#2 Two-Sample (Independent Samples) t-Test TEST summary: x x CONDITION ONE Scores CONDITION TWO Scores = ()2 = X = N= 2= = ()2 = 2= X = N= (X1-X2)-(1-2) tobt = Sx1-Sx2 ? _ (x)2 - N-1 N Spooled= (n-1)s+(n1)S2 (n-1)+(n2-1) 5x1 -Sx2 = (S2 pooled) ((1+12) (S-x)(-tcrit) + (1 - X) - S-x2)(+tcrit) + ( - X2) d= X1-X2 pooled 2 rb= pb= (tobt) (tobt)+df STEP ONE STEP TWO HYPOTHESIS Two Sample Independent t-TEST Create either the two-tailed or one-tailed Ha and H. (Experimental and statistical hypotheses) Two-tailed Ha: - 0 Ho: 1- = 0 One-tailed Ha: 1- > 0 Ho: 1-2 0 SAMPLING DISTRIBUTION Set up the sampling t-distribution and do not assume a normal distribution until df=120 Select x Locate region of rejection Determine critical value --use df=(n-1) + (n2-1) to find tcrit in the t-table COMPUTE OBTAINED VALUE (n-1)s+(n1)S pooled (n-1)+(n2-1) STEP Compute tobt THREE tobt (1-2)-(1-2) = Sx1 x2 s= -(x) N N-1 Sx1 -5x2 = (S2 pooled) (+1) STEP FOUR INTERPRET AND REPORT RESULTS Compare tobt to tcrit. If tobt is beyond tcrit the results are significant. If tobt is not beyond tcrit the results are not significant If significant compute confidence interval - (Sx2)(tcrit) + (X - ) 2 Sx2)(+tcrit) + (X - X) Significant results t(df) tobt, p < .05 Using Cohen's d d = X1-X2 Report the results Non-significant results = t(df) tobt, p> .05 Describe the Effect Size Using Proportion of Variance Accounted for pooled Values of Interpretation d of Effect Size r2 (tobt) pb d=.2 Small (tobt)+df d=.5 Medium d=.8 Large Socioeconomic status and Distress during Covid-19 A survey was conducted to measure socioeconomic difference in distress (anxiety and depression) among college students during the height of the Covid-19 lockdown period. Socioeconomic status is measured by annual household income (either >$100,000 or $100,000 CONDITION ONE x 100 x Lower Income tobt = (X1-X2)-(1-2) Sx1-5x2 (6.76-34-07)-0 = 3.03 x - (X) N-1 N = 5, = -17.31 3.03 5276-477.94 489.06 81225 5276- 17 17-1 = 16 E 30.57 16 5.75 17809-16252,07 1556.93 = 119.76 13 13 S. 2 S pooled = (1-1)s+(n1)s (n1-1)+(n2-1) = 17809-227529 14-1 14 (17-1) 30.57 + (14-1) 119.76 1-7-1)/30.57 (17-1)+(14-1) 2045-88 Sx1-Sx2 = (S pooled) (12) = (16) 30.57 + (13) 119.76 16+13 489+1556.88 29 70.55 29 10.55 (tatty) = 70.55 (.06+.07) = 70.55 (.13)=9.17 = = (S-2)(terit) + (1 - ) 1-2 Sx2)(+tcrit) + (X1 - X2) (3.03) (-2.045)+(1676-3407) -6.196 + -17.31 -23.506 3.03 (2.045) + (16.76-34.07) 6.196 + -17.31 - 11.11 d = X1-X2 -17.31 -17.31 17.31 = pooled 70.55 = -2.06 = 70.558.39 (tobt) (tobt)+df (-5.71)2 = (-5.71)2+29 = 3.03 32.604 32.604 = = .53 32.604729 61.6041