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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

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
• matched-subjects (2 related groups)
• within subjects design ~
Independent Measures Hypothesis Test
• Select 2 independent samples
• are they from same population?
• Experiment
• select 2 samples
• are the samples the same? ~
Experimental Outcomes
• Do not expect to be exactly equal
• sampling error
• How big a difference to reject H0 ? ~
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~~

Sample statistic:

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

[df = n1 + n2 - 2]

The Test Statistic
• Since m1 - m2 = 0

[df = n1 + n2 - 2]

Estimated Standard Error
• *Standard error of difference between 2 sample means
• must calculate s2p first ~
Pooled Variance (s2p)
• Average of 2 sample variances
• weighted average if n1n2
• if n1 =n2
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
• 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: 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: 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: n1 = n2
• compute s2p
Example: n1 = n2
• compute test statistic
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: n1¹n2
• Unequal sample sizes
• weight each variance
• bigger n ---> more weight
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: 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: 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: n1¹n2
• compute s2pooled
• compute
• compute test statistic

[df = n1 + n2 - 2]

Example: n1¹n2

4. Interpret

Is tobsbeyond tCV?

If yes, Reject H0.