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Independent-Measures Hypothesis Testing Unit 8 Ch 10: 1-5, 7, 9, 11, 13, 15, 19 (pp. 282-286) Comparing 2 sets of data 2 general research strategies data sets come from 2 separate groups independent samples between groups design 2 sets of data from 1 group dependent or related samples

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Independent-Measures Hypothesis Testing

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Independent measures hypothesis testing l.jpg

Independent-Measures Hypothesis Testing

Unit 8

Ch 10: 1-5, 7, 9, 11, 13, 15, 19 (pp. 282-286)


Comparing 2 sets of data l.jpg

Comparing 2 sets of data

  • 2 general research strategies

  • data sets come from 2 separate groups

    • independent samples

    • between groups design

  • 2 sets of data from 1 group

    • dependent or related samples

      • matched-subjects (2 related groups)

    • within subjects design ~


Independent measures hypothesis test l.jpg

Independent Measures Hypothesis Test

  • Select 2 independent samples

    • are they from same population?

  • Experiment

    • select 2 samples

    • 1 receives treatment

    • are the samples the same? ~


Experimental outcomes l.jpg

Experimental Outcomes

  • Do not expect to be exactly equal

    • sampling error

  • How big a difference to reject H0 ? ~


Hypotheses independent measures l.jpg

Hypotheses: Independent Measures

  • Nondirectional

    • H0: m1 - m2 = 0 H1: m1 - m2 0

    • or H0: m1 = m2 H1: m1m2

  • Directional (depends on prediction )

    • H0: m1 - m2 < 0H1: m1 - m2 > 0

    • or H0: m1<m2H1: m1 > m2

  • no value specified for either

    • Group 1 scores = Group 2 scores~~


T test independent samples l.jpg

  • Sample statistic:

t test: Independent Samples

  • Same basic structure as single sample

  • Independent samples

[df = n1 + n2 - 2]


The test statistic l.jpg

The Test Statistic

  • Since m1 - m2 = 0

[df = n1 + n2 - 2]


Estimated standard error l.jpg

Estimated Standard Error

  • *Standard error of difference between 2 sample means

  • must calculate s2p first ~


Pooled variance s 2 p l.jpg

Pooled Variance (s2p)

  • Average of 2 sample variances

    • weighted average if n1n2

  • if n1 =n2


The test statistic assumptions l.jpg

The Test Statistic: Assumptions

1. Samples are independent

2. Samples come from normal populations

3. Assume equal variance s21 = s22

  • does not require s21 = s22

  • homogeneity of variance

  • t test is robust

    • violation of assumptions

    • Little effect on P(rejecting H0) ~


  • Example independent samples l.jpg

    Example: Independent Samples

    • Is exam performance affected by how much sleep you get the night before a test?

    • Dependent variable?

    • independent variable?

      • Grp 1: 4 hrs sleep (n = 6)

      • Grp 2: 8 hrs sleep (n = 6) ~


    Example n 1 n 2 l.jpg

    Example: n1 = n2

    1. State Hypotheses

    H0: m1 - m2 = 0 orH0: m1= m2 H1: m1 - m2 ¹ 0 or H1: m1 ¹m2

    2. Set criterion for rejecting H0:

    nondirectional

    a = .05

    df = (n1 + n2 - 2)

    = (6 + 6 - 2) = 10

    tCV.05 =


    Example n 1 n 213 l.jpg

    Example: n1 = n2

    3. select sample, compute statistics

    do experiment

    • mean exam scores for each group

      • Group 1: M1 = 15 ; s1 = 4

      • Group 2: M2 = 19; s2 = 3

    • compute

      • s2p

      • s M1-M2

      • tobs~


    Example n 1 n 214 l.jpg

    Example: n1 = n2

    • compute s2p


    Example n 1 n 215 l.jpg

    Example: n1 = n2

    • compute


    Example n 1 n 216 l.jpg

    Example: n1 = n2

    • compute test statistic


    Example n 1 n 217 l.jpg

    Example: n1 = n2

    4. Decision?

    • Is tobs in critical region?

    • No, fail to reject H0

  • If directional test or change level of significance

    • change critical value of t (tcv)

    • just like other tests ~


  • Pooled variance n 1 n 2 l.jpg

    Pooled Variance: n1¹n2

    • Unequal sample sizes

      • weight each variance

      • bigger n ---> more weight


    Example n 1 n 219 l.jpg

    Example: n1¹n2

    Supplementary Material

    • What effect does the amount of sleep the night before an exam have on exam performance?

    • Dependent variable

    • independent variable

      • Grp 1: 4 hrs sleep (n = 6)

      • Grp 1: 8 hrs sleep (n = 7) ~


    Example n 1 n 220 l.jpg

    Example: n1¹n2

    1. State Hypotheses

    H0:m1 = m2 or m1 - m2 = 0

    H1:m1¹ m2 or m1 - m2 ¹ 0

    2. Set criterion for rejecting H0:

    nondirectional

    a = .05

    df = (n1 + n2 - 2)

    = (6 + 7 - 2) = 11

    tCV = + 2.201 ~


    Example n 1 n 221 l.jpg

    Example: n1¹n2

    3. select sample, compute statistics

    do experiment

    mean exam scores for each group

    • Group 1: M1 = 14 ; s1= 3

    • Group 2: M2 = 19; s2= 2

  • compute

    • s2pooled

    • sM1- M2

    • tobs~


  • Example n 1 n 222 l.jpg

    Example: n1¹n2

    • compute s2pooled

    • compute

    • compute test statistic

    [df = n1 + n2 - 2]


    Example n 1 n 223 l.jpg

    Example: n1¹n2

    4. Interpret

    Is tobsbeyond tCV?

    If yes, Reject H0.


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