1 General Purpose
Because biological processes are full
of variations, statistical tests give no certainties, only chances.
Particularly, the chance that a prior hypothesis is true. What
hypothesis? Often, a nullhypothesis, which means no difference in
your data from a zero effect. A zero effect indicates that a
factor, like an intervention or medical treatment does not have any
effect. The one sample t-test is adequate for assessment.
2 Schematic Overview of Type of Data File
3 Primary Scientific Question
Is the mean outcome value significantly
different from the value zero.
4 Data Example
The reduction of mean blood pressure
after treatment is measured in a sample of patients. We wish to
know whether the mean reduction is significantly larger than zero.
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Outcome
-
3
-
4
-
−1
-
3
-
2
-
−2
-
4
-
3
-
−1
-
2
-
outcome = decrease of mean blood pressure after treatment (mm Hg)
5 Analysis: One-Sample T-Test
The data file is in
extras.springer.com, and is entitled “chapter1onesamplecontinuous”.
Open it in SPSS . For analysis the module Compare Means is
required. It consists of the following statistical models:
-
Means,
-
One-Sample T-Test ,
-
Independent-Samples T-Test,
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Paired-Samples T-Test and
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One Way ANOVA
Command:
-
Analyze....Compare Means ....One-Sample T-Test ....Test Variable(s): enter "mean blood pressure reduction"....click OK.
In the output sheets is the underneath
table.
One-sample test
|
Test value = 0
|
||||||
|---|---|---|---|---|---|---|
|
t
|
df
|
Sig. (2-tailed)
|
Mean difference
|
95 % confidence interval of the
difference
|
||
|
Lower
|
Upper
|
|||||
|
VAR00001
|
2,429
|
9
|
,038
|
1,70000
|
,1165
|
3,2835
|
It shows that the t-value equals
2,429, which means that with 10–1 = 9 degrees of freedom a
significant effect is obtained at p = 0,038. The reduction of mean
blood pressure has an average value of 1,7000 mm Hg, and this
average reduction is significantly larger than a reduction of
0,00 mm Hg.
6 Alternative Analysis: One-Sample Wilcoxon Signed Rank Test
If the data do not follow a Gaussian
distribution, this method will be required, but with Gaussian
distributions it may be applied even so.
Command:
-
Analyze....Nonparametric tests....One Sample Nonparametric Test s ....click Fields ....Test Fields: enter "mean blood pressure reduction"....click Settings....click Choose Tests....mark Customize Tests....mark Compare median to hypothesized ....Hypothesized median: type "0,00"....click Run.
The underneath table is in the output
sheet. The median of the mean blood pressure reductions is
significantly different from zero. The treatment is, obviously,
successful. The p-value is very similar to that of the above one
sample t-test .
Hypotheses test summary
7 Conclusion
The significant effects indicate that
the nullhypothesis of no effect can be rejected. The treatment
performs better than no treatment. It may be prudent to use
non-parametric test s , if normality is doubtful or can not be
proven like with small data as those in the current example.
8 Note
The theories of null hypotheses and
frequency distributions are reviewed in Statistics applied to
clinical studies 5th edition, Chaps. 1 and 2, entitled “Hypotheses
data stratification” and “The analysis of efficacy data”, Springer
Heidelberg Germany, 2012, from the same authors.