Chi-square Test of Goodness of Fit

Chi-square Test of Goodness of Fit

Parametric tests such as ANOVA and t-test have differences with non-parametric tests because of assumptions they assume. The first difference is the assumption of data distribution. A parametric analysis will assume that the distribution of data is known; for example, an independent two-sample t-test assumes a normal distribution of the sample data and homogeneous of variance between the two groups. Non-parametric, on the other hand, does not assume that the distribution of the data is known (Shaheen, Awan & Cheema, 2016). The second difference is that parametric tests apply only when the measurement level of the provided data is on an interval or ratio scale. Whereas in non-parametric, the tests can be accomplished even when the data is measured in ordinal or nominal scale.

According to D’Agostino (2017), chi-square goodness of fit expected frequency is calculated using the formula E=np where E represents the expected frequency, n is the number of infants that got attracted by a particular color, and p represents the proportion of each category of color. Proportion is calculated by dividing n by the total number of infants experimented. The table below shows the expected frequencies.

We may want to know if the sample size of infants was drawn from a population that follows a normal distribution or not. Therefore, the null hypothesis will be;

Ho: The sample size came from a population with a normal distribution

Ha: the sample size did not come from a normally distributed population.

chi^2 = χ 2 = (3, N=60) =4.53 is to be compared with critical value at p > 0.05 to conclude whether the null hypothesis is true. At p = 0.05, the critical value is 7.82. The chi-square statistic calculated is less than the critical value. Hence, we fail to reject the null hypothesis and conclude that the sample size of infants came from a normally distributed population.