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Two Means - Matched Pairs (Dependent Samples) definitions

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  • Matched Pairs
    Samples where each value in one group is uniquely paired with a value in another, often through before-and-after or related individuals.
  • One-to-One Relationship
    A direct pairing between values in two samples, ensuring each value is linked to exactly one counterpart.
  • Mean Difference
    The average of the differences calculated between each matched pair, serving as the central measure in analysis.
  • Sample Mean Difference
    The computed average of all individual differences in matched pairs, denoted as d-bar.
  • Standard Deviation of Differences
    A measure of variability among the differences in matched pairs, represented as s sub d.
  • Null Hypothesis
    The default claim that there is no difference between paired values, typically stating the mean difference equals zero.
  • Alternative Hypothesis
    A claim suggesting a significant change or difference exists between paired values, challenging the null hypothesis.
  • Confidence Interval
    A range constructed around the sample mean difference, estimating where the true population mean difference likely falls.
  • Margin of Error
    The product of the critical t-value and the standard deviation of differences divided by the square root of the number of pairs.
  • Critical t-value
    A cutoff from the t-distribution, based on confidence level and degrees of freedom, used in interval and error calculations.
  • Degrees of Freedom
    A value calculated as the number of pairs minus one, used to select the appropriate t-distribution.
  • p-value
    The probability, under the null hypothesis, of observing a test statistic as extreme as the one calculated from the data.
  • Level of Significance
    A threshold, often denoted alpha, used to decide whether to reject the null hypothesis based on the p-value.
  • Point Estimator
    A single value, such as the sample mean difference, used as the best guess for the population parameter.
  • Independent Samples
    Groups where values in one sample have no unique pairing or relationship with values in the other sample.