Psyc 203 1st Edition Lecture 21Outline of Last Lecture I. Exam ReviewOutline of Current Lecture I. Review II. T-test for Independent Groups Current LectureI. Review a. Famous 8 Steps i. 1. State the hypotheses ii. 2. Set the significance level (alpha) iii. 3. Select the appropriate inferential test statisticiv. 4. Use the selected inferential test to compute a test statistic. The test statistic is a single number that comes from the formula for the specific test. These test statistics can be used to compute p- values. v. 5. Determine the CRITICAL VALUE for the test statistic. This is the minimum value needed to reject the null hypothesis. In other words, this is the value needed to REJECT THE NULL. vi. 6. Compare your obtained test statistic to the critical value. vii. 7. If the obtained value is bigger than the critical value, Reject the Null Hypothesis 1. When the obtained value is bigger than your critical value, your p-value is smaller than your cutoff. viii. 8. If the obtained value is smaller than the critical value, ix. Fail to Reject the null hypothesis This means your p-value is bigger than your cutoff These notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.b. One Sample Z testi. Use it when we want to test the difference between a sample mean and the population mean 1. Ex: is the average depression score from this sample different from the population?2. Is the average SAT score from this class different from the population of college students?ii. Formulas: z= (xbar-μ)/ SEMiii. SEM=σ/√II. T-test for Independent Groups a. Widely Used. Published in 1908 b. AKA the between subjects t-test c. Students’ test because he worked for Guiness and couldnt use his name when he published his work d. When do we use it? i. When we want to test the difference between two sample means from two separate groups e. Examplesi. Is there a difference between the treatment and control group in a simple experiment? ii. Is there a difference between men and women in terms of narcissism? iii. Men vs. Women, blue vs. Red (placebo) pillf. What you need i. The mean, standard deviation, and sample size for each groupii. Basic structure of the t statistic: 1. t= Group Difference / SE of Difference iii. Steps 1. Null and Alternative Hypothesis 2. Set Alpha to .05 (our default for the two-tailed tests)3. Pick a test a. If independent samples pick the t-test 4. Compute the test statistic 5. Find the critical valuea. We want to know if our p-value is bigger or smaller than our alpha (.05) b. The book lists various Critical Values c. Every combination test statistic and total sample size has a corresponding p-value. d. Online calculators, Excel, or SPSS can tell you this p-value precisely e. Excel =TDIST (Value, df, 2) f. Where df = Combined Sample Size – 2; and 2 is the default for a Two-Tailed Test [Standard] g. We will always use the two-tailed test h. Use the table in the book to find the degrees of freedomi. Use the .05 columni. Essentially, you are comparing the sample means of groups A & Bj. If group 1 scores lower than group 2 it’s negative k. If group 2 scores lower than group 1 it’s positivel. The denominator is the expected variability m. Ideally you want the numerator to be larger thanthe denominator n. You want a large ratio for there to be statistical significance o. A test question could be: i. You have this kind of design, which significance test will you use?p. In this class we will only use the 2 tail test and .05 and 2.5 levels (from chart in book) as rule ofthumbi. When you don’t have a lot of cases your numbers are going to get higher and higher ii. In the example we would reject the nulliii. If t is negative, the critical value is also