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Hypothesis Tests
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There are five single sample hypothesis tests available in ASP.
You are given the option of calculating the sample statistics for these tests
from variables in a data matrix or of entering the sample statistics directly:
t Test Of Population Mean. The
output generated by this option includes the difference between the sample mean and the
hypothesized population mean along with the value of the t statistic for the null
hypothesis that this difference is equal to zero. The degrees of freedom for this t
statistic are listed along with the probability value and the probability value divided by
two. The standard error of the estimated difference between the sample mean and the
hypothesized population mean is also given.
Test Of Population Proportion. The
output generated by this option includes the difference between the sample proportion and
the hypothesized population proportion along with the value of the Z statistic for the
null hypothesis that this difference is equal to zero. The Probability value and the
probability value divided by two for this statistic are also listed. Finally, the standard
error of the estimated difference between the sample proportion and the hypothesized
population proportion is given.
Sign Test For Median (Single Sample). The
output generated by this option includes the number of successes or failures, the
probability value of this number, and this probability value divided by two.
Runs Test. The output generated by
this option includes the Z statistic for the null hypothesis that the set of runs is
random, the probability value and the probability value over two for this Z statistic, and
the standard error of the number of positive runs.
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There are nine two sample hypothesis test options on the HYPOTHESIS
TESTS menu. You are given the option of calculating the sample
statistics for these tests from variables in a data matrix or of entering the
sample statistics directly:
Difference Of Means Tests. The
output for this test depends on whether the test samples are independent or contain
matched pairs:
For independent samples the output generated includes the
difference between the two sample means along with the value of the Z statistic for the
null hypothesis that the population difference is equal to zero. The probability value and
the probability value divided by two for this statistic are listed, and an estimate of the
standard error of the estimated difference between the two population means is given.
For matched pairs the output generated includes the value of the
t statistic for the null hypothesis that the mean of the differences is equal to zero. The
degrees of freedom for this t statistic are also listed along with its probability value
and its probability value divided by two. The standard error of the estimated mean of the
matched pair differences is given.
Difference Of Proportions Tests. The
output generated by this option includes the difference between the two sample proportions
along with the value of the Z statistic for the null hypothesis that this difference is
equal to zero. The probability value and the probability value divided by two for this
statistic are also listed along with the standard error of the estimated difference
between the two population proportions.
Wilcoxon Rank-Sum Test. The output
generated by this option includes the Z statistic for the null hypothesis that the two
populations are identical, the probability value and the probability value over two for
this statistic, and the standard error of the sum of the ranks.
Mann-Whitney Test. The output
generated by this option includes the Mann-Whitney U statistic for the null hypothesis
that the two populations are identical, the probability value and the probability value
over two for this statistic, and the standard error of the sum of the ranks.
Sign Test (Two Sample). The output
generated by this option includes the probability value of the number of positive values,
given the null hypothesis that the two samples are identical, along with this value
divided by two and the standard error of the estimated number of positive values.
Wilcoxon Signed-Rank Test. The
output generated by this option includes the Z statistic for the null hypothesis that the
two populations are identical, the probability value and the probability value over two
for this statistic, and the standard error of the minimum sum of the negative and positive
signed ranks statistic.
Rank Order Correlation Test. The
output generated by this option depends on the hypothesized population correlation
coefficient:
When the hypothesized population correlation coefficient is not equal to
0, the output generated includes the Fisher r to z transform, the Z statistic for the null
hypothesis that the correlation between the two variables is equal to the hypothesized
population value, the probability value and the probability value over two for this
statistic, and the standard error of the estimated correlation coefficient.
When the hypothesized population correlation coefficient is equal to 0,
the output generated includes the t statistic for the null hypothesis that the correlation
between the two variables is equal to 0, the probability value and the probability value
over two for this statistic, and the standard error of the estimated correlation
coefficient.
Product Moment Correlation Test. The
output generated by this option depends on the hypothesized population correlation
coefficient:
When the hypothesized population correlation coefficient is not equal to
0, the output generated includes the Fisher r to z transform, the Z statistic for the null
hypothesis that the correlation between the two variables is equal to the hypothesized
population value, the probability value and the probability value over two for this
statistic, and the standard error of the estimated correlation coefficient.
When the hypothesized population correlation coefficient is equal to 0,
the output generated includes the t statistic for the null hypothesis that the correlation
between the two variables is equal to 0, the probability value and the probability value
over two for this statistic, and the standard error of the estimated correlation
coefficient.
There are four multiple sample nonparametric test options available in
ASP:
Kruskal-Wallis Test. The output
generated by this option includes the chi square statistic, along with its degrees of
freedom and probability value, for the null hypothesis that the samples come from the same
population.
Friedman Test. The output for this
option consists of the chi square statistic, along with its degrees of freedom and
probability value, for the null hypothesis that there are no differences in effects of the
N treatments on the experimental groups.
Cochran’s Q Test. The output
generated by this option includes the Cochran’s Q statistic, along with its degrees
of freedom and probability value, for the null hypothesis that there are no differences in
the effects of the N treatments on the experimental groups.
Kendall’s Coefficient Of Concordance. The
output generated by this option includes Kendall’s coefficient of concordance
statistic and a chi square statistic, along with its degrees of freedom and probability
value, for the null hypothesis that the rankings are random.
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The output generated by this option includes the chi square statistic for
the null hypothesis that the observed values are generated by the distribution from which
the expected values are generated along with its degrees of freedom and probability value.
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The output from this option includes the Kolmogorov-Smirnov D statistic.
The chi square statistic implied by the Kolmogorov-Smirnov D for the null hypothesis that
the observed and expected values represent two independent samples that are generated from
the same distribution is also given, along with the degrees of freedom for this statistic
and its probability value.
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