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

The t Test for Two Independent Samples Compare method for two gatherings Experimentalâtreatment versus control Existing groupsâmales versus females Notationâsubscripts 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

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

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

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

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

S 2 Pooled Variance Homogeneity of fluctuation Assume two specimens originate from populaces with equivalent Ï 2 âs Two appraisals of Ï 2 â and Weighted normal

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

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

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

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

t (15) = â2.325, p < .05 (exact p = 0.0345)

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

t (28)= â.947, p > .05

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

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

Output Example 1

Effect size Cohenâs d = Example 1 Cohenâs d Example 2 Cohenâs d r 2 or Î· 2 G = fabulous mean

Factors Influencing t âtest and Effect Size Mean distinction M 1 â M 2 Larger contrast, bigger t Larger contrast, bigger r 2 and Cohenâs d

Example 1, subtract 1 from first gathering, add 2 to second gathering M 1 â M 2 increments from â3.257 to â6.257 unaffected t increments from â2.325 to â4.466 r 2 increments from

Magnitude of test differences As test fluctuations expand: t diminishes Cohenâs d and r 2 diminishes SS Explained unaltered, SS Error and SS Total builds, S 2 pooled builds

Sample size