Independent t-tests

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Independent t-tests
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• Uses a sampling distribution of differences
  between means

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The test statistic for independent samples t-tests

• Recall the general form of the test statistic for
  t-tests
• Recall the test statistic for the single sample
  t-test

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Horizontal axis value sample mean
Distribution mean mean of distribution of
sample means
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Distribution SD SD of distribution of sample
means
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The test statistic for independent samples t-tests

• So how about the independent samples t-test?

Horizontal axis value ?
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The test statistic for independent samples t-tests

• So how about the independent samples t-test?

Horizontal axis value difference between 2
sample means
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The test statistic for independent samples t-tests

• So how about the independent samples t-test?

Distribution mean ?
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The test statistic for independent samples t-tests

• So how about the independent samples t-test?

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SD of sampling distribution ?
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The test statistic for independent samples t-tests

• So how about the independent samples t-test?

SD of sampling distribution ?
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the SD of the distribution of differences between
2 sample means
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On the SD of the distribution

• Look at the SD (SEM) in more detail

Where
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What affects significance?

• Mean difference
• With larger observed difference between two
  sample means, it is less likely that the observed
  difference in sample means is attributable to
  random sampling error
• Sample size
• With larger samples, it is less likely that the
  observed difference in sample means is
  attributable to random sampling error
• Sample SD
• With reduced variability among the cases in each
  sample, it is less likely that the observed
  difference in sample means is attributable to
  random sampling error
• See applet
• http//physics.ubishops.ca/phy101/lectures/Beaver/
  twoSampleTTest.html

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d of f for the test statistic

• The d of f changes from the one-sample case
• comparing two independent means

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becomes
If the 2 groups are of equal size
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Reporting t-test in text
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Descriptive statistics for the time to exhaustion
for the two diet groups are presented in Table 1
and graphically in Figure 1. A t-test for
independent samples indicated that the 44.2 (?
2.9) minute time to exhaustion for the CHO group
was significantly longer than the 38.9 (? 3.5)
minutes for the regular diet group (t18 - 3.68,
p ? 0.05). This represents a 1.1 increase in
time to exhaustion with the CHO supplementation
diet.
Should also consider whether the difference is
meaningful see effect sizes, later
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Reporting t-test in table

• Descriptives of time to exhaustion (in minutes)
  for the 2 diets.

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Group n Mean SD
Reg Diet 10 38.9 3.54
CHO sup 10 44.2 2.86
Note indicates significant difference, p ? 0.05
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Reporting t-test graphically
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Figure 1. Mean time to exhaustion with different
diets.
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Reporting t-test graphically
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Figure 1. Mean time to exhaustion with different
diets.
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Summary/Assumptions of theindependent t-test

• Use when the assumption of no correlation between
  the samples is valid
• Dont test for itjust examine whether the
  assumption is fair
• Use when the two samples have similar variation
  (SD)
• Test for in output (see next few slides)

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t-tests in SPSS

• First note the data format one continuous
  variable (in this case, age)

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t-tests in SPSS

• Second, run the procedure

drag the test variable over
and specify µ
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t-tests in SPSS

• Third, check the output

N, Mean, SD, SEM
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significance (if a .05, then lt .05 is
significant)
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df n-1 19
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independent-tests in SPSS

• First, check the data

One grouping variable
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One test variable
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independent-tests in SPSS

• Second, run the procedure

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independent-tests in SPSS

• Second, run the procedure

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1. slide variables over
2. click define groups
3. define groups
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independent-tests in SPSS

• Third, examine the output

N, Mean, SD, SEM
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test for equal variances (gt .05 is good)
significance (if a .05, then lt .05 is
significant)
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