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Two Variances and F Distribution definitions

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  • F Distribution
    An asymmetric, right-skewed distribution with two degrees of freedom, used to compare two sample variances.
  • Degrees of Freedom
    Values calculated as sample size minus one for each group, determining the shape of the F distribution.
  • F Statistic
    A ratio of two sample variances, with the larger variance always placed in the numerator for hypothesis testing.
  • Sample Variance
    A measure of data spread within a sample, calculated as the average squared deviation from the sample mean.
  • Null Hypothesis
    The default assumption that two population variances are equal in a two-sample variance test.
  • Alternative Hypothesis
    A claim that the population variances differ, specifying a direction or inequality based on the research question.
  • P Value
    The probability, calculated from the F distribution, of observing a test statistic as extreme as the one obtained.
  • Critical Value
    A threshold from the F distribution used to decide whether to reject the null hypothesis in variance tests.
  • Significance Level
    A pre-set probability, often 0.05, representing the risk of incorrectly rejecting the null hypothesis.
  • Chi Squared Distribution
    A right-skewed distribution used for one-sample variance tests, similar in shape to the F distribution.
  • Independence
    A condition where the two samples do not influence each other, required for valid two-sample variance tests.
  • Normality Assumption
    The requirement that each population follows a normal distribution for the F test to yield valid results.
  • Graphing Calculator
    A tool used to compute p values and critical values for the F distribution in two-sample variance tests.
  • Right-Tailed Probability
    The area under the F distribution curve to the right of the observed F statistic, used to determine the p value.
  • Standard Deviation
    The square root of variance, sometimes compared in two-sample tests using the F distribution.