Nonparametric Test

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Nonparametric Test

Chi-Square Test for Independence

The test is used to determine whether two categorical variables are independent.

Notation for the Chi-Square Test for Independence (Please note that the notation varies

depending on the text)

O represents the observed frequency of an outcome

E represents the expected frequency of an outcome

r represents the number of rows in the contingency table

c represents the number of columns in the contingency table

n represents the total number of trials

Test Statistic

 

 

  

2

2

1 1

O E

E

df r c

 

  

The Chi-Square test is a hypothesis test. There are seven steps for a hypothesis test.

1. State the null hypothesis

2. State the alternative hypothesis

3. State the level of significance

4. State the test statistic

5. Calculate

6. Statistical Conclusion

7. Experimental Conclusion

Example

A university is interested to know if the choice of major has a relationship to gender. A

random sample of 200 incoming freshmen students was taken (100 male and 100

female). There major and gender were recorded. The results are shown in the

contingency table below.

 

Major Female Male

Math 5 15

 

 

Nursing 44 10

English 10 10

Pre-Med 17 20

History 4 5

Education 15 20

Undecided 5 20

 

To determine if there is a relationship between the gender of a freshmen student and

thei declared major perform the hypothesis test (Use level of significance 0.05  ) .

Step 1: Null Hypothesis

0 : Gender and Major of Freshmen students are independentH

Step 2: Alternative Hypothesis

: Gender and Major of Freshmen students are not independentAH

Step 3: Level of Significance

0.05 

Step 4: Test Statistic

 

 

  

2

2

1 1

O E

E

df r c

 

  

Step 5: Calculations

There are several calculations for this test. We have to find the expected frequency for

each cell in the contingency table. The expected frequency is the probability under the

null hypothesis times the total frequency for the given row. Here the probability under

the null hypothesis is .5, as the probability of being male and female is equal.

rE pn

Major Female Male

Math   1 .5 20 10E     2 .5 20 10E  

Nursing   3 .5 54 27E     4 .5 54 27E  

English   5 .5 20 10E     6 .5 20 10E  

Pre-Med   7 .5 37 18.5E     8 .5 37 18.5E  

 

 

History   9 .5 9 4.5E     10 .5 9 4.5E  

Education   11 .5 35 17.5E     12 .5 35 17.5E  

Undecided   13 .5 25 12.5E     14 .5 25 12.5E  

 

Know calculate the test statistic.

 

 

       

       

       

   

2

2

2 2 2 2

2

2 2 2 2

2 2 2 2

2 2

2

5 10 15 10 44 27 10 27

10 10 27 27

10 10 10 10 17 18.5 20 18.5

10 10 18.5 18.5

4 4.5 5 4.5 15 17.5 20 17.5

4.5 4.5 17.5 17.5

5 12.5 20 12.5

12.5 12.5

2.5 2.5 10.7 10.7 0 0 .1216

obs

obs

obs

O E

E 

 

       

       

       

   

      

2

.1216 .0556 .0556 .357 .357 4.5 4.5

36.4684obs

      

 

The calculation for degrees of freedom is as follows:

     

  

1 1 7 1 2 1

6 1 6

df r c

df

     

 

The critical value for the Chi-Square with 6 degrees of freedom at a level of significance

0.05  is 12.592. This is found by using the Chi Square table.

Step 6: Statistical Conclusion

Since 2 2

6, 0.0536.4684 12.592obs df       then reject the null hypothesis.

Step 7: Experimental Conclusion

There is sufficient evidence to indicate that gender has an effect on choice of major for

the incoming freshmen.

 

 

 

 

Mann-Whitney

The Mann-Whitney test is a nonparametric version of the independent sample t-test.

This study is used when there are two independent samples of ordinal scores.

Test Statistic

 

 

 

1 1

1 1 2 1

2 2

2 1 2 2

1

2

1

2

n n U n n R

n n U n n R

   

   

 

Notation:

 

1

2

1

2

number of scores in group 1

n number of score in group 2

R sum of ranks for score in group 1

R sum of ranks for score in group 2

n 

 

The Mann-Whitney test is a hypothesis test. There are seven steps for a hypothesis

test.

1. State the null hypothesis

2. State the alternative hypothesis

3. State the level of significance

4. State the test statistic

5. Calculate

6. Statistical Conclusion

7. Experimental Conclusion

 

Example:

Suppose there was race between an Antelope and a mountain lion. The Antelope won

but you want to know if this could be extended to a general statement that Antelope will

win in a race against a mountain lion. A random sample of 10 Antelopes and 10

mountain lions are put in a race. The order in which they finish is recorded. ( A for

antelope and L for mountain lion)

AALALLLAAALAALLAALLL

Step 1: Null Hypothesis

 

 

0 : Probability of the Antelope winning is no different than the probalility of the

mountain lion wining the race.

H

Step 2: Alternative Hypothesis

: Probability of the Antelope winning is different than the probalility of the

mountain lion wining the race.

AH

Step 3: Level of Significance

0.05 

Step 4: Test Statistic

 

 

 

1 1

1 1 2 1

2 2

2 1 2 2

1

2

1

2

n n U n n R

n n U n n R

   

   

 

Step 5: Calculations

The results are ranked according to the in order in which they finished the race.

Rank

A 1

A 2

L 3

A 4

L 5

L 6

L 7

A 8

A 9

A 10

L 11

A 12

A 13

L 14

L 15

A 16

A 17

L 18

L 19

 

 

L 20

 

Let the Antelope be sample one and the mountain lion be sample 2.

 

1

2

1

2

number of scores for the Antelopes

n number of score for the mountain lions

R sum of ranks for score for the Antelopes

R sum of ranks for score for the mountain lions

n 

 

Find the sum of the ranks for each group.

Antelope Mountain Lion

1 3

2 5

4 6

8 7

9 11

10 14

12 15

13 18

16 19

17 20

Sum 92 118

 

The number of for each animal is 10 because 10 antelopes and 10 mountain lions

raced.

Now plug the information into the test statistic

 

 

 

 

    

 

    

1 1

1 1 2 1

1

1

1

2 2

2 1 2 2

2

2

2

1

2

10 10 1 10 10 92

2

100 55 92

63

1

2

10 10 1 10 10 118

2

100 55 118

37

n n U n n R

U

U

U

n n U n n R

U

U

U

   

   

  

   

   

  

 

 

Find the critical value for the test statistic. Use the appropriate U table found in the

appendix of the textbook. Look for alpha to be 0.05 and then the number of scores for

each category to be 10. Then you see the following critical values.

1,

2,

23

77

crit

crit

U

U

 

Step 6: Statistical Conclusion

The statistical conclusion tells whether to reject or fail to reject the null hypothesis. The

rejection rule is as follow.

1

2

If then reject the null hypothesis

If then reject the null hypothesis

crit

crit

U U

U U

Since 1 1,63 23 critU U   then fail to reject the null hypothesis also 2 2,37 77 critU U  

then fail to reject the null hypothesis.

Step 7: Experimental Conclusion

Since we failed to reject the null hypothesis we can say that there is not significant

evidence to support the claim that the probability of the antelope winning is any different

than the probability of the mountain lion winning the race.

 

 

 

Kruskal-Wallis Test

The Kruskal-Wallis Test is a nonparametric version of the one-way ANOVA. This test

however does not assume normality or homogeneity of variance. The test requires

ordinal scaling of the dependent variable and must have at least 5 data values in each

sample.

Notation

k number of sample or groups

n number of data values in each group

N number of data values in all samples combined

R sum of the ranks for each sample

Test Statistic

 

   

2

2 12 3 1

1

1

R N

N N n

df k

   

          

 

The Kruskal-Wallis test is a hypothesis test. There are seven steps for a hypothesis

test.

1. State the null hypothesis

2. State the alternative hypothesis

3. State the level of significance

4. State the test statistic

5. Calculate

6. Statistical Conclusion

7. Experimental Conclusion

Example

A gym has decided to recommend a diet to their clients. They have narrowed down the

choice to three and they want to test which diet is best. They have randomly selected 21

volunteers from the gym to participate in the diet. All the participants have similar health

and body type as well as general exercise routine. The amount of weight loss was

recorded.

Diet A Diet B Diet C

10 11 1

 

 

12 4 8

13 2 17

7 6 0

3 16 16

15 9 18

5 14 19

 

Step 1: Null Hypothesis

0 : There is no difference amoung the dietsH

Step 2: Alternative Hypothesis

: There is a difference between the dietsAH

Step 3: Level of Significance

0.05 

Step 4: Test Statistic

 

   

2

2 12 3 1

1

1

R N

N N n

df k

   

          

 

Review the three “Non Parametric” test videos in the Calculations section of the “Statistics Visual Learner” media piece.

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Review the three “Non Parametric” test videos in the Calculations section of the “Statistics Visual Learner” media piece.

How would you create a statistical analysis based on the scenario below? Explain. What level of significance would you test at and why?

A researcher is examining preferences among four new flavors of ice cream. A sample of n = 80 people is obtained. Each person tastes all four flavors and then picks a favorite. The distribution of preferences is as follows. Do these data indicate any significance preferences among the four flavors using the chi-square test?

Ice Cream Flavor
ABCD
12182822

Determine possible causes of aggressive behavior in this setting, according to the theories of aggression.

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Assignment Content

  1. Issues related prejudice, discrimination, and aggression are present in many different aspects of offender behavior and interactions. Sometimes it could be an offender’s prejudicial attitude that produces a negative consequence, but it could also be aspects of the criminal justice system that have been ineffectively designed to address these issues. This assignment asks you to analyze the issues that relate to the concepts during offender rehabilitation.

    Write a 1,050- to 1,400-word analysis of the occurrence of prejudice, discrimination, and aggression among offenders while receiving correctional program support services for rehabilitation. Include the following:

    • Determine possible causes of aggressive behavior in this setting, according to the theories of aggression.
    • Describe possible effects of prejudice, discrimination, and aggression on offenders and their social relationships.
    • Describe potential organizational issues that may arise due to prejudice, discrimination, or aggression.
    • Describe possible methods to prevent issues related to these concepts from recurring.
    • Include a minimum of three sources.
      Format your paper according to APA guidelines.

Assignment Content

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Assignment Content

  1. Issues related prejudice, discrimination, and aggression are present in many different aspects of offender behavior and interactions. Sometimes it could be an offender’s prejudicial attitude that produces a negative consequence, but it could also be aspects of the criminal justice system that have been ineffectively designed to address these issues. This assignment asks you to analyze the issues that relate to the concepts during offender rehabilitation.

    Write a 1,050- to 1,400-word analysis of the occurrence of prejudice, discrimination, and aggression among offenders while receiving correctional program support services for rehabilitation. Include the following:

    • Determine possible causes of aggressive behavior in this setting, according to the theories of aggression.
    • Describe possible effects of prejudice, discrimination, and aggression on offenders and their social relationships.
    • Describe potential organizational issues that may arise due to prejudice, discrimination, or aggression.
    • Describe possible methods to prevent issues related to these concepts from recurring.
    • Include a minimum of three sources.
      Format your paper according to APA guidelines.

Based on what you’ve learned about bystander intervention and diffusion of responsibility, what actions could you take to increase the likelihood that someone would help you in an emergency that happens in front of a large crowd? What obstacles to helping could persist?

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Based on what you’ve learned about bystander intervention and diffusion of responsibility, what actions could you take to increase the likelihood that someone would help you in an emergency that happens in front of a large crowd? What obstacles to helping could persist?

 

The rough draft should include all of the elements of the final literature review, specifically:

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The rough draft should include all of the elements of the final literature review, specifically:

  1. Title Page: Includes elements identified in EOP Manual.
  2. University Publication License/Copyright: Includes elements identified in EOP Manual.
  3. Abstract: The abstract is limited to 200 words, and highlights the purpose, method (literature sampling strategy), major finding(s) from analyses, and conclusion.
  4. Table of Contents: Includes elements identified in EOP Manual.
  5. Introduction: Identifies the student’s specific literature review topic, explicitly articulating a unifying, overarching theme that will guide the project
  6. Literature Review: Summarizes the general state of the literature (cumulative knowledge base) on the specific research question by synthesizing themes, methods, results, and/or theoretical framework used in current literature. Each theme should end with a short conclusion and transition to the next section.
  7. Discussion:  Synthesis of critical analysis of the literature (Reiterate common themes – what can you learn from what others have studied by looking at the whole picture?) Identifies new knowledge gained through integration of literature findings (What new knowledge have you or do you anticipate being able to generate based on your review? How can this information add to our understanding of the overall topic?
  8. References: Includes a complete reference list, formatted to APA standards. References are from scholarly sources and current (within the last ten years).
  9. Rubric: Complete a self-assessment of your literature review using the rubric and attach it to the assignment. This is intended to help you focus on the standards for assessing the literature review and to evaluate your progress. This will facilitate dialogue with your instructor about areas for improvement.

popular usage of the word “theory” may sometimes imply a singular, often grand idea

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popular usage of the word “theory” may sometimes imply a singular, often grand idea. The world, however, is complex, and the systems designed to understand it, such as theory, are often intricate in order to sufficiently explain the world as it is. Indeed, as you will learn this week, theory is nuanced, and it can also be viewed as a combination of variables, ideas, or constructs to test or advance a research question. In addition, theory tends to play a different role in qualitative, quantitative, and mixed methods research.

For this Discussion, you will consider the role of theory in research and the relationship between theory and philosophical orientations. You will also familiarize yourself with a theory in your field so that you may become more conversant in your discipline’s theoretical foundations.

With these thoughts in mind:

Post an explanation of the role of theory in research. Next, identify a theory in your discipline and explain its basic tenets. Then, with this theory in mind, consider your answer to the following question posed by Dr. Burkholder in last week’s reading: “What do I have to believe about the world and about human beings in order for me to accept or use this theory?” Finally, describe the extent to which the epistemological and ontological assumptions of your chosen theory align with the philosophical orientation that reflects your worldview.

Be sure to support your Main Issue Post and Response Post with reference to the week’s Learning Resources (attached) and other scholarly evidence in APA Style.

RESOURCE FILE: Students will develop a resource file containing at least 5 disorders discussed in class.

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RESOURCE FILE: Students will develop a resource file containing at least 5 disorders discussed in class.  Each disorder entry should include a summary of the disorder(summary should be a half page to full page in length), books, articles, websites, support groups, and literature. Topics that may be included in the resource file are: Stroke, TBI, Alzheimer’s Disease, Pick’s Disease, Dementia, Frontotemporal disorders, Cerebral Vascular Accident (CVA), Aphasia, Parkinson’s Disease, Traumatic Brain Injury, Multiple Sclerosis, ALS, Huntington’s Disease, Arterial Venous Malformation (AVM), Aneurysm, Progressive Supranuclear Palsy, HIV Encephalopathy, Primary Progressive Aphasia.  All of the aforementioned accepted topics must refer to the adult population only.  Please refer to rubric for content and criteria.

Rubric for Resource File 15 points

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Rubric for Resource File 15 points

Summary of disorder (5.0)

All five entries contain a brief summary of the disorders. (5.0)

Four entries contain a brief summary of the disorders. (4.0)

Three entries contain a brief summary of the disorders. (3.0)

Two entries contain a brief summary of the disorders. (2.0)

Less than two entries contain a brief summary of the disorders. (0)

Books and articles (5.0)

All five entries contain a minimum of 2 books, including title, author and publisher and a minimum of 2 journal articles including title, author, and journal publication. (5.0)

Four entries contain a minimum of 2 books, including title, author and publisher and a minimum of 2 journal articles including title, author, and journal publication. (4.0)

Three entries contain a minimum of 2 books, including title, author and publisher and a minimum of 2 journal articles including title, author, and journal publication. (3.0)

Two entries contain a minimum of 2 books, including title, author and publisher and a minimum of 2 journal articles including title, author, and journal publication. (2.0)

Less than two entries contain a minimum of 2 books, including title, author and publisher and a minimum of 2 journal articles including title, author, and journal publication (0)

Websites, support groups and literature (5.0)

All five entries contain a minimum of 2 websites, 2 support groups and 1 piece of literature. (5.0)

Four entries contain a minimum of 2 websites, 2 support groups and 1 piece of literature. (4.0)

Three entries contain a minimum of 2 websites, 2 support groups and 1 piece of literature. (3.0)

Two entries contain a minimum of 2 websites, 2 support groups and 1 piece of literature. (2.0)

Less than two entries contain a minimum of 2 websites, 2 support groups and 1 piece of literature. (0)

The field of Forensic Psychology focuses on psychology as it relates to the emergence of psychology

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The field of Forensic Psychology focuses on psychology as it relates to the emergence of psychology, the law, and the legal system. In forensic settings, you will likely assist individuals from diverse backgrounds in a variety of different contexts. Please tell us in 750 words (three-typed pages) reasons why you want to become a Forensic Psychologist. Describe your career aspirations (working with at-risk-youth girls), and discuss some of the challenges you might encounter when working with diverse individuals.