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GROUP 10 PRESENTATION. What is this about?. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Maecenas porttitor congue massa. Fusce posuere, magna sed pulvinar ultricies, purus lectus malesuada libero, sit amet commodo magna eros quis urna ..

MEMBERS. MEMBERS. 1. Ronald H. Cruda 2. Rhyan A. Arquelada 3. Romulo Gloria 4. Carlo F. Magno 5. Aaron Paul E. Velasco 6. Jaymilett D. Nomorosa 7. Paul Rodriguez 8. Silver Paul R. Madalipay 9. Joan Kristine T. De Luna.

NON-PARAMETRIC STATISTICS. CHAPTER 12. What is this about?.

INTRODUCTION. OBJECTIVES. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Maecenas porttitor congue massa..

IN THIS CHAPTER, WE WILL LEARN…. The differences between parametric and nonparametric tests When to compute different nonparametric tests.

TOPIC OUTLINE. Parametric Vs Non Parametric Non Parametric Test For Nominal Data, Independent-Group Designs with Nominal Outcome Measures, and Chi-Square Goodness of Fit Computation of χ 2 Goodness of Fit Test Using SPSS, Computation of Equal Frequencies, and Computation of Different Distribution.

PARAMETRIC VERSUS NONPARAMETRIC. OBJECTIVES. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Maecenas porttitor congue massa..

PARAMETRIC TEST. Normal Distribution. T- test, Z- test, F-test, ANOVA.

NONPARAMETRIC TEST. Skewed Distribution. Chi Square test, Kruskal Wallis test, Mann Whitney U tets.

PARAMETRIC TEST NON –PARAMETRIC TEST Normal Distribution Skewed Distribution Quantitative Data Qualitative Data Interval and Ratio Nominal & Ordinal More Powerful Less Powerful Compare Mean and SD Compare Percentage & Proportion Complete information about population Incomplete information about population Certain Assumptions are made about population No assumptions are made about population Applicability is in variables Applicability is in variables and Attributes Eg. T- test, Z-test, F-test, ANOVA Eg. Chi Square test, Kruskal Wallis Test, Mann Whitney U Test.

THE CHI-SQUARE (χ2) TEST. OBJECTIVES. Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Maecenas porttitor congue massa..

Chi-Square ( χ2) is the non-parametric test used with nominal data that compared (E)expected and (O)observed frequencies. There are two types of chi-square tests; A) the chi-square goodness of fit is appropriate for studies with one nominal variable and B) the chi-square test for independence is appropriate for studies with two nominal variables..

CHI- SQUARE FOR GOODNESS FIT. A nonparametric test used with one nominal variable having two or more categories; tests whether the observed frequencies of the categories reflect the expected population frequencies..

Let’s take an examples. We are interested in whether there is a difference in the number of MALES and FEMALES who are reported for CHEATING . The χ2 goodness of fit is used to test whether the frequency (number) of males who are reported for cheating is different from the frequency (number) of females who are reported. Our hypotheses would state: Ho: The number of males and females reported for cheating will be equal. Ha: The number of males and females reported for cheating will differ. Or In numerical terms, where f is the symbol used to denote frequency: Ho ƒmales = ƒfemales Ha: ƒmales ≠ ƒfemales.

In computing the the chi-square ( χ2) goodness of fit test, we make several assumptions:.

The process of computing the χ2 goodness of fit is very simple. You begin by counting the frequency of responses in each category , called the observed frequency (O ) . Take note that we can have more than two categories for a variable, but we are working with only two categories in this example for simplicity’s sake. Let us assume that in a particular school, 8 males and 22 females were reported for cheating . We would then have observed frequencies for each gender of: O males = 8 and O females = 22.

Next, we determine the expected frequency (E). Because we expect the number of males and females to be the same (according to our null hypothesis), we expect that half of those reported for cheating will be male and half will be female. Thus, our expected frequency (E) is half of the total number of our sample or N /2. If we had three categories then we would have an expected frequency of one-third for each category or N/3, and so on. The general formula for expected frequency (E) then is: E = N/k where k = the number of categories which is 2 (Male & Female) ; N = total number in our sample which is 30 Students. Or Let’s Say; E = N/k = 30/2 = 15.

1- where 0 obselved frequency; E = expected frequency. Inserting our sample observed and expected frequencies, we would have: (22-15)2 ( 7) (+7)2 49 49 lobt = 15 15 15 15 15 15.

To determine if the difference is large enough for this conclusion, we compare our computed χ2 to a sampling distribution of χ2 values obtained with the same degrees of freedom ( df ) as our sample when there is no difference between the frequencies. The df for a goodness of fit test are equal to the number of categories minus one or: df = k – 1 where k = number of categories. For our sample, where k = 2, we have: df = 2 - 1 = 1..

Levels of Significance 1 2 3 4 5 6 7 .05 3.84 5.99 7.81 9.49 11.07 12.59 14.07 .025 5.02 7.38 9.35 11.14 12.83 14.45 16.01 .01 6.63 9.21 11.34 13.28 15.09 16.81 18.48 .005 7.88 10.60 12.84 14.86 16.75 18.55 20.28 .001 10.83 13.82 16.27 18.47 20.51 22.46 24.32.

Distribution with Unequal Frequencies. Let us assume the frequency of cheating in a school where the student population is 75% female and 25% male. We may want to know if the frequency of each gender caught cheating is different from the school population. The null hypothesis would predict that the frequency of each gender caught cheating would represent the school population..

Distribution with Unequal Frequencies. Then, of the 30 students caught cheating, we would expect 75% of the sample or 22.5 to be female and 25% or 7.5 to be male. This changes the expected values (E) in our formula so that they represent the school population. The alternative hypothesis would predict that the gender of those caught cheating would differ from that of the school population. The same assumptions are made as we are still computing a χ 2 goodness of fit. So our hypotheses are: H0 : The number of males and females reported for cheating will represent the gender division (75% female, 25% male) in the school population. Ha : The number of males and females reported for cheating will differ from the gender division (75% female, 25% male) in the school population..

Or in numerical terms: Ho: ffemales = 3(fmales) Ela: f females fmales) In this case, the observed values for males (0 = 8) and females (0 = 22) remain the same, but our expected frequencies for males (E = 7.5) and for females (E = 22.5) now reflect the school population. Entering these values into the chi-square formula: (8-75)2 (22-225)2 loti = 75 225 E (-5)2 .25 .25 75 2.5 7.5 25.

. CARLO MAGNO.

. Data are entered in one column representing the single variable being analyzed. (Each category of the variable is coded).

COMPUTATION OF EQUAL FREQUENCIES. In SPSS we click on: “Analyze”, “Nonparametric tests,” “Legacy Dialogs,” and then on “Chi-square.” We move our variable (Cheating) to the “Test Variable List” box. When we click OK the output, shown in Table 12.3, is produced..

COMPUTATION OF EQUAL FREQUENCIES. A change can also be requested in the x 2 analysis..

THE CHI-SQUARE TEST FOR INDEPENDENCE. AARON PAUL E. VELASCO.

WHAT IS THE CHI-SQUARE TEST FOR INDEPENDENCE?. a type of Pearson’s chi-square test non parametric test for TWO CATEGORICAL Variables used to determine whether your data are SIGNIFICANTLY different from what you expected calculations are based on the OBSERVED frequencies the test compares the OBSERVED frequencies to the frequencies you would expect if the two variables are unrelated (EXPECTED frequencies).

CONTINGENCY TABLE.

EXPECTED VALUES. Intervention Pamphlet Phone call Control N = 300 Column totals Recycles 89 (98 x 259) 300 84 (92 x 259) 300 86 (110 x 259) 259 Does not recycle = 84.61 = 79.43 = 94.97 9 (98 x 41) 300 (92 x 41) 300 24 (110 x 41) = 13.39 12.57 = 15.03 Row totals 98 92 110.

WHEN TO USE THE CHI-SQUARE TEST FOR INDEPENDENCE?.

HOW TO CALCULATE THE TEST STATISTICS (FORMULA).

HOW TO PERFORM THE CHI-SQUARE TEST FOR INDEPENDENCE?.

WHEN TO USE DIFFERENT TEST. Several tests are similar to the chi-square test of independence, so it may not always be obvious which to use. The best choice will depend on your variables, your sample size, and your hypotheses..

SAMPLE WRITE-UP OF THE RESULTS IN THE EXAMPLE STUDY USING CHI-SQUARE DEPENDENT GROUP DESIGNS WITH NOMINAL OUTCOME MEASURES.

RESULTS. A 2 × 2 chi-square test for independence was computed to examine the relationship between student race and annoyance with a partner’s use of a cell phone. The interaction was significant and the strength of the relationship was moderate, χ 2 (1, N = 60) = 5.14, p < .023, φ 2 = .086. More of the Black students (N = 10, approximately 40%) than the White students (N = 5, approximately 14%) disagree with the statement, “I would not be bothered if my partner talked on a cell phone when we are together.”.

SPSS OUTPUT FOR CH—SQUARE TEST FOR INDEPENDENCE. Race • Phone not Bother Crosstabulation Phone not Bother Total Count Black Count Count White Expected Count Count Ex ted Count No 10 6.3 5 8.8 15 15.0 Total Pearson Chi-Square U-.e$.-.V.aU4-Ca.ses Value 5.1 Chl- uare Tests Dt Asymp. Sig. (2 Yes 15 25 18.8 25.0 30 35 26.3 35.0 45 60 45.0 60.0 Exact Sig. (2- Exact Sig. (1- side 1 4 4 si ,023 a. O cells (.0%) have expected count less than 5. The mlnlmtrn expected cotnt is 6.25. b. Convuted only tor a 2x2 table S mmetric Measures Phl Norninal by Nominal Cramer's V N of Valid Cases a. Not assuming the null hypothesis. Value 60 rox. Si .023 b. Using the asyrnptotlc standard error assumhg the null h•mthesis..

DEPENDENT-GROUP DESIGNS WITH NOMINAL OUTCOME MEASURES.

THE MCNOMAR TEST AND COCHRAN Q TEST. PAUL DAVID RODRIGUEZ.

MCNEMAR TEST. McNemar test: A nonparametric statistic used to analyze nominal data from a study using two dependents (matched or repeated measures) groups..

MCNEMAR TEST. The McNemar test is similar to the chi-square tests that were covered in the previous sections. The McNemar test is used when you have repeated or matched measures for two categories. For example, you may ask psychology majors whether they like (yes or no) studying research at the beginning of a Research Methods course and again at the end. We thus have nominal data in two categories (yes, no) from two time periods (before and after taking Research Methods) or repeated measures..

Response to “I Like Studying Research”. After Taking RM Yes Before Taking RM Yes No No.

MCNEMAR TEST. Remember that the McNemar test is only used for designs using matched or repeated nominal dichotomous measures, whereas the chi-square test of independence is used with designs that have two independent groups measured on a nominal scale..

COCHRAN Q TEST. Cochran Q test: A nonparametric statistic used to analyze nominal data from a study that includes three or more dependent groups..

COCHRAN Q TEST. The Cochran Q test is the statistical test used to analyze three or more dependent groups assessed on a nominal variable. The nominal variable is always dichotomous or has only two possible values (0 and 1, yes and no, etc.). The data are presented in blocks of the three-plus treatments, with each block representing a matched group or single participant measured three or more times..

COCHRAN Q TEST. For example, a researcher may be interested in whether three 10-minute videos that discuss the signs of child abuse and the appropriate reporting process differ in their effectiveness. Suppose the researcher matched (in trios) elementary teachers on their number of years teaching and then randomly assigned one teacher in each of the trios to view one of the videos. The teachers then report (Yes or No) whether the film is effective in helping them to identify child abuse. The Cochran’s Q test would determine whether there are differences in the teacher’s ratings of the types of films..

COCHRAN Q TEST. Treatments 1 2 3 FILM 1 X11 X12 X13 FILM 2 X21 X22 X23 FILM 3 X31 X32 X33.