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Inferences for the Correlation Coefficient - Excel definitions

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  • Correlation Coefficient
    A numerical measure indicating the strength and direction of a linear relationship between two variables in a dataset.
  • Population Correlation Coefficient
    A parameter representing the true linear relationship between two variables across an entire population.
  • Sample Correlation Coefficient
    A statistic calculated from sample data to estimate the strength and direction of a linear relationship.
  • Null Hypothesis
    A statement asserting no linear correlation exists between two variables, often represented by a population parameter equal to zero.
  • Alternative Hypothesis
    A claim suggesting a linear correlation exists between two variables, differing from the null hypothesis.
  • Degrees of Freedom
    A value calculated as sample size minus two, used in statistical tests for correlation significance.
  • Test Statistic
    A calculated value used to assess the evidence against the null hypothesis in hypothesis testing.
  • T Score
    A value derived from the sample correlation coefficient and degrees of freedom, used to determine statistical significance.
  • P Value
    A probability indicating the likelihood of observing the sample data if the null hypothesis is true.
  • Alpha
    A threshold probability used to decide whether to reject the null hypothesis, commonly set at 0.05.
  • Two-Tailed Test
    A hypothesis test evaluating whether a parameter differs from a specified value in either direction.
  • Linear Correlation
    A relationship where changes in one variable are associated with proportional changes in another variable.
  • Excel Function
    A built-in formula used to compute statistical values such as correlation coefficients and p-values.
  • R Squared
    A value obtained by squaring the correlation coefficient, representing the proportion of variance explained.
  • Significance
    A determination that observed results are unlikely to have occurred by chance, based on statistical testing.