Chi-Square Test
A chi-squared test, also referred to as chi-square test or
test, is any statistical hypothesis test in which the sampling distribution of the test statistic is a chi-squared distribution when the null hypothesis is true. Also considered a chi-squared test is a test in which this is asymptotically
true, meaning that the sampling distribution (if the null hypothesis is
true) can be made to approximate a chi-squared distribution as closely
as desired by making the sample size large enough.Some examples of chi-squared tests where the chi-squared distribution is only approximately valid:
- Pearson's chi-squared test,
also known as the chi-squared goodness-of-fit test or chi-squared test
for independence. When the chi-squared test is mentioned without any
modifiers or without other precluding context, this test is usually
meant (for an exact test used in place of
- Yates's correction for continuity, also known as Yates' chi-squared test.
- Cochran–Mantel–Haenszel chi-squared test.
- McNemar's test, used in certain 2 × 2 tables with pairing
- Turkey's test of additivity
- The portmanteau test in time-series analysis, testing for the presence of autocorrelation
- Likelihood-ratio tests in general statistical modelling, for testing whether there is evidence of the need to move from a simple model to a more complicated one (where the simple model is nested within the complicated one).
One case where the distribution of the test statistic is an exact chi-squared distribution is the test that the variance of a normally distributed population has a given value based on a sample variance. Such a test is uncommon in practice because values of variances to test against are seldom known exactly.
Chi-square is a statistical test commonly used to compare observed data with data we would expect to obtain according to a specific hypothesis. For example, if, according to Mendel's laws, you expected 10 of 20 offspring from a cross to be male and the actual observed number was 8 males, then you might want to know about the "goodness to fit" between the observed and expected. Were the deviations (differences between observed and expected) the result of chance, or were they due to other factors. How much deviation can occur before you, the investigator, must conclude that something other than chance is at work, causing the observed to differ from the expected. The chi-square test is always testing what scientists call the null hypothesis, which states that there is no significant difference between the expected and observed result.
Step-by-Step Procedure for Testing Your Hypothesis and Calculating Chi-Square:-
1. State the hypothesis being tested and the predicted results. Gather the data by conducting the proper experiment (or, if working genetics problems, use the data provided in the problem).
2. Determine the expected numbers for each observational class. Remember to use numbers, not percentages.
Chi-square should not be calculated if the expected value in any category is less than 5.
