Independent Samples T-Tests - Lab 5

Independent Samples T-Tests So Far... one sample, one population "most research requires comparison of 2+ sets of Sample dana. meaun difference between 2+ Sets of data data sets can come from separate groups of participants Political affiliation for men vs. women grades for students with vs. Students without laptops data can come from same group of participants - depression levels pre- and post-intervemion Independent-Samples t-test: Review in terms of research design.... - type of design called "independent measures or between suraleats" this design that uses a separate group of participants for each treatment condition/population in terms of Statistical analyses. type of analysis used: "independent Samples t-test" evaluate mean difference between two populations/treatment Conditions Independent-Samples t-test: Types of Hypothesis two-tailed test null hypothesis Ho: M= * no difference between means alternative hypothesis *Η.: μ.μ. *difference between means one-tailed tests null hypothesis I alternative hypothesis! null hypothesis 2 Ho: M alternative hypothesis *Ημ. Independent-Samples t-test: Determing Critical Value • 1) determine alpna - usually 0.05 • 2) determine if conducting a one-tailed or two-tailed test "this depends on the set of hypotheses you're making df= (n-1) + (n-1) CRIT For hypothesis testing, use their for either one or two-tailed test when Calculating 95% confidence interval, use twait for two-tailed test Independent-Samples t-test: Basic Full Equation basic structure of the + statistic is the same for independent-Samples and one-sampies t= Sample Statistic-hypothesized population parameter estimated Standard error independent-samples t-test doubles elements of one-sample t-test Standard deviation one-sample t-test: sm where Sm = independent-Samples t-test: simi-m2) where M approximates Sm or Sim-ms): Standard error average distance between a sample Statistic and corresponding population parameter 기 Independent-Samples t-test: Bottom of Equation •Simi-ms) (Standard error of both Samples) = (312 «(M1-1)) + (522xCm2-1)) (n-1)+(n-1) X breaking this equation down..... -Sp' (pooled variance) = ($12+ (NI-1))+(522+(m-1)) (11-1)+(12-1) - df (degrees of treedom) = (ni-1)+(12-1) Independent-Samples t-test: Full Equation independent Sample t-test = m.-m. (5, (n-1)) 45,-1))(1) (3-1)+(-) where m. and m₂ = mean of sample I and Sampie 2, respectively. S. and St: Standard deviation of sample I and Sample 2. respectively and n. sample size for sample I and sample 2, respectively MM n. Independent-Samples t-test: Effect Size Cohen's d = $ where M. and Me are the means for each respective sample [Sp² = (512x(n-1)) + (522x(12-1)) (n-1)+(12-1) Independent-Samples t-test: Confidence Intervals lower end of confidence interval = (Mi-me)-(toRIT XSE) upper end of confidence interval = (m.-M2) + (tCRIT XSE) where... m. and my are the means for each respective Sample CRIT is the positive two-tailed valve, thus teen tass SE (512x(1-1)) + (522x(2-1)) (n-1)+(n-1) (註) Independent-Samples +-test: By Hand you want to know if stats students are more stressed than non-stats Students. you ask to people who are Currently taking Statistics and 10 who are not taking Statistics how stressed they are currently feeling (from 1= no Stress at all to 7= extremely stressed). for Stats Students, M. =3.40 and S.=1.43 For non Stats Students, M: 3.00 and Se=1.15 use alpha =.05 Step 1 State hypothesis Ho Stats Students will be less stressed than or equally stressed to non-Stats Students (Mina) H. Stats Students will be more stressed than non-Stats Students (M) Since there is a direction Stated in the problem ("more" stressed), this will be a one-tailed test Step 2: find the critical value look at 1-tauble: *0:0.05 * one-tailed df=(10-1)+(10-1) = 18 Critical valve (tCRIT): 1.734 Since this is a one-tail test, we have one critical valve. we are Significantly more stressed, So this is a positive critical value predicting that Stats students will be Step 3: compute the test valve find Sp (pooled variance): Sp': (Sit (ni-1))+(strx (2-1)) = (1.43×(10-1)) + (1.15x (10-1)) - 1.68 (11-1)+(12-1) (10-1)+(10-1) plug Sp into full t-test equation: m-ms MI-MI MEM: 3.40 3.00 40.68 58 (1-0)+(1-14) Step 4: make the decision fail to reject the null hypothesis, 0.68 21.73 Step 5: Summarize the results Stats students are not significantly more stressed than non. Stats Students, t(18)=0.66, 07.05 Step 6: Calculate effect size (conenid) •d: Sp 3.40-3.00.51 1.08 this would be a small effect according to Cohen's conventions: Small: 20-49 medium 50-79 large: 80+ Step 7: Calculate 95% confidence interval (mi-ms)-(ta/SE)