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Two Means - Matched Pairs (Dependent Samples) definitions

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  • Matched Pairs
    Samples uniquely related, often through before-and-after comparisons, with each value paired in a one-to-one relationship.
  • Dependent Samples
    Groups where values are linked, such as repeated measures on the same individuals, affecting each other's outcomes.
  • Mean Difference
    Average of the differences calculated between paired values, serving as the point estimator in analysis.
  • Standard Deviation of the Difference
    Measure of variability among the differences in matched pairs, used in margin of error calculations.
  • Null Hypothesis
    Default assumption stating no difference exists between paired values, often set to zero in matched pairs tests.
  • Alternative Hypothesis
    Statement suggesting a significant change or difference between paired values, guiding the direction of the test.
  • Confidence Interval
    Range constructed around the mean difference, indicating where the true population difference likely falls.
  • Margin of Error
    Amount added and subtracted from the mean difference, calculated using the critical t-value and standard deviation.
  • Critical t-value
    Threshold from the t-distribution, determined by confidence level and degrees of freedom, used in interval and error calculations.
  • Degrees of Freedom
    Value found by subtracting one from the number of pairs, influencing the shape of the t-distribution.
  • Point Estimator
    Best guess for the population mean difference, typically the sample mean difference in matched pairs analysis.
  • One-to-One Relationship
    Direct pairing of values from two samples, ensuring each value is uniquely matched for comparison.
  • Random Sample
    Selection process ensuring each individual has an equal chance of inclusion, supporting valid statistical inference.
  • p-value
    Probability of observing results as extreme as those found, given the null hypothesis is true, used for decision-making.
  • Level of Significance
    Threshold for deciding whether to reject the null hypothesis, commonly set at 0.05 in hypothesis testing.