Testing Difference of Averages in Two Independent Samples (Non-Parametric)-II | BIO733_Topic139
Watch on YouTubeVideo summary
When comparing the averages of two independent groups, a critical prerequisite is often the assumption of normality; however, if this assumption does not hold, researchers must turn to non-parametric tests to assess differences between the groups. This module focuses on performing the Mann-Whitney Wilcoxon test using SPSS, illustrated through an experiment investigating the effects of prolonged inhalation of cadmium oxide. In this study, hemoglobin levels were measured in 15 laboratory animals exposed to cadmium oxide and compared against 10 similar unexposed control animals. Since the normality assumption was deemed invalid for this dataset, the standard independent samples t-test could not be used, necessitating the application of the Mann-Whitney test to determine if significant differences existed between the two groups.
To conduct the hypothesis test, the researcher first establishes a null hypothesis stating that the medians of the two groups are equal ($M_X = M_Y$) against an alternative hypothesis that they are not equal ($M_X \neq M_Y$), utilizing a two-sided test with a significance level ($\alpha$) of 0.05. Data entry in SPSS requires organizing the information into two specific variables: one quantitative variable for the hemoglobin levels and one nominal grouping variable to distinguish between exposed animals (coded as 1) and unexposed animals (coded as 2). By navigating to the Analyze menu, selecting Nonparametric Tests, and choosing Legacy Dialogues followed by Two Independent Samples, the user designates hemoglobin levels as the test variable and the study group codes as the grouping factor. While options for calculating descriptive statistics or performing exact tests exist, the procedure here focuses on the asymptotic Mann-Whitney U test.
Upon running the analysis, SPSS generates output that includes mean ranks for both groups, the sum of ranks, and key test statistics such as the Mann-Whitney U and Wilcoxon W values. The most critical result is the asymptotically significant two-tailed P-value, which in this case was found to be 0.006. According to the decision rule, if the P-value is less than or equal to the significance level of 0.05, the null hypothesis is rejected. Since 0.006 is significantly lower than 0.05, the null hypothesis that the medians are equal is rejected, indicating a statistically significant difference between the groups.
The rejection of the null hypothesis leads to the conclusion that the median hemoglobin levels in the exposed group differ from those in the unexposed group. Consequently, it can be inferred that exposure to cadmium oxide has a significant impact on the hemoglobin levels of the laboratory animals. This example demonstrates how non-parametric methods provide a robust alternative for analyzing data that does not meet normality assumptions, allowing researchers to draw valid conclusions about differences between independent groups even when traditional parametric tests are not applicable.
Read the full video transcript
When we are
making a comparison of
the averages in the two groups,
one important assumption is the testing
for normality.
If the normality assumption does not
holds true,
we end up performing the non-parametric
test
to make comparison between the averages
of the two groups.
In this module,
we will learn how to perform
this two-group
independent samples
non-parametric test, that is,
Mann-Whitney Wilcoxon test using SPSS.
Let's take an example
where a researcher designed an
experiment to assess the effects of
prolonged inhalation of cadmium oxide.
Where they looked at 15 laboratory
animals served
as experimental subjects, while 10
similar animals served as controls.
So, the variable of interest was
hemoglobin level following the
experiment, and we wish to know if
there's any difference between the
hemoglobin levels in two groups.
Our data is given.
To to to perform the test of hypothesis,
we assume
that the normality assumption does not
holds true.
We assume
that both the groups are independent of
each other.
Hence, we can confidently perform
Mann-Whitney test procedure.
So, the Mann-Whitney test, the first
step is to state the null hypothesis and
alternative hypothesis.
Since our goal is to see if there's any
significant difference
or not,
it's going to be a two-sided test, where
null hypothesis states that MX is equals
to MY against alternative that MX is not
equals to MY.
We'll keep usual level of significance
alpha to be 0.05.
Test statistics for the Mann-Whitney
test is T.
We'll perform the calculations using
SPSS.
Our decision rule states that we reject
the null hypothesis if P value is less
than equals to alpha and the usual
conclusion.
Since we are testing
the hypothesis whether the median in the
two groups is are equal or not.
To test this hypothesis, it's very
important that we learn how to enter the
data.
Since these are two independent groups,
for two independent groups test,
our
variable of interest, that is hemoglobin
level, will be entered as one variable
and the other variable will be grouping
indicator.
So,
here we have hemoglobin
as a whole hemoglobin levels
for of grams for 25 laboratory animals,
which is a quantitative variable.
The other group
variable is actually a grouping variable
that
represents the study group,
where one represents the exposed animals
and two represents the unexposed
animals.
It's again treated as a nominal measure.
Using this information, we've entered
the data in and to perform the test for
the significance, we'll go to analyze
and non-parametric.
Since we already assume
that the assumption for normality does
not holds true,
we cannot perform two groups independent
sample T test.
Since we are unable to perform two
groups independent sample T test because
of the normality assumption,
we are performing this non-parametric
test, that is Mann-Whitney Wilcoxon
test.
And this can be performed by going
through analyze non-parametric test
and legacy dialogues and two independent
samples. Our test variable
is our variable of interest.
And here it is hemoglobin levels.
So, it goes as the test variable.
Our grouping variable will be our study
groups
where one represents
the exposed animals and two represents
unexposed animals.
So, we're using this code
to define the grouping. One can
calculate the descriptive statistics and
quartiles. And moreover, one can also
perform Monte Carlo or exact test over
here. But here we are right now using
asymptotic only. We want to test
Mann-Whitney U test.
We press okay.
It gives us the output. The The output
for the Mann-Whitney test is
pretty simple.
We're firstly, in the ranks,
it gives us the mean rank
for the exposed animal and mean rank for
the unexposed animal.
The sum of the ranks is 145
and then 180.
And
here is, in the test statistics, we have
Mann-Whitney
U and Wilcoxon W statistics. So, these
are the results for the test statistics.
And then there is this approximate test
that is Z.
And here are the P values. We will use
asymptotically significant two-tailed P
value.
That is 0.006.
So, in this test, the P value is 0.006,
which is
lesser than our stated
level of significance alpha, that is
0.05.
And our decision rule states that we
reject the null hypothesis if the P
value is less than equals to alpha.
And right here, the P value
that is 0.006 is less than 0.00 0.05,
hence we
may reject the null hypothesis.
And if we are rejecting the null
hypothesis, we can say
that
we can say that the median of exposed
animal is not equals to the median of
unexposed animals. Hence, we can
conclude
that there is a significant difference
in the hemoglobin levels of exposed
and unexposed animals. And since in this
case, we are looking at the exposure to
the cadmium oxide,
hence
the cadmium cadmium oxide has a
significant impact
on the hemoglobin levels
of animals.