Download Psych Stats: Testing Hypotheses & Confidence Intervals for Correlations & Proportions and more Slides Statistics for Psychologists in PDF only on Docsity! Introduction to Statistics in Psychology PSY 201 Lecture 24 Correlations and proportions Can you read my mind? Part II HYPOTHESIS TESTING four steps 1. State the hypothesis. 2. Set the criterion for rejecting H0. 3. Compute the test statistic. 4. Interpret the results. 2 CONFIDENCE INTERVALS sometimes have five steps if want to include CIs 1. State the hypothesis. 2. Set the criterion for rejecting H0. 3. Compute the test statistic. 4. Confidence interval. 5. Interpret the results. 3 SAMPLING DISTRIBUTION frequency of di!erent r values, given a population parameter ! not usually a normal distribution! often skewed to the left or the right cannot find area under curve! 4 FISHER z TRANSFORM formula for creating new statistic zr = 1 2 loge ! """# 1 + r 1! r $ %%%& where loge is the “natural logarithm” function also sometimes designated as ln -1 -0.5 0 0.5 1 r -2 -1 0 1 2 z r 5 FISHER z TRANSFORM for large samples, the sampling distribution of zr is normally distributed (regardless of the value of !) with a mean z! = 1 2 loge ! """# 1 + ! 1! ! $ %%%& and with standard error (standard deviation of the sampling distribution) szr = '(((((() 1 n! 3 where n is the sample size 6 docsity.com CONFIDENCE INTERVAL Suppose we find r = 0.61 from a sample of size n = 30. Build CI90. (e.g. family income and attitudes about democratic childrearing) calculate standard error szr = '(((((() 1 n! 3 = '((((() 1 27 = 0.192 find the critical value from the t distribution table (bottom row) we find that the critical value is 1.645 7 CONFIDENCE INTERVALS construct interval in zr values and then convert back to r values CI = statistic ± (critical value) (standard error) CI90 = zr ± (1.645)(szr) CI90 = 0.709± (1.645)(0.192) CI90 = (0.393, 1.025) 8 CONFIDENCE INTERVALS convert zr CI90 into r, correlation coe"cients use the r to Fisher z calculator in reverse zr = 0.393" r = 0.374 zr = 1.025" r = 0.773 (note, approximations! actual values not listed!) so, in terms of r values CI90 = (0.374, 0.773) 9 A SPECIAL CASE Last time we noted that while we needed Fisher’s z transformation to convert the sampling distribution into a normal distribution it is not necessary for testing ! = 0 10 EXAMPLE n = 32 scores calculated to get r = !0.375 1. State the hypothesis. H0 : ! = 0, Ha : ! #= 0, " = 0.05 2. Set the criterion for rejecting H0. From the t distribution table for df=n! 2 = 30 tcv = ±2.042 3. Compute the test statistic. t = r '(((((() n! 2 1! r2 = (!0.375) '((((() 30 0.859 = !2.216 reject H0 4. Construct the confidence interval. 5. Interpret the results. 11 CONFIDENCE INTERVALS BE CAREFUL!!! we just concluded that we can reject H0, which means we accept the statement Ha : ! #= 0 when we construct a confidence interval we should use the Fisher z transform (we just concluded that ! #= 0, so we would not want to use the t distribution to make the confidence interval) everything is just like last time 1. convert r " zr 2. Calculate CI in z transformed scores. 3. Convert zr " r to get CI in r scores 12 docsity.com
