Lecture 15: March 14, 2017 (Chapter 9 and Chapter 10) REVIEW from March 7 Ttests OVERVIEW Chapters 9, 10 and 11 I. Why ttests? They are more versatile. You can use them to A. compare a sample to a population when you dont know the population SD (one sample t) Chapter 9 B. compare two independent samples to one another (between subjects independent samples t). Chapter 10 C. compare each persons performance to themselves in a sample (within subjectspaired samples t) Chapter 11 *Notice that there are no populations in B and C. We only have samples but we are still making inferences about populations! (Taking off the training wheels.....) REVIEW II. One sample ttest (Chapter 9) A. You use it when you have IVDV study with 2 levels in IV, one from population, scale DV but NO population SD (). You use sample SD (s) to estimate when you have a ttest. * However, you can also use it to compare a samples performance to a set value (e.g. the expected value you would get in the population, if everyone was guessing on an exam). B. You use a different sampling distribution (the t distribution instead of the z distribution, though both are based on the sampling distribution of the mean) 1. To use it, you need to calculate degrees of freedom (df) 2. Only critical values are listed (based on one or two tailed test, alpha .05, 01 etc). C. The formulas are (slightly) different 1. REVIEW: You use the standard deviation for the SAMPLE (the formula with n1 in the denominator) 2. t = Mm SM= estimated standard error of Mean SM SM= ssquare root (n). *Note M (the value of the sample mean you expect if Ho is true is the value of the general population mean) D. In APA statement .. the statistical section (after the statement of significance you say for example, There is a significant effect : t(14) = 8.97, p < .05, two tailed. *Notice you indicate the degrees of freedom (df) in parentheses E. Examples 1. Standard (two tailed, alpha () = .05). The Default (REVIEW) 2. Exotic tests (only do these when ASKED) a. Conservative tests (chosen alpha is less than .05 e.g .01) b. Liberal (e.g. Onetailed test) F. The Frills 1. Cohens d... just use the sample SD in the denominator! 2. Confidence intervals *Notice you can do Confidence intervals for zs too..... We are doing the same thing... only with estimated standard errors (sm) rather than actual ones (sm) III. Between subjects (Independent samples) t (CHAPTER 10) A. You use it when you have an IVDV design with 2 levels in the IV and a scale DV.