Download Confidence Intervals, Effect Size and Power - Statistics for the Behavioral Sciences - Lecture Slides and more Slides Behavioural Science in PDF only on Docsity! Statistics for the Behavioral Sciences Confidence Intervals, Effect Size and Power Docsity.com Point Estimates The best estimate of a population mean is the sample mean. When we use a sample to estimate parameters of the population, it is called a point estimate. How accurate is our point estimate? The sampling distribution of the mean is used to evaluate this. Docsity.com Levels of Confidence A 95% confidence interval means that if a series of confidence intervals were constructed around different means, about 95% of them would include the true population mean. When you use 99% as your confidence interval, then 99% would include the true pop mean. Docsity.com Calculating Different Levels For 95% use the critical values for z scores that cutoff 5% in the tails: 533 ± (1.96)(11) = 554.56 & 511.44 where M = 533 and σM = 11 For 99% use the critical values that cutoff 1% in the tails: 533 ± (2.58)(11) = 561.38 & 504.62 Docsity.com Sample Size Increasing the sample size decreases the variability of the sampling distribution of the mean: Docsity.com Effect Size Effect size is a measure of the difference between two populations. One population is the null population assumed by the null hypothesis. The other population is the population to which the sample belongs. For easy comparison, this difference is converted to a z-score by dividing it by the pop std deviation, σ. Docsity.com Effect Size Effect Size X1 X2 Docsity.com A Significant Effect Effect Size X1 X2 Critical Value Critical Value Docsity.com Probabilities of Error Probability of a Type I error is α. Most of the time α = .05 A correct decision exists .95 of the time (1 - .05 = .95). Probability of a Type II error is β. When there is a large effect, β is very small. When there is a small effect, β can be large, making a Type II error likely. Docsity.com When there is no effect… 1.65 .05 COMMON α = .05 Sample means that produce a type I error Hypothesized and true distributions coincide Docsity.com Effect Size and Distribution Overlap Cohen’s d is a measure of effect size. The bigger the d, the bigger the difference in the means. http://www.bolderstats.com/gallery/normal/cohenD.html Docsity.com Large Effects Have More Power Effect Size X1 X2 Critical Value Critical Value Power Docsity.com Calculating Power Most researchers use special purpose software or internet power calculators to determine power. This requires input of: Population mean, sample mean Population standard deviation Sample size Significance level, 1 or 2-tailed test http://www.stat.ubc.ca/~rollin/stats/ssize/n2.html Docsity.com Sample Power Graph 1 Docsity.com β Decreases with Larger N’s Note: This is for an effect in the negative direction (H0 is the red curve on the right). Docsity.com Increasing Power Strengthen the effect by changing your manipulation (how the study is done). Decrease the population’s standard deviation by decreasing noise and error (do the study well, use a within subject design). Increase sample size. Change the significance level. Docsity.com
