Statistics: Test for Difference in Blood Pressure, Time to Complete Exam, Reading Ability, and Cancer Grades

Statistics
Statistics
Student name:
Instructor:
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Statistics
NUMBER ONE
Test for the difference in blood pressure in mmHg taken while standing and while seated. The
appropriate statistical test to be run in this case is a paired sample t-test. This is so because two
datasets was obtained from the same sample. It is a “before and after” kind of data. Since paired
sample t-test is a parametric test there was need to verify the normality of the data we are dealing
with. There are various assumptions to be made before the parametric test is applied. The first
one is normality. The data is tested for normality since the parametric tests as mentioned earlier
are very sensitive to normality. Presence of outliers in a data affects the distribution of the data
hence making the data not to be normal. The outliers also affect the measures of central
tendencies such as the mean. There are various methods to ascertain normality of a distribution.
One of them is the use of histogram. The histogram will be able to present the distribution of the
data graphically so that it can be viewed or looked at and interpretations made with respect to the
shape of the histogram. It can be skewed to the left, right or normally distributed. When it is
skewed to the left, the curve on the histogram appears to have a long tail to the right. When it is
skewed to the right, the curve on the histogram appears to have a long tail to the left. In cases of
normal distribution, the curve appears to be bell-shaped. The other method to assess normality is
by the use of q-q plots. If the data points appear to cluster along the diagonal line on the plot,
then it means the data is normally distributed. If many points appear not to be along the diagonal
line then the data is not normally distributed. The other method to assess normality is by the use
of descriptive statistics under distribution. In this case we check the kurtosis values. For a
normally distributed data, the kurtosis value should be zero or towards zero. A histogram was
thus employed to establish the distribution. The graph is as shown below;
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Statistics
Histogram of standing BP
Figure 1
As can be observed from figure 1, the histograms show that the distribution of the blood pressure
while seated and standing are normally distributed. For a normal distribution, the normal curve
assumes a bell-shape. It is sometimes referred to as a symmetrical curve. It can be skewed to the
left, right or normally distributed. When it is skewed to the left, the curve on the histogram
appears to have a long tail to the right. When it is skewed to the right, the curve on the histogram
appears to have a long tail to the left. In cases of normal distribution, the curve appears to be
bell-shaped. Looking at the skewness in figure 1, it can be confirmed that the data was neither
skewed to the right nor to the left. It also has a low kurtosis since the peak is not high and sharp.
It is therefore confirmed that the paired sample t-test can be used to run the test.
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Statistics
Histogram of seated BP
Figure 2
As can be observed from figure 2, the histograms show that the distribution of the blood pressure
while seated and standing are normally distributed. For a normal distribution, the normal curve
assumes a bell-shape. It is sometimes referred to as a symmetrical curve. It can be skewed to the
left, right or normally distributed. When it is skewed to the left, the curve on the histogram
appears to have a long tail to the right. When it is skewed to the right, the curve on the histogram
appears to have a long tail to the left. In cases of normal distribution, the curve appears to be
bell-shaped. Looking at the skewness in figure 2, it can be confirmed that the data was neither
skewed to the right nor to the left. It also has a low kurtosis since the peak is not high and sharp.
It is therefore confirmed that the paired sample t-test can be used to run the test.
Paired sample t-test
Hypothesis
H0: There is no difference in mean standing BP and seated BP.
H1: There is a significant difference in mean standing BP and seated BP.
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