INDEPENDENT T TEST 2
Independent t Test
Within statistics there are multiple resources in which are used to better understand the
data given. Some of
... [Show More] these resources include, histograms, descriptive statistics, Shapiro-Wilk test,
and the Levene test. Each different data collector is used in order to provide statistical data in
different forms in order to see different aspects. Seeing each form in different aspects allows for
more data to be recorded as well as a better outcome from the research. These four resources
help better the statistical data field as they are used to see curves, difference in numbers per two
variables, and much more. This data is useful knowledge as with all these combined it allows for
difference of patterns to be noticed that could point to the research needing to be redone or better
yet the research to be scientifically and mathematically proven. Some variables that are able to
be looked at through these resources are the gpa of students as well as their gender. These two
variables together can show correlations as well as differences when used with the resources
above.
Section 1: Data File Description
The data set that will be looked at over the next few sections are the gpa and gender of a
selected sample group. When it comes to these two variables they can be described as a predictor
variable and an outcome variable. With using gpa and gender, the gpa will be used as the
outcome variable. The gpa which is also known as grade point average will be used on a grading
scale of 4.0. The 4.0 is the highest level of gpa a student can receive. This then leaves the
predictor variable as the gender. According to Warner (2013) “ Predictor variables in regression
may be either quantitative or categorical variables.” (p.615). Meaning because gender cannot be
measured it then falls into the quantitative or categorical variable. This would then conclude that
the data set for gender would be female and male. With both variables described the last
description would be the sample size, which is 105.
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Section 2: Testing Assumptions
When it comes to the independent t test there are three assumptions that are typically taken. The
first assumption per Warner (2013) being that the Y variable will end up being normally
distributed. With that it will show a normal curve rather than a peaked curve. The second
assumption from Warner (2013) would be that the Y scores will end up being homogenous
throughout. This will produce an equal outcome of the variables. Lastly the assumption that will
be made is by looking at the independence of the t test. Warner (2013) states that with the
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independence of the observation the variable should only be appearing once.
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Figure 1.1: Histogram per SPSS of gpa
While looking at the histogram of gpa scores above, there assumptions above all appear to
have been met. The first assumption of normal distribution seems to be met as there are no real
outliers that can be seen. The data also does not seem to be skewed in either direction leaving an
equally tailed curve on the histograms data. Per instruction George and Mallery (2014) the
kurtosis should also be evaluated. “Kurtosis is a measure of the “peakedness” or the “flatness” of
a distribution.” (George and Mallery, 2014, p.114). With this description it can be concluded that
the kurtosis appears to be normal as there is no high peak or a low peak. Below are the
descriptive statistics on the skewness and kurtosis of gpa.
Descriptive Statistics
N Skewness Kurtosis
Statistic Statistic Std. Error Statistic Std. Error
Gpa 105 -.220 .236 -.688 .467
Valid N (listwise) 105
Table 1.1: SPSS output of descriptive statistics for gpa
Table 1.1 shows the descriptive statistics of the gpa data. Within this data it is shown that
the skewness is at -.220, meaning the skew is within ±1. This then helps conclude that the
distribution is in fact a normal distribution. While looking at the kurtosis data collected within
table 1.1, it shows the kurtosis at a -.688. The -.688 also will fall within the ±1 range, which
George and Mallery (2014) state for kurtosis is within the excellent range.
Tests of Normality
Kolmogorov-Smirnova Shapiro-Wilk
Statistic df Sig. Statistic df Sig.
gpa .100 105 .012 .961 105 .004
a. Lilliefors Significance Correction
Table 1.2: Showing Shapiro- Wilk test results for gpa
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When looking at the table 1.2 the p value is determined at .004. With a p value at .004 it is
then significant with p < .05, this then means according to Warner (2013) “An obtained p value
represents a (theoretical) risk of Type I error; researchers want this risk of error to be low, and
usually that means they want p to be less than .05” (p.121). Therefore with the results showing p
<.05 the null hypothesis is rejected. With the sample size of this test being 105 the results could
vary with p <.05. This is because there is now an indication that an error could occur.
Another area to look at when evaluating the data is the Levene test. The visual is inputted
below. The interpretation of the Levene test is p has a value of .758. With the p value being .758
it then shows that p > .05, therefore the null hypothesis will not be rejected. With the null
hypothesis not being rejected per Warner (2013) the homogeneity of variance has not been
violated.
While looking at the data above, the above assumptions are interpreted. When it comes to the
normal distribution figure 1.1 as well as table 1.1 show a normal distribution [Show Less]