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chi square test ( homo)

chi square test

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chi square test ( homo)

  1. 1. CHI-SQUARE TEST X2 Another most widely used test of significance ( non- parametric). Particularly useful in test involving cases where persons, events or objects are grouped in two or more nominal categories such as yes or no, approved-undecided disapprove or class “A,B,C,D.”
  2. 2. • By using the Chi-square , we can test for the significant differences between the observed distribution of data among categories and expected distribution of data based upon the null hypothesis. • It is useful in case of one-sample analysis, two independent samples or k independent samples
  3. 3. 1. One variable Chi-square( goodness- of –fit test) Compares a set of observed frequency (0) for each categories. ( Example: political candidates, contestant 1,2,3) 2. Two variable chi- square( test of independence) With two or more categories/ produce to determine whether two or more variables are statistically independent ( Example: Classification of heights as first variable and weight as second variable) 3. Test of Homogeneity the test is concerned with two or more samples, with only one criterion variable.  It is used to determine if two or more populations are homogeneous. X2
  4. 4. • 1.Make a problem statement • 2. Hypotheses • H0: The distributions of the two populations are the same. • Ha: The distributions of the two populations are not the same.
  5. 5. • The significance level, α corresponds to the size of the rejection region. It determines how small the p-value should be in order to reject the null hypothesis. The common choices for α are 0.05, 0.01, or 0.10.
  6. 6. P-value • The p-value is the probability of getting a value for the test statistic as large or larger than the observed value of the test statistic just by random chance. • To determine a p-value look at the χ2 table with df degrees of freedom and find where the observed value of the χ2 statistic falls on this table.
  7. 7. Level of Significance: • Degrees of freedom. • DF = (r - 1) (c - 1) • where r is the number of populations/no. of rows, and • c is the number of levels for the categorical variable/no. of columns.
  8. 8. • X2 = ∑ • Where: • X2 = the chi-square test • O = the observed frequencies • E = the expected frequencies
  9. 9. • there are two ways to make a decision in this test • Classical Reject null hypothesis if χ2 ≥ χ2 α,df Fail to reject null hypothesis if χ2 < χ2 α,df OR P-value: • this method is preferred by researchers currently conducting research Reject null hypothesis if p-value ≤ α Fail to reject null hypothesis if p-value > α
  10. 10. • The conclusion is a statement written to convey the results of the research. If possible, avoid statistical terminology and should be written in a form that can be easily understood by non-statisticians. • Example • If the null hypothesis is rejected then conclude that the two variables are not homogeneous at the specified significance level. • If the null hypothesis is not rejected then conclude that the variables are homogeneous at the specified significance level.

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