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One way to test the hypothesis that magnets reduce pain is to test
the null hypothesis that there is no difference in post-treatment ratings
of pain. If this null hypothesis can be rejected, then it can be concluded
that there is an effect of treatments, i.e. a difference in ratings
between those treated with active magnets and those treated with placebo
magnets. An independent-groups t-test can be used for this. This test
makes three assumptions:
- The populations are each normally distributed.
- The variances in the populations are equal.
- Each observation is sampled randomly and is therefore independent
of each other observation.
The histograms in the section on descriptive
statistics indicate clearly that the distributions are not normal. Moreover,
the active magnet group ratings were more variable (sd= 3.14) then were
the ratings of the placebo group (sd = 1.86). An F test of the difference
in variances can be computed by dividing the variance of the group with
the larger variance by the variance of the group with the smaller variance.
Since it was not known a priori which condition would have the
larger variance, the resulting probability value should be multiplied
by 2. The variances are significantly different.
The F statistic for this test is:
2.86
1.69
0.35
The "Analysis
Lab" can be used to test the consequences of these assumption violations
by simulation. An investigation shows that the test that the probability
of a Type I error is actually
lower than 0.05 when the 0.05 level is used. This means that a significant
difference can be used to reject the null
hypothesis even with the assumption violation.
If a true null hypothesis is rejected less than 0.05 of the time then
the significance test is
accurate
conservative
Below are the results of a t-test done in SPSS (slightly modified for
clarity). SPSS reports both the t-test corrected for inequality of variances
(known as the Welch t-test) and not corrected for inequality of variances.
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t
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df
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Sig.
(2-tailed)
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Mean Diff
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95% Confidence Interval
of the Mean Difference
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Lower
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Upper
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Equal variances assumed
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-5.264
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48
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< .001
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-4.049
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-5.596
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-2.503
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Welch test
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-5.695
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46.42
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< .001
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-4.049
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-5.480
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-2.618
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What is the uncorrected t-value for the t-test on post-treatment scores?
-5.70
-5.26
-5.48
-5.6
Where would you look to find out if the corrected t value is significant?
Under t
Under Mean Difference
Under Significance
Under df
Can the null hypothesis that the treatment had no effect be rejected?
Yes
No
Can it be concluded that the treatment lowered pain?
Yes
No
All values in the 95% confidence interval are negative. This means that
the control group was in less pain
the direction of the treatment effect can be inferred
the value of t should be squared
every subject was in pain
Even the low end of the interval (in absolute terms) of 2.5, is a substantial
reduction in pain.
How to do this
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