Overview
This lecture explains how to use the chi-square distribution to find critical values for variance confidence intervals and other statistical tests.
Chi-Square Distribution Characteristics
- The chi-square distribution is used for tests involving variance and categorical data.
- It is always right-tailed because the distribution is based on squared values and cannot be negative.
- The distribution's values start at zero and only include positive numbers.
Uses of Chi-Square Critical Values
- Commonly used in goodness-of-fit and categorical association tests, which are right-tailed.
- For variance confidence intervals, both lower and upper critical values are needed (two-tailed).
Calculating Critical Values
- To find critical values, specify the confidence level (e.g., 95%, 99%) and the degrees of freedom.
- Example: For 19 degrees of freedom and 95% confidence, the lower limit is 8.907, and the upper limit is 32.852.
- For 99% confidence with the same degrees of freedom: lower critical value is 6.843, upper critical value is 38.583.
- These numbers are critical values, not the actual confidence intervals.
Key Terms & Definitions
- Chi-square distribution — A statistical distribution used with variance and categorical data, based on squared values.
- Degrees of freedom — The number of independent values in a calculation, often related to sample size minus one.
- Critical value — A cutoff value used in hypothesis testing and confidence intervals to determine significance.
- Confidence interval — A range of values estimated to contain a population parameter with a specified probability.
Action Items / Next Steps
- Practice using StatKey or tables to find chi-square critical values for various confidence levels and degrees of freedom.