The t Test for Two Autonomous Specimens.


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The t Test for Two Autonomous Examples Analyze method for two gatherings Trial—treatment versus control Existing gatherings—guys versus females Documentation—subscripts demonstrate bunch M 1 , s 1 , n 1 M 2 , s 2 , n 2 Invalid and option speculations
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Slide 1

The t Test for Two Independent Samples Compare method for two gatherings Experimental—treatment versus control Existing groups—males versus females Notation—subscripts show bunch M 1 , s 1 , n 1 M 2 , s 2 , n 2 Null and option theories makes an interpretation of into deciphers into

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Criteria for utilization Dependent variable is quantitative, interim/proportion Independent variable between-subjects Independent variable has two levels t - test Basic structure One specimen

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Two example Difference between test means M 1 - M 2 Population parameter Sampling appropriation of the distinction Difference between M 1 and M 2 drawn from populace

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Standard lapse of the distinction Population change known Sum of Estimate from tests Differences more variable than scores

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Variability of mean contrasts Randomly created arrangement of 1000 means Μ = 50, σ M = 10 Take distinction between sets

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S 2 Pooled Variance Homogeneity of fluctuation Assume two specimens originate from populaces with equivalent σ 2 ’s Two appraisals of σ 2 — and Weighted normal

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df = df 1 + df 2 = (n 1 - 1) + (n 2 - 1) = n 1 + n 2 - 2 t - test

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Hypothesis testing Two-tailed H 0 : µ 1 = µ 2 , µ 1 - µ 2 = 0 H 1 : µ 1 ≠ µ 2 , µ 1 - µ 2 ≠ 0 One-tailed H 0 : µ 1 ≥ µ 2 , µ 1 - µ 2 ≥ 0 H 1 : µ 1 < µ 2 , µ 1 - µ 2 < 0 Determine α Critical estimation of t df = n 1 + n 2 - 2

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Assumptions Random and autonomous examples Normality Homogeneity of fluctuation SPSS—test for correspondence of changes, unequal differences t test t - test is powerful

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H 0 : µ 1 = µ 2 , µ 1 - µ 2 = 0 H 1 : µ 1 ≠ µ 2 , µ 1 - µ 2 ≠ 0 df = n 1 + n 2 - 2 =10 + 7 – 2 = 15  =.05 t (15) = 2.131 Example 1

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t (15) = –2.325, p < .05 (exact p = 0.0345)

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df = n 1 + n 2 - 2 = 15 + 15 – 2 = 28  =.05, t (28) = 2.049 Example 2

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t (28)= –.947, p > .05

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Confidence Interval for the Difference Example 1 - 3.257 - (2.131*1.401) < µ1 - µ 2 < - 3.257 + (2.131*1.401) = - 6.243 < µ1 - µ 2 < - 0.272 Example 2 - 0.867 - (1.701*5.221) < µ1 - µ 2 < - 0.867 + (1.701*5.221) = - 9.748 < µ1 - µ 2 < 8.014 Includes 0 hold H 0

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SPSS Analyze Compare Means Independent-Samples T Test Dependent variable(s)—Test Variable(s) Independent variable—Grouping Variable Define Groups Cut point quality Output Levene’s Test for Equality of Variances t Tests Equal fluctuations expected Equal changes not accepted

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Output Example 1

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Effect size Cohen’s d = Example 1 Cohen’s d Example 2 Cohen’s d r 2 or η 2 G = fabulous mean

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Factors Influencing t –test and Effect Size Mean distinction M 1 – M 2 Larger contrast, bigger t Larger contrast, bigger r 2 and Cohen’s d

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Example 1, subtract 1 from first gathering, add 2 to second gathering M 1 – M 2 increments from –3.257 to –6.257 unaffected t increments from –2.325 to –4.466 r 2 increments from

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Magnitude of test differences As test fluctuations expand: t diminishes Cohen’s d and r 2 diminishes SS Explained unaltered, SS Error and SS Total builds, S 2 pooled builds

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Sample size

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