ttest

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t-test 3Two related samples

• HED 489 Biostatistics

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• t-test 3 determines whether the mean difference
  between two sets of scores for the same people is
  statistically significant. This is commonly used
  in "pre-test/post-test" studies where you hope to
  change something about a group of people by
  subjecting them to some sort of program. In the
  weight loss program example, you would weigh each
  person before the program started, administer the
  program, and weigh each person again. What you
  input into the bottom part of the t-test formula,
  as you should be able to see from the formula on
  the right, are these "difference" scores. This
  makes t-test 3 very easy to calculate, even if
  by hand.
• So, what t-test 3 does is divide the standard
  deviation of the difference scores into the
  difference between the mean of the groups.

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• In this example  researcher want to see if the
  subjects in the table below have seen a decrease
  in their systolic blood pressure.  Thus, subject
  one had his blood pressure taken at point 'A',
  have had an experimental activity (i.e.,
  medication) and then had their blood pressure
  taken at point 'B'. 
• The null hypothesis for this study is
• H0 There is no difference in blood pressure
  between pre and post testing.
• The alternative hypothesis is
• H1 There is a difference in blood pressure
  between pre and post testing.

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Step 1

• Step 1 is to write the scores down in two
  columns, being sure to match the scores with the
  subject's pre score.

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Formula for t-test 3
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t-test 3 Is the mean of the BP
pre-scoredifference from post-test
score? Step2 D X - Y
In Step 2, you subtract the values in the second
column, labeled "Y," from the value in the
first column, "X." Again, each X and
corresponding Y score much match for the same
pair of people. Or, if you're doing a pre-post
test, the scores have to match for the same
person. Then, you square each value.
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Step 3
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• Square the differences found in Step 2 and then
  sum them. This is "square first, then sum."

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Step 4
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• Step 4 really has three parts first, you sum the
  difference scores. Second, you square that value.
  This is "sum first, then square." Third, you
  divide that squared value by the number of
  scores.

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Step 5
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• Step 5 subtracts the squared sum of the
  difference scores, divided by the number of
  scores, from the sum of the squared difference
  scores. This is subtract Step 4 from Step 3, and
  it completes the numerator under the square root
  sign.

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Step 6
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• Divide the results in Step 5 by N(N-1).
• In this example, that is 107/14(14-1)

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Step 7
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• Obtain the means (averages) from both groups.

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Step 8
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• Subtract mean for Group 2 from mean of Group 1
• 93.50 97.14 -3.64

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Step 9
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• Divide value from Step 8 by value obtained in
  Step 6

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Step 10

• Figure out degrees of freedom (df)
• dfN-1 13
• Find t-table (inside back cover of Kuzma)
• Find t-value of .05 with 13 df
• 2.16
• The t-value obtained is bigger than 2.16, we can
  say that there was a significant increase from
  the pre-test to the post-test

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One more thing
Pull down Tools to get to Data Analysis
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Youll highlight t-test, paired
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In the white/red box, click to highlight your
data make sure you click labelsthen click OK
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Here are the results. Ive highlighted in yellow
the two key parts. Note that Excel reports the
t-value in a negative component (remember we said
at one point you can ignore the negatives). The
program also reports the probability. As you can
see, that probability is well below .05.
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Assignment

• Is the mean systolic blood pressure of 20 men at
  risk for heart disease significantly different
  after a stress-reduction program? Download here