Any statistical hypothesis test in which the sampling distribution of the test statistic is a chi-squared distribution when the null hypothesis is true. It 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.

If a sample of size *n* is taken from a population having a normal distribution, then there is a result (see distribution of the sample variance) which allows a test to be made of whether the variance of the population has a pre-determined value.

**Main Objective – **to determine whether there is a significant difference between the expected frequencies and the observed frequencies in one or more categories.

Chi Square Requirements

- Quantitative data.
- One or more categories.
- Independent observations.
- Adequate sample size (at least 10)
- Simple random sample.
- Data in frequency form.
- All observations must be used.

7.

Step by Step procedure for doing the same

- 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).
- Determine the expected numbers for each observational class. Remember to use numbers, not percentages
- Calculate
^{chi }square using the formula. Complete all calculations to three significant digits. Round off your answer to two significant digits. - Use the chi-square distribution table to determine significance of the value.

a.) Determine degrees of freedom and locate the value in the appropriate column.

b.) Locate the value closest to your calculated *chi ^{2}* on that degrees of freedom

*df*row.

c.) Move up the column to determine the p value.

5. State your conclusion in terms of your hypothesis.

a.) If the *p* value for the calculated ^{2} is *p > *0.05, accept your hypothesis. ‘The deviation is small enough that chance alone accounts for it. A *p* value of 0.6, for example, means that there is a 60% probability that any deviation from expected is due to chance only. This is within the range of acceptable deviation.

b.) If the p value for the calculated ^{2} is *p < *0.05, reject your hypothesis, and conclude that some factor other than chance is operating for the deviation to be so great. For example, a p value of 0.01 means that there is only a 1% chance that this deviation is due to chance alone. Therefore, other factors must be involved.

By:

Uttpreksha

13PGP057

Group 7 ,Section A