Chi Squared Test

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

  1. Quantitative data.
  2. One or more categories.
  3. Independent observations.
  4. Adequate sample size (at least 10)
  5. Simple random sample.
  6. Data in frequency form.
  7. All observations must be used.


Step by Step procedure for doing the same

  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
  3. Calculate chi square using the formula. Complete all calculations to three significant digits. Round off your answer to two significant digits.
  4.  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 chi2 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.




Group 7  ,Section A


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