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PSY 311 1ST Edition Lecture 4Outline of Last Lecture I. Why can’t we use z a. William Gossett II. Student’s t statistic a. T distribution III. Hypothesis Testing IV. Effect size – Cohen’s d Outline of Current Lecture I. Effect Size - r²II. Point Estimates III. Interval Estimates a. How do we find µIV. A Much More Insignificant Goal Current Lecture : Introduction to the t statistic I. Effect Size - r²An alternative method for measuring effect size is to determine how much of the variability inthe scores is explained by the treatment effect. The concept behind this measure is that thetreatment causes the scores to increase (or decrease), which means that the treatment iscausing the scores to vary. - Why are scores different? - Different people , individual differences and many more differences - Variability comes in 2 forms: - Things we try to explain- Things we do not try to explain - r² is the proportion of variance explained - never get less than 0 or more than 1 - r²= t²/ (t²+df) - the t is the calculated t statistic - Between .01- and .09 – small effect - Between .09 and .25 – medium effect - > .25 – large effect II. Point Estimates - Estimate using single number - The point estimate for µ is M - The point estimate for is s - The point estimate for m is sm - The advantage is that it is precise and there is no ambiguity but the disadvantage is that it is probably inaccurate III. Interval Estimates - Estimate using range of numbers - The wider the range, the greater the confidence - The smaller the range, the more precise a. How do we find µ?- Remember the formula: - T = (M-µ)/sm- This means that: - µ = M- t(sm)- And because the t cutoff can be either positive or negative - µ = M + or – t(sm)- Note that when t=0 , the point estimate of µ is M - As t gets larger, the estimate also gets larger - Remember, t gets larger as gets smaller - (1-) is the confidence level -Confidence intervals are always 2- tailed- T(sm) is called the “margin of error”IV. A much More Insignificant Goal - Note that (1-) confidence intervals can be used to assess 2- tailed null hypotheses - e.g., 95% confidence interval can be used to assess 2 tailed null hypotheses with = .05 - If the value of µ from the null hypothesis is in the confidence interval then - It is indeed a plausible value for µ- Thus, we accept the null

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