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Independence Tests definitions

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  • Independence
    A property where two variables do not influence each other; their outcomes are unrelated in the context of categorical data.
  • Categorical Variable
    A variable that takes on values representing distinct groups or categories, such as grade levels or height ranges.
  • Null Hypothesis
    The default assumption stating that two variables are unrelated; used as a starting point in statistical testing.
  • Alternative Hypothesis
    A statement suggesting that two variables are related; considered when evidence contradicts the default assumption.
  • Chi-square Test Statistic
    A value calculated from observed and expected frequencies to measure the discrepancy between them in a contingency table.
  • Observed Frequency
    The actual count of occurrences recorded in each category or cell of a data table.
  • Expected Frequency
    A calculated value predicting the count in each category, assuming independence, based on row and column totals.
  • Contingency Table
    A matrix displaying the frequency distribution of two categorical variables, organized by rows and columns.
  • Degrees of Freedom
    A parameter determined by the formula (rows-1)(columns-1), indicating the number of values free to vary in the test.
  • P-value
    A probability quantifying how likely observed results are under the null hypothesis; used to guide decision-making.
  • Significance Level
    A threshold, often denoted as alpha, for deciding whether to reject the null hypothesis based on the p-value.
  • Random Sample
    A selection method ensuring each member of a population has an equal chance of inclusion, supporting valid inference.
  • Goodness of Fit Test
    A statistical procedure comparing observed frequencies to a claimed distribution for a single categorical variable.