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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

Independent-Measures Hypothesis Testing

Unit 8

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

comparing 2 sets of data
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
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
Experimental Outcomes
  • Do not expect to be exactly equal
    • sampling error
  • How big a difference to reject H0 ? ~
hypotheses independent measures
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 < 0 H1: m1 - m2 > 0
    • or H0: m1<m2 H1: m1 > m2
  • no value specified for either
    • Group 1 scores = Group 2 scores~~
t test independent samples

Sample statistic:

t test: Independent Samples
  • Same basic structure as single sample
  • Independent samples

[df = n1 + n2 - 2]

the test statistic
The Test Statistic
  • Since m1 - m2 = 0

[df = n1 + n2 - 2]

estimated standard error
Estimated Standard Error
  • *Standard error of difference between 2 sample means
  • must calculate s2p first ~
pooled variance s 2 p
Pooled Variance (s2p)
  • Average of 2 sample variances
    • weighted average if n1n2
  • if n1 =n2
the test statistic assumptions
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
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
Example: n1 = n2

1. State Hypotheses

H0: m1 - m2 = 0 or H0: 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
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
Example: n1 = n2
  • compute s2p
example n 1 n 216
Example: n1 = n2
  • compute test statistic
example n 1 n 217
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
Pooled Variance: n1¹n2
  • Unequal sample sizes
    • weight each variance
    • bigger n ---> more weight
example n 1 n 219
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
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
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
Example: n1¹n2
  • compute s2pooled
  • compute
  • compute test statistic

[df = n1 + n2 - 2]

example n 1 n 223
Example: n1¹n2

4. Interpret

Is tobsbeyond tCV?

If yes, Reject H0.