The Chi-Square Statistic: Tests For Goodness Of Fit And Independence

CHAPTER 18

Parametric tests (such as t or ANOVA ) differ from nonparametric tests (such as chi-square ) primarily in terms of the assumptions they require and the data they use . Explain these differences

Parametric tests are used to test data that are normally distributed and the dependent variable is measured at intervals . This would mean that the data is gathered from a random sample , thus the sample size is relatively small . The data also is measured as intervals , any dependent variable that has at least 2 or 3 categories or has 2 or more

levels Nonparametric tests are used to test data that are large and have not been randomly sampled since it is assumed that large samples generally will resemble the normal distribution . The data for nonparametric tests should be ordinal or nominal that does not require an interval level Parametric tests also test assumptions with directionality and the strength of the relationship , effect or influence of the variables . On the other hand , nonparametric tests only test associations and to determine how different the surveyed data are from the expected values

3 ) A developmental psychologist would like to determine whether infants display any color preferences . A stimulus consisting of four color patches (red , green , blue , and yellow ) is projected onto the ceiling above a crib . Infants are placed in the crib , one at a time , and the psychologist records how much time an infant spends looking at each of the four colors . The color that receives the most attention during a 100-second test period is identified as the color for that infant . The colors for a sample of 60 infants are shown in the following table

RED GREEN BLUE YELLOW

21 11 18 10 Do the data indicate any significant preferences among the four colors ? Test at the .05 level of significance

No significant preference for any of the four colors

Red Green Blue Yellow Actual 21 11 18 10 60

Expected 15 15 15 15 60

Chi 2 .4 1 .06 .6 1 .66 5 .72

n 60

df k- 1 4-1

df 3

alpha .05

chi square computed 5 .72

chi square critical 7 .82

Decision : chi square computed chi square critical

Reject the null hypothesis...