Psy 230 Ch100 (1)

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    Ways to collect two sets of data: Independent Measures (Between-Subjects) design:

    Group 1 VS. Group 2

    Repeated Measures (Within-subjects) design:

    Time 1 VS. Time 2

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    Notation for Independent

    Samples Design Null Hypothesis (H0)

    No difference between group means

    H0: 12 = 0

    Alternative Hypothesis (H1)

    There is a difference between groups

    H1:12 0

    Group 1 Group 2

    n1 n2

    M1 M2

    1 2

    SS1 SS2

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    Formulas for Independent-

    Measures Hypothesis Test Single sample t-test:

    t= M

    sM

    Two sample (independent measures) t-test:

    t= (M1M2) (12)S(M1M2)

    t= (M1M2)S(M1M2)

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    Calculating Estimated Standard

    Error Single sample t-test:

    sM

    = s2

    n

    Two sample (independent measures) t-test:

    S(M1M2) = s2 s2 n1 n2

    1 2+

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    Pooled Variance

    Used when sample sizes are different

    Single sample t-test:

    s2 = SS

    df

    Two sample (independent measures) t-test:

    s2 = SS1 + SS2df1 + df2

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    An example of the reason for

    pooled variance. Equal Sample Sizes:

    Sample 1: n = 6, SS= 50

    Sample 2: n = 6, SS= 30

    Unequal Sample Sizes:

    Sample 1: n = 3, SS= 20 Sample 2: n = 9, SS= 48

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    Computing t-statistic for

    Independent Samples

    t= (M1M

    2) (

    1

    2)

    S(M1M2)

    t= data hypothesis

    error

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    Lets practice.

    We are testing the effects of orange juice on

    mathematical ability. Determine whether

    there is a significant difference between the

    groups in average math score.

    OJ Group No OJ Group

    n=10 n=10M=26 M=18

    SS=200 SS=160

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    Step 1: State Hypotheses and

    select alpha levelHypotheses:

    H0:12 = 0 H1:12 0

    = .05

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    Step 2: Set Criteria for a Decision

    (Critical Region)a) Find the degrees of freedom

    b) Use the t Distribution Table (p. 531) tofind the t-values that define the critical

    region

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    Step 3: Collect Data and

    Compute Sample Statisticsa) Find the pooled variance for the 2 samples

    b) Used the pooled variance to compute the

    standard error

    c) Compute the tstatistic

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    Step 4: Make a Decision Accept or reject the null hypothesis??

    -2.101 2.101

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    Measuring Effect Size for

    Independent Measuresr2 = variability accounted for

    total variability

    r2 = ___t2___

    t2 + df

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    Writing it up...Give the facts:

    The group who drank orange juice scored higher on

    the math test (M= 26, SD = 4.71) than the group thatdid not drink orange juice (M= 26, SD = 4.71).

    State what the facts mean in terms of significance:

    This difference was significant, t(18) = 4.00, < .05,

    r2 = .47.

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    More practice with a one-tailed test Psychologists predict that girls have higher verbal

    scores at age 5 than boys. What value of t would

    be necessary to conclude that girls scoresignificantly higher using a one-tailed test with

    = .01?

    Girls Boys

    n=5 n=5

    M=83 M=71

    SS=200 SS=120

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    Think about sample variance How does sample variance influence ourt-

    statistics and treatment effects (dorr2)

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    Independent tTest Assumptions Scores in the two groups are independent

    (not related)

    Sample data are normally distributed

    Variances of the two groups are about equal

    (homogenous)

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    One more practiceWe would like to know if people respond more

    quickly to red lights or green lights. Determine

    whether there is a significant difference betweenthe groups in reaction time (in milliseconds):

    Green Light Reaction Time: 432, 408, 388, 370,

    523, 354, 603, 445Red Light Reaction Time: 452, 429, 391, 368, 546,

    352, 592, 478, 679, 483

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    Chapter 10 Homework

    Submit the following problems from the end

    ofChapter 10:

    1, 3, 6, 10, 14, 16, 18, 20, 24

    SHOW YOUR WORK!!!!

    Due atthe beginningof class tomorrow!

    PSY 230 - ROH

    LFIN

    G