CHAPT 7 Hypothesis Testing Applied to Means Part B t-Static

t-Static 3. Related Samples t-test or Repeated Measures Experiment AKA Within Subject Designs or Paired Sample t-Test.

t-Static Repeated Measure Experiment, Related/Paired Sample t-test or,Within Subject Experiment Design

Repeated Measure Experiment, or Related/Paired Sample t-test Within Subject Experiment Design A single sample of individuals is measured more than once on the same dependent variable. The same subjects are used in all of the treatment conditions.

t-Statistics: Null Hypothesis If the Population mean or µ is unknown the statistic of choice will be t-Statistic Repeated Measure Experiment, or Related/Paired Sample t-test If non-directional/two tailed test, then Step. 1 H0 : µD = 0 H1 : µD ≠ 0

t-Statistics: Null Hypothesis If directional or one tailed tests Step. 1 H0 : µD ≤ 0 H1 : µD > 0 or, Step. 1 H0 : µD ≥ 0 H1 : µD < 0

Step 2 None-directional Hypothesis Test

Calculations for t-test Step 3: Computations/ Calculations or Collect Data and Compute Sample Statistics t= MD-μD SMD SMD = S/√n or SMD= MD-μD t MD= t.SMD + μD μD = MD – SMD . t SMD= estimated standard error of the mean difference

Calculations for t-test Step 3: Computations/ Calculations or Collect Data and Compute Sample Statistics df = n-1 Difference Score D= X2-X1 MD = ΣD n

FYI Variability SS, Standard Deviations and Variances X σ² = ss/N Pop 1 σ = √ss/N 2 4 s = √ss/df 5 s² = ss/n-1 or ss/df Sample SS=Σx²-(Σx)²/n new SS  SS=ΣD²-(ΣD)²/n SS=Σ( x-μ)² Sum of Squared Deviation from Mean

Cohn’s d=Effect Size for t Use S instead of σ for t-test d = MD/s S= MD/d MD= d . S

Percentage of Variance Accounted for by the Treatment (similar to Cohen’s d) Also known as ω² Omega Squared

Problem 1 Research indicates that the color red increases men’s attraction to women (Elliot & Niesta, 2008). In the original study, men were shown women’s photographs presented on either white or red background. Photographs presented on red were rated significantly more attractive than the same photographs mounted on white.

In a similar study, a researcher prepares a set of 30 women’s photographs, with 15 mounted on a white background and 15 mounted on red. One picture is identified as the test photograph, and appears twice in the set, once on white and once on red. Problem 1

Problem 1 Each male participant looks through the entire set of photographs and rated the attractiveness of each woman on a 12-point scale. The data in the next slide summarizes the responses for a sample of n=9 men. Set the level of significance at α=.01 for two tailed. Do the data indicate the color red increases men’s attraction to women ?

Problem 1 MD = For SPSS enter X2 values first then X1 Participants White background X1 Red Background X2 D=X2-X1 D² A 6 9 +3 9 B 8 9 +1 1 C 7 10 +3 9 D 7 11 +4 16 E 8 11 +3 9 F 6 9 +3 9 G 5 11 +6 36 H 10 11 +1 1 I 8 11 +3 9 ΣD =27 ΣD²=99 MD = For SPSS enter X2 values first then X1

Null Hypothesis Step. 1 H0 : µD = 0 H1 : µD ≠ 0 For Non-Directional or two tailed tests Step. 1 H0 : µD = 0 H1 : µD ≠ 0

Problem 2 One technique to help people deal with phobia is to have them counteract the feared objects by using imagination to move themselves to a place of safety. In an experiment test of this technique, patients sit in front of a screen and are instructed to relax. Then they are shown a slide of the feared object for example, a picture of a spider, (arachnophobia). The patient signals the researcher as soon as feelings of anxiety begin to arise, and the researcher records the amount of time that the patient was able to endure looking at the slide.

Problem 2 The patient then spends two minutes imagining a “safe scene” such as a tropical beach (next slide) before the slide is presented again. If patients can tolerate the feared object longer after the imagination exercise, it is viewed as a reduction in the phobia. The data in next slide summarize the items recorded from a sample of n=7 patients. Do the data indicate the imagination technique effectively alters phobia? Set the level of significance at α=.05 for one tailed test.

Problem2 Participant Before X1 After X2 Imagination D=X2-X1 D² A 15 24 +9 81 B 10 23 +13 169 C 7 11 +4 16 D 18 25 +7 49 E 5 14 +9 81 F 9 14 +5 25 G 12 21 +9 81 ΣD =56 ΣD²=502 MD =

Null Hypothesis For Directional or one tailed tests Step. 1 H0 : µD ≤ 0 (The amount of time is not increased.) H1 : µD > 0 (The amount of time is increased.)

df = n-1 MD = ΣD n SS=ΣD²-[(ΣD)²/n] s² = ss/n-1 or ss/df Difference Score D= X2-X1 MD = ΣD n SS=ΣD²-[(ΣD)²/n] s² = ss/n-1 or ss/df

Calculations for t-test Step 3: Computations/ Calculations or Collect Data and Compute Sample Statistics t= MD-μD SMD SMD = S/√n or SMD= MD-μD t SMD= estimated standard error of the mean difference