in the context of Chi-Square for Categorical Data and specifically using Chi-Square, Cramer’s V, and Lambda in a 2 x 2 table; there are some inferences that can already be done. Some of the inferences based on percentages include:
There are significantly more women (53%) who have diabetes than men (47%).
Additionally, the results of the chi-square test show that the chi-square value is 0.09 and the p-value is <0.0001 an indication that the test is significant meaning that there a significant difference between the number of women who are diabetic compared to men who are diabetic.
T-Tests for Continuous Data
The t-test was used to compare the two groups i.e. Sample A (no diabetes) and Sample B (diabetes) and the t-test reported the t-test value as well as p-value. The t-test values for variables such as age, height, weight as well as BMI are reported in the table shown below. In addition, the two-tailed p-values are also shown and the are all below <0.05 and indication that the tests are significant which means there are significant differences between the two groups (i.e. Sample A and Sample B) with regards to the considered variables.
Table 3: Data Summary
A
B
Total
t-test value
Two-tailed p-value
N
191
109
300
Age
Mean
39.0052
70.5229
50.4567
-20.69
<0.0001
Height
Mean
65.0209
70.422
66.9833
-16.63
<0.0001
Weight
Mean
142.7016
187.8716
159.1133
-16.33
<0.0001
BMI
Mean
23.5628
26.5239
24.6387
-14.35
<0.0001
The average age of those without diabetes is 39 years and for those with diabetes is 70.5 years. Those with diabetes were significantly older/younger (p<0.05).
The average height of those without diabetes is 65.02 centimeters and for those with diabetes is 70.4 centimeters. Those with diabetes were significantly shorter/taller (p<0.05).
The average weight of those without diabetes is 132.7 lbs and for those with diabetes is 187.8 lbs. Those with diabetes were significantly heavier/lighter (p<0.05).
The BMI of those without diabetes is 23.6 and for those with diabetes BMI is 26.5. The BMI for those with diabetes is significantly higher/lower (p<0.05).
References
Corder, G. W. & Foreman, D. I. (2014). Nonparametric Statistics: A Step-by-Step Approach. New York, NY: Wiley.
Greenwood, P. E. & Nikulin, M. S. (1996) A guide to chi-squared testing. New York, NY: Wiley.
Markowski, C. A. & Markowski, E. P. (1990). Conditions for the Effectiveness of a Preliminary Test of Variance.The American Statistician, 44(4), 322–326.
Sawilowsky, S. S. (2005). Misconceptions Leading to Choosing the t Test over the Wilcoxon Mann–Whitney Test for Shift in Location Parameter. Journal of Modern Applied Statistical Methods, 4(2), 598–600.
VassarStats (2015). Procedures Applicable to Categorical Frequency Data. Available at: http://www.vassarstats.net/ (Accessed on November 26 2015).
VassarStats (2015). t-Tests & Procedures. Available at: http://www.vassarstats.net/ (Accessed on November 26 2015).
Zimmerman, D. W. (1997). A Note on Interpretation of the Paired-SamplestTest. Journal of Educational and Behavioral Statistics, 22(3), 349–360.
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For this assignment, you write a paper covering answers to assigned problems in Lessons 22 and 23 of your course text.
• Lesson 22: problems 1–4 (page 150)
• Lesson 23: problems 1–5 (page 155)
Your paper should be written using APA 6th edition guidelines. There is a sample paper on page 41 of the Publication Manual which you may use as a reference. Your paper must meet the following requirements:
• Include explanation and justification of all answers.
• Include an APA Results section for each problem set. (There is an example on page 167 of the course text)
• Include presentation, discussion and explanation of all figures and tables
• Include a properly formatted H10 (null) and H1a (alternate) hypothesis which cover all possible situations related to a problem
I will email the questions for this paper
Working with SPSS and PASW Software Sample Answer
Some of the descriptive statistics on the Kudi algebra test are as summarized in Table 1.
Table 1:
Statistics
Kudi
N
Valid
30
Missing
0
Mean
54.63
Median
55.00
Mode
55
Skewness
-.255
Std. Error of Skewness
.427
Sum
1639
The hypothesis that need to be tested in this case is:
H0: there is no significance difference in the mean algebra scores.
H1: There in a significance difference between the mean algebra scores.
The total sum of the algebra score is 1639, with the average score of 54.63. The one-sample t-test analysis results summary is as follows:
One-Sample Test
Test Value = 0
t
Df
Sig. (2-tailed)
Mean Difference
95% Confidence Interval of the Difference
Lower
Upper
kudi
28.975
29
.000
54.633
50.78
58.49
The test value is 4.18
The results indicate that the t-test value is 28.975, with the mean algebra score of 633. The algebra scores lie at the 95% confidence interval of 50.78 and 58.49. The p-value is < 0.001.
This result indicates that the null hypothesis will be rejected. This is because the significance values <0.001 are less than α = 0.05. Thus, the conclusion will be that there exists a significant difference between the mean algebra scores.
The one sample t-test on the dataset (hap_sad) is summarized in Table 3.
Table 3:
One-Sample Test
Test Value = 0
t
df
Sig. (2-tailed)
Mean Difference
95% Confidence Interval of the Difference
Lower
Upper
hap_sad
8.267
19
.000
8.750
6.53
10.97
Since the significance value (p-value) < 0.001 is less than α = 0.05, the null hypothesis will be rejected and a conclusion will be made that the classical music had a different impact on peoples (Stevens, 2012).
Figure 1: Histogram of classical music effect ratings.
Figure 2: The boxplot of classical music effect ratings.
Figure 2 illustrates that the data negatively skewed since it has a long tail towards the right (Lem, 2013).
The total sum of the life stress at different ages is summarized in Table 4.
Table 4:
Statistics
Interpersonal life stress at age 40
Occupational life stress at age 40
Interpersonal life stress at age 60
Occupational life stress at age 60
N
Valid
45
45
45
45
Missing
0
0
0
0
Sum
3519
3314
3375
2784
Table 5 is a summary of the paired t-test;
Table 5:
Paired Samples Statistics
Mean
N
Std. Deviation
Std. Error Mean
Pair 1
Interpersonal life stress at age 40
78.20
45
11.655
1.737
Interpersonal life stress at age 60
75.00
45
7.711
1.149
Pair 2
Occupational life stress at age 40
73.64
45
9.547
1.423
Occupational life stress at age 60
61.87
45
6.625
.988
The overall change in stress level at the age of 40, and at the age of 60 is illustrated in Figure 4 and 5.
Figure 4: Occupational life stress at age 40
Figure 5: Occupational life stress at age 60.
Figure 6: Interpersonal life stress at age 40.
Figure 7: Interpersonal life stress at age 60.
These graphs indicate that there is a general decline in both the occupational and interpersonal life stress with age.
Table 6:
Paired Samples Test
Paired Differences
t
df
Sig. (2-tailed)
Mean
Std. Deviation
Std. Error Mean
95% Confidence Interval of the Difference
Lower
Upper
Pair 1
Interpersonal life stress at age 40 – Interpersonal life stress at age 60
3.200
13.942
2.078
-.989
7.389
1.540
44
.131
Pair 2
Occupational life stress at age 40 – Occupational life stress at age 60
11.778
12.696
1.893
7.964
15.592
6.223
44
.000
In testing whether overall life stress increases or decreases with age, the results indicate that interpersonal life stress at 40 and 60 has no significant difference since the p-value 0.131 is greater than α = 0.05 (Hampel, 2011). In addition, occupational life stress indicates that there is a significance difference at age 40 and 60 since the p-value < 0.001 is less than α = 0.05. This deduces that the hypothesis that Mike made were valid.
Table 7:
Paired Samples Statistics
Mean
N
Std. Deviation
Std. Error Mean
Pair 1
Husband’s infertility anxiety score
57.46
24
7.337
1.498
Wife’s infertility anxiety score
62.54
24
12.441
2.540
The results are clear that the wife’s infertility, anxiety score has high means scores of 62.54 with a standard deviation of 12.441. The husband’s infertility, anxiety score has the least mean score of 57.46 and standard deviation of 7.337 (Samuels, 2012).
The t-statistics can be summarized in the table below.
The p-value, in this case, is 0.03, and the t-test value is -3.256.
The results indicate that there exists a significant difference between husband’s infertility, anxiety score and wife’s infertility, anxiety scores, since this the p-value = 0.03 is less than α = 0.05.
To compare the variability and distribution of the data, a boxplot was plotted, and its output is as illustrated in Figure 8.
Figure 8: The boxplot of husband’s infertility, anxiety score and wife’s infertility, anxiety scores.
The boxplot shows that wife’s infertility, anxiety scores shows a high variability, this is because the wife’s infertility, anxiety scores has a great spread of data (has higher upper quartile and least lower quartile) (Leech, 2012).
Working with SPSS and PASW Software References
Hampel, F. R., Ronchetti, E. M., Rousseeuw, P. J., & Stahel, W. A. (2011). Robust statistics: the approach based on influence functions (Vol. 114). John Wiley & Sons.
Leech, N. L., Barrett, K. C., & Morgan, G. A. (2012). IBM SPSS for intermediate statistics: Use and interpretation. Routledge.
Lem, S., Onghena, P., Verschaffel, L., & Van Dooren, W. (2013). The heuristic interpretation of box plots. Learning and Instruction, 26, 22-35.
Samuels, M. L., Witmer, J. A., & Schaffner, A. (2012). Statistics for the life sciences. Pearson Education.
Stevens, J. P. (2012). Applied multivariate statistics for the social sciences. Routledge.
