Inferential Statistics: Chi Square (X2) - DAY 6 - B.ED - 8614 - AIOU
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Inferential Statistics: Chi Square (X2) - The Chi-Square Distribution - Chi-Square (X2) Goodness-of-Fit test - Chi-Square Independence Test
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Inferential Statistics: Chi Square (X2) - DAY 6 - B.ED - 8614 - AIOU
- 3. The chi-square (χ2) statistics is commonly used for testing relationship between categorical variables. It is intended to test how likely it is that an observed difference is due to chance. In most situations it can be used as a quick test of significance.
- 4. The Chi-Square (or the Chi-Squared - χ2) distribution is a special case of the gamma distribution (the gamma distribution is family of right skewed, continuous probability distribution. These distributions are useful in real life where something has a natural minimum of 0) a chi- square distribution with n degree of freedom is equal to a gamma distribution.
- 5. The Chi-square (χ2) test represents a useful method of comparing experimentally obtained results with those to be expected theoretically on some hypothesis. Thus Chi-square is a measure of actual divergence of the observed and expected frequencies.
- 6. Chi-square as we have seen is a measure of divergence between the expected and observed frequencies and as such if there is no difference between expected and observed frequencies the value of Chi-square is 0. Under the Null Hypothesis we state that there is no significant difference between the observed (experimental) and the theoretical or hypothetical values, i.e., there is a good compatibility between theory and experiment. For example, if 10 samples are taken from the normal distribution, then degree of freedom df = 10. Chi-square distributions are always right skewed. The greater the degree of freedom, the more the chi- square distribution looks like a normal distribution.
- 7. The chi-square distribution has many uses which include: i) Confidence interval estimation for a population standard deviation of a normal distribution from a sample standard deviation. ii) Independence of two criteria of classification of qualitative variables (contingency tables). iii) Relationship between categorical variables. iv) Sample variance study when the underlying distribution is normal. v) Tests of deviations of differences between expected and observed frequencies (one-way table). vi) The chi-square test (a goodness of fit test).
- 8. A Chi-Square Statistic is one way to a relationship between two categorical (non- numerical) variables. The Chi-Square Statistic is a single number that tells us how much difference exists between the observed counts and the counts that one expects if there is no relationship in the population.
- 9. There are two different types of chi-square tests, both involve categorical data. These are: a) A chi-square goodness of fit test, and b) A chi-square test of independence. In the coming lines these tests will be dealt in some details.
- 10. The chi-square (χ2) goodness of fit test (commonly referred to as one-sample chi- square) is the most commonly used goodness of fit test. It explores the proportion of cases that fall into the various categories of a single variable, and compares these with hypothesized values
- 11. In some simple words we can say that it is used to find out how the observed value of a given phenomena is significantly different from the expected value. The null hypothesis for the chi-square goodness of fit test is that the data does not come from the specified distribution. The alternate hypothesis is that the data comes from the specified distribution.
- 12. For using chi-square (χ2) goodness of fit test we will have to set up null and alternate hypothesis. A null hypothesis assumes that there is no significance difference between observed and expected value. Then, alternate hypothesis will become, there is significant difference between the observed and the expected value.
- 13. a) The chi-square test can only be used to put data into classes. If there is data that have not been put into classes then it is necessary to make a frequency table of histogram before performing the test. b) It requires enough sample size in order for chi-square approximation to be valid.
- 14. The chi-square goodness of fit test is appropriate when the following conditions are met: The sampling method is simple random. The variable under study is categorical. The expected value of the number of sample observation in each level of the variable is at least 5.
- 15. States the null hypothesis (H0) It might take the form: The data are not consistent with a specified distribution. ii) States the alternate hypothesis (Ha) This is an opposite statement to the null hypothesis The data are consistent with a specified distribution.
- 16. Find the p-value The range of our p-value can be found by comparing test statistic to table values. v) Reach a conclusion We need a p-value less than the significance level, generally less than 5% (p < .05), to reject the null hypothesis. It is suitable to write a sentence in the context of the question, i.e. “the data appears to follow a normal distribution”
- 17. A chi-square (χ2) test of independence is the second important form of chi-square tests. It is used to explore the relationship between two categorical variables. Each of these variables can have two of more categories.
- 18. It determines if there is a significant relationship between two nominal (categorical) variables. The frequency of one nominal variable is compared with different values of the second nominal variable. The data can be displayed in R*C contingency table, where R is the row and C is the column.
- 19. Both the chi-square tests are sometime confused but they are quite different from each other. The chi-square test for independence compares two sets of data to see if there is relationship. The chi-square goodness of fit test is to fit one categorical variable to a distribution.