Question

State examples of the Chi-Square technique outcomes

Answer 1

The chi-squared distribution has many uses in statistics, including:

• Confidence interval estimation for a population standard deviation of a normal distribution from a sample standard deviation.
• Independence of two criteria of classification of qualitative variables.
• Relationships between categorical variables (contingency tables).
• Sample variance study when the underlying distribution is normal.
• Tests of deviations of differences between expected and observed frequencies (one-way tables).
• The chi-square test (goodness of fit test).

For example, if you want to test whether attending class influences how students perform on an exam, using test scores (from 0-100) as data would not be appropriate for a Chi-square test. However, arranging students into the categories "Pass" and "Fail" would. Additionally, the data in a Chi-square grid should not be in the form of percentages, or anything other than frequency (count) data. Thus, by dividing a class of 54 into groups according to whether they attended class and whether they passed the exam, you might construct a data set like this:

	Pass	Fail
Attended	25	6
Skipped	8	15

Pass	Fail	Total
Attended	25 (18.94)	6 (12.05)	31
Skipped	8 (14.05)	15 (8.94)	23
Total	33	21	54

We have 1 degree of freedom, so our p-value is calculated as 0.0006. In other words, if this distribution was due to chance, we would see exactly this distribution only 0.06% of the time!

We can thus safely say that the null hypothesis is incorrect; attending class and passing are definitely dependent on one another.