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Two Variances and F Distribution definitions

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  • F Distribution
    An asymmetric, right-skewed distribution used to compare two sample variances, characterized by two degrees of freedom.
  • Degrees of Freedom
    Values calculated as sample size minus one for each sample, determining the shape of the F distribution.
  • Sample Variance
    A measure of spread within a sample, used as the numerator and denominator in the F statistic calculation.
  • F Statistic
    A ratio of two sample variances, with the larger variance placed in the numerator for hypothesis testing.
  • Critical Value
    A threshold from the F distribution table used to decide whether to reject the null hypothesis.
  • P Value
    A probability calculated from the F distribution indicating the likelihood of observing the test statistic under the null hypothesis.
  • Null Hypothesis
    The assumption that two population variances are equal, serving as the starting point for the test.
  • Alternative Hypothesis
    A statement suggesting a difference or inequality between two population variances.
  • Significance Level
    A predetermined threshold, often 0.05, used to assess whether the p value is small enough to reject the null hypothesis.
  • Chi Squared Distribution
    A right-skewed distribution used for one-sample variance tests, similar in shape to the F distribution.
  • Right-Tailed Probability
    The area under the F distribution curve to the right of the test statistic, representing the p value.
  • Random Sample
    A subset of data selected so each member of the population has an equal chance of inclusion, ensuring unbiased results.
  • Normal Population
    A population whose data follows a bell-shaped curve, a key assumption for valid F tests.
  • Hypothesis Test
    A structured procedure for comparing variances, involving calculation of test statistics and p values.
  • Standard Deviation
    A measure of spread related to variance, sometimes tested using the F distribution in two-sample scenarios.