A goodness-of-fit statistic tests the following hypothesis:

The chi-square goodness-of-fit test is applied to binned data (i.e., data put into classes).

For goodness-of-fit testing, notably of continuous distributions,.

You use the chi-square test of goodness-of-fit when you have one nominal variable, you want to see whether the number of observations in each category fits a theoretical expectation, and the sample size is large.

If p-value is less than alpha, you cannot accept null hypothesis.

Use the chi-square test of goodness-of-fit when you have one with two or more values (such as red, pink and white flowers). You compare the observed counts of observations in each category with the expected counts, which you calculate using some kind of theoretical expectation (such as a 1:1 sex ratio or a 1:2:1 ratio in a genetic cross).

We start with a categorical variable with n levels and let pi be the proportion of the population at level i. Our theoretical model has values of qi for each of the proportions. The statement of the null and alternative hypotheses are as follows:


Chi-Square Goodness of Fit Test - ThoughtCo

The chi-square goodness-of-fit test is based on certain approximations which, as a rule of thumb, hold as long as all the expected counts are at least 5. Before conducting a chi-square goodness-of-fit test, check that this rule of thumb is satisfied as follows.

Chi-square Statistic for Goodness of Fit

The statistical is that the number of observations in each category is equal to that predicted by a biological theory, and the alternative hypothesis is that the observed numbers are different from the expected. The null hypothesis is usually an extrinsic hypothesis, where you knew the expected proportions before doing the experiment. Examples include a 1:1 sex ratio or a 1:2:1 ratio in a genetic cross. Another example would be looking at an area of shore that had 59% of the area covered in sand, 28% mud and 13% rocks; if you were investigating where seagulls like to stand, your null hypothesis would be that 59% of the seagulls were standing on sand, 28% on mud and 13% on rocks.

Chi-Square Goodness of Fit Test - Statistics Solutions

A goodness-of-fit test, in general, refers to measuring how well do the observed data correspond to the fitted (assumed) model. We will use this concept throughout the course as a way of checking the model fit. Like in a linear regression, in essence, the goodness-of-fit test compares the observed values to the expected (fitted or predicted) values.

Null hypothesis for a chi-square goodness of fit test

To conduct the chi-square test, the researcher enters observed frequencies corresponding to combinations of levels of relevant factors (here, called "condition" and "group," but these are labels of convenience). Sums of elements within rows and within columns are then computed (call these ). The chi-square test of independence is used to test the null hypothesis that the frequency within cells is what would be expected, given these marginal Ns. The chi-square test of goodness of fit is used to test the hypothesis that the total sample N is distributed evenly among all levels of the relevant factor.

Null hypothesis for a chi-square goodness of fit test 1

Since we have a very miniscule p-value, we reject the null hypothesis. We conclude that M&Ms are not evenly distributed among the six different colors. A follow-up analysis could be used to determine a confidence interval for the population proportion of one particular color.