The most common goodness-of-fit test is the chi-square test, typically used for discrete distributions. The chi-square test is used exclusively for data put into classes (bins), and it requires a sufficient sample size to produce accurate results.

Test Your Understanding

1. State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
2. Formulate an analysis plan. For this analysis, the significance level is 0.05.
3. Analyze sample data.
4. Interpret results.

Question: When We Carry Out A Chi-square Goodness-of-fit Test For A Normal Distribution, The Null Hypothesis States That The Population 1 Does Not Have A Normal Distribution.

The null hypothesis of the Chi-Square test is that no relationship exists on the categorical variables in the population; they are independent.

We now run the test using the five-step approach.

1. Set up hypotheses and determine level of significance.
2. Select the appropriate test statistic.
3. Set up decision rule.
4. Compute the test statistic.
5. Conclusion.
6. Set up hypotheses and determine level of significance.
7. Select the appropriate test statistic.
8. Set up decision rule.

This is the basic format for reporting a chi-square test result (where the color red means you substitute in the appropriate value from your study). X2 (degress of freedom, N = sample size) = chi-square statistic value, p = p value.

The smallest chi-square value possible is 0, but there is no upper bound: it depends on the size of the numbers. Notice that the less the difference between observed and expected, the smaller the value of chisquare will be.

Correlation equivalents The correlation statistic can be used for continuous variables or binary variables or a combination of continuous and binary variables. In contrast, t-tests examine whether there are significant differences between two group means.

A t-test tests a null hypothesis about two means; most often, it tests the hypothesis that two means are equal, or that the difference between them is zero. A chi-square test tests a null hypothesis about the relationship between two variables.

Spearman rank correlation: Spearman rank correlation is a non-parametric test that is used to measure the degree of association between two variables.

A t-test is a hypothesis test for the difference in means of a single variable. A correlation test is a hypothesis test for a relationship between two variables.

The correlation coefficient is measured on a scale that varies from + 1 through 0 to – 1. Complete correlation between two variables is expressed by either + 1 or -1. When one variable increases as the other increases the correlation is positive; when one decreases as the other increases it is negative.