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Two Means - Unknown, Equal Variance definitions

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  • Pooled Standard Deviation
    Weighted average of two sample standard deviations, used to estimate population standard deviation when variances are assumed equal.
  • Hypothesis Test
    Statistical procedure for evaluating claims about population parameters using sample data and probability.
  • Null Hypothesis
    Initial assumption stating no difference exists between two population means; serves as the default claim.
  • Alternative Hypothesis
    Statement suggesting a difference or effect between two population means, supported if evidence rejects the null.
  • T-Score
    Calculated value measuring the difference between sample means relative to pooled standard deviation and sample sizes.
  • P-Value
    Probability of observing a test statistic as extreme as the one calculated, assuming the null hypothesis is true.
  • Significance Level
    Threshold probability, often denoted as alpha, used to decide whether to reject the null hypothesis.
  • Degrees of Freedom
    Sum of each sample size minus one, used in t-distribution calculations for two-sample tests.
  • Independent Random Samples
    Groups selected so each observation is unrelated and chosen randomly, ensuring valid statistical inference.
  • Normality Assumption
    Requirement that data distribution is normal or sample sizes are sufficiently large for accurate inferential results.
  • Sample Mean
    Average value calculated from a sample, used to estimate the corresponding population mean.
  • Sample Standard Deviation
    Measure of variability within a sample, used in calculations for pooled standard deviation and t-score.
  • Population Variance
    Measure of spread for an entire population, assumed equal in this test to justify pooling sample variances.
  • Alpha
    Chosen probability threshold for significance, commonly set at 0.05, guiding decision to reject or retain the null.
  • Weighted Average
    Calculation combining values with different sample sizes, giving more influence to larger samples in pooled statistics.