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Two Means - Unknown, Unequal Variance definitions

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  • Null Hypothesis
    Default assumption that two population means are equal; serves as the starting point for statistical testing.
  • Alternative Hypothesis
    Statement suggesting a difference exists between two population means; tested against the null hypothesis.
  • Test Statistic
    Numerical value calculated from sample data to assess evidence against the null hypothesis in a two-sample test.
  • Degrees of Freedom
    Value based on the smallest sample size minus one; determines the shape of the t-distribution used in calculations.
  • P Value
    Probability of observing results as extreme as those in the sample, assuming the null hypothesis is true.
  • Alpha
    Threshold for statistical significance; commonly set at 0.05 to decide whether to reject the null hypothesis.
  • Confidence Interval
    Range constructed from sample data that likely contains the true difference between two population means.
  • Point Estimate
    Best guess for the difference in population means, calculated as the difference between sample means.
  • Margin of Error
    Amount added and subtracted from the point estimate to form the confidence interval; depends on t-value and sample statistics.
  • Critical Value
    T-score determined by confidence level and degrees of freedom; used in margin of error and hypothesis testing.
  • Two-Tailed Test
    Statistical test where evidence for differences in either direction is considered; alternative hypothesis uses not equal to.
  • Sample Standard Deviation
    Measure of variability within each sample; used to calculate standard error and margin of error.
  • Standard Error
    Estimate of variability in the difference between sample means; calculated using both sample standard deviations and sizes.
  • Pooled
    Option in statistical software indicating whether to assume equal population variances; set to 'no' for unknown, unequal variances.
  • Confidence Level
    Probability that the constructed interval contains the true difference in means; commonly set at 90% or 95%.