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# ~st08 independent measures.ppt - PowerPoint PPT Presentation

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)

• 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 ~

• Select 2 independent samples

• are they from same population?

• Experiment

• select 2 samples

• are the samples the same? ~

• Do not expect to be exactly equal

• sampling error

• How big a difference to reject H0 ? ~

• 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

• Same basic structure as single sample

• Independent samples

[df = n1 + n2 - 2]

• Since m1 - m2 = 0

[df = n1 + n2 - 2]

• *Standard error of difference between 2 sample means

• must calculate s2p first ~

• Average of 2 sample variances

• weighted average if n1n2

• if n1 =n2

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) ~

• 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

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.