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An introduction to hypothesis testing using the t-distribution. It covers the steps involved in hypothesis testing, including calculating the appropriate test statistic and critical value, evaluating sample data, and reaching a conclusion. The document also discusses effect size as a way to quantify the magnitude of a treatment effect.
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Introduction to t
Hypothesis testing with Z, a review
a) What is the appropriate test statistic? b) What is the critical value?
Hypothesis testing with Z, a review
a) What is the appropriate test statistic? b) What is the critical value? With a known μ, and σ , we can calculate
Z = M - μ σ M σ (^) M =
standard deviation? We have to estimate it from our sample: Remember: SS = x- M )^2 Population Sample Variance: σ 2=SS/N s^2 =SS/n- Standard Deviation: σ =^ S/N s= S/n-
Similarly, estimate the standard error: Also, remember your estimates of population values get better with sample size. Also, df = n-
Previously we argued that the distribution of sample means was normal (central limits theorem), so we could use Z to test hypotheses about those means. The t distribution is a probability distribution (similar to Z) that takes into account that we are estimating the standard deviation, and this estimate changes with degrees of freedom (sample size). The distribution is normal when n is large, but flatter than normal for small values of n.
Steps
α =.
Other examples
Effect Size
Effect Size Cohen’s d Measures how big the effect is by comparing it to the standard deviation. Cohen’s d = mean difference/standard dev. In our basketball example: Cohen’s d = 76-69/1.63 = 4.
Effect Size
r^2 = t^2 /( t^2 + df) = 8.54^2 /(8.54^2 +3) =. That is, 96% of the variance from the population mean can be explained by the fact that my sample is basketball players. Effect Size