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# The t Test for Two Autonomous Specimens.

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Description
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
Transcripts
Slide 1

The t Test for Two Independent Samples Compare method for two gatherings Experimentalâtreatment versus control Existing groupsâmales versus females Notationâ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 Î = 50, Ï 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 Ï 2 âs Two appraisals of Ï 2 â 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 : Âµ 1 = Âµ 2 , Âµ 1 - Âµ 2 = 0 H 1 : Âµ 1 â  Âµ 2 , Âµ 1 - Âµ 2 â  0 One-tailed H 0 : Âµ 1 â¥ Âµ 2 , Âµ 1 - Âµ 2 â¥ 0 H 1 : Âµ 1 < Âµ 2 , Âµ 1 - Âµ 2 < 0 Determine Î± Critical estimation of t df = n 1 + n 2 - 2

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

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H 0 : Âµ 1 = Âµ 2 , Âµ 1 - Âµ 2 = 0 H 1 : Âµ 1 â  Âµ 2 , Âµ 1 - Âµ 2 â  0 df = n 1 + n 2 - 2 =10 + 7 â 2 = 15 ï¡ =.05 t (15) = 2.131 Example 1

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t (15) = â2.325, p < .05 (exact p = 0.0345)

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df = n 1 + n 2 - 2 = 15 + 15 â 2 = 28 ï¡ =.05, t (28) = 2.049 Example 2

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t (28)= â.947, p > .05

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Confidence Interval for the Difference Example 1 - 3.257 - (2.131*1.401) < Âµ1 - Âµ 2 < - 3.257 + (2.131*1.401) = - 6.243 < Âµ1 - Âµ 2 < - 0.272 Example 2 - 0.867 - (1.701*5.221) < Âµ1 - Âµ 2 < - 0.867 + (1.701*5.221) = - 9.748 < Âµ1 - Âµ 2 < 8.014 Includes 0 hold H 0

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SPSS Analyze Compare Means Independent-Samples T Test Dependent variable(s)âTest Variable(s) Independent variableâGrouping Variable Define Groups Cut point quality Output Leveneâ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 Cohenâs d = Example 1 Cohenâs d Example 2 Cohenâs d r 2 or Î· 2 G = fabulous mean

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Factors Influencing t âtest and Effect Size Mean distinction M 1 â M 2 Larger contrast, bigger t Larger contrast, bigger r 2 and Cohenâs d

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

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Magnitude of test differences As test fluctuations expand: t diminishes Cohenâ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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