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Independent Samples Ttest

• With previous tests, we were interested in comparing a single sample with a population • With most research, you do not have knowledge about the population -- you don’t know the population mean and standard deviation

INDEPENDENT SAMPLES T-TEST: • Hypothesis testing procedure that uses separate samples for each treatment condition (between subjects design) • Use this test when the population mean and standard deviation are unknown, and 2 separate groups are being compared Example: Do males and females differ in terms of their exam scores? • Take a sample of males and a separate sample of females and apply the hypothesis testing steps to determine if there is a ...view middle of the document...

1 (s=2.57, n=19), and the mean test score for males is 26.7 (s=3.63, n=20) Step 1: State the hypotheses H0: µ1-µ2=0 (µ1=µ2) H1: µ1-µ2≠0 (µ1 ≠µ2) • This is a two-tailed test (no direction is predicted)

Step 2: Set the criterion • α=? • df= n1+n2-2=? • Critical value for the t-test ? Step 3: Collect sample data, calculate x

and s

From the example we know the mean test score for females is 27.1 (s=2.57, n=19), and the mean test score for males is 26.7 (s=3.63, n=20)

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Step 4: Compute the t-statistic

t=

(x1 − x2 )− (µ1 − µ 2 )

s x1 − x2

where

s x1 − x2 =

s2 pooled n1

+

s2 pooled n2

• Calculate the estimated standard error of the difference

s

2 pooled

(df1 ) s 21 + (df 2 ) s 2 2 = df1 + df 2

(18)2.57 2 + (19)3.63 2 18 + 19

s2 pooled =

=

=

(18)6.61 + (19)13.18 37

118.98 + 250.36 37

=

369.34 = 9.98 37

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• Compute the standard error (continued)

s x1 − x2 =

s x1 − x2 =

s2 pooled n1

+

s2 pooled n2

9.98 9.98 = .525 + .499 = 1.01 + 19 20

•Calculate the t statistic

t=

t=

(x1 − x2 )− (µ1 − µ 2 )

s x1 − x2

*This always defaults to 0

(27.1 − 26.7) .4 = = .396 1.01 1.01

Step 5: Make a decision about the hypotheses • The critical value for a two-tailed t-test with df=37 (approx. 40) and α=.05 is 2.021 • Will we reject or fail to reject the null hypothesis?

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Assumptions for the Independent t-Test: • Independence: Observations within each sample must be independent (they don’t influence each other) • Normal Distribution: The scores in each population must be normally distributed • Homogeneity of Variance: The two populations must have equal variances (the degree to which the distributions are spread out is approximately equal)

Repeated Measures T-test

• Uses the same sample of subjects measured on two different occasions (within-subjects design) • Use this when the population mean and standard deviation are unknown and you are comparing the means of a sample of subjects before and after a treatment • We are interested in finding out how much difference exists between subjects’ scores before the treatment and after the treatment

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DIFFERENCE SCORE (or D) • The difference between subjects’ scores before the treatment and after the treatment • It is computed as x2-x1, where x2 is the subjects’ score after the treatment and x1 is the subjects’ score before the treatment • We use the sample of difference scores to estimate the population of difference scores (µD)

Example: Does alcohol affect a person’s ability to drive? A researcher selects a sample of 5 people and sets up an obstacle course.

– Each subject drives the course and the number of cones he or she knocks over is counted. – Next, the researcher has each subject drink a six-pack of beer, then drive the course again, counting the number of cones each subject knocks over.

NOTE: Theory has shown that alcohol decreases motor and cognitive skills

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Step 1: State the hypotheses...

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