Introduction
The study intended to compare the academic performance of male students and female students. The variable for measuring performance was the GPA of individual students. Therefore, the study sought to compare the GPA of male students and the GPA of female students. The study used a sample instead of the population. Population refers to all elements that are of interest to the researcher whereas a sample is a sub-section of the population. In this case, there were two populations of interest to the researcher. The two populations were all male students in the school and all female students in the school.A sample was considered appropriate because time and financial constraints. A sample of 25 female students and 25 male students was used. A random sample was selected. Random sampling was used to eliminate researcher’s bias.
Two sample t-test
Data was collected from the sample and descriptive statistics generated. It is noteworthy that the obtained GPA mean was the sample means and not the population mean for the two population. Therefore, two sample t-tests were used to compare the mean of the two populations. The first step of the hypothesis test is formulating the null hypothesis and alternate hypothesis. The null hypothesis preludes that there is no statistical significance in the observations made by the researcher. It negates the researcher’s expectations. The alternate hypothesis opposes the null hypothesis. It preludes that there is statistical significance in the observations made by the researcher. It expresses the researcher’s expectations.
The null hypothesis is that the difference between the mean GPA of male students and the mean GPA of female students is equal to zero. In other words, the mean GPA of male students is the same as the mean GPA of female students.The alternate hypothesis is that the difference between the mean GPA of male students, and the mean GPA of female students is not equal to zero. In other words, the mean GPA of male students is not the same as the mean GPA of female students. It can be represented mathematically as follows;
Ho : µ1 -µ2 = 0
Ho : µ1 -µ2 ≠ 0
The sample mean GPA for male students was 3.06 and the sample mean GPA for female students was 2.936. The difference bewteen the two sample means is 0.124. The study tested the difference between the population means at 95 per cent confidence level. Therefore, the significance level is 0.05. Significance level is obtained by subtracting the confidence level from 1.
Therefore;
Significance level = 1 – 0.95 = 0.05
Significance level is the maximum tolerable probability of type 1 error. Type 1 error is the chance that a researcher rejects the null hypothesis when in in fact it is true. In other words, the resaercher will be 95 per cent certain of the accuracy of the results that will be obtained from study. If the obtained p-value is lower than the significance level we reject the null hypothesis and if the obtained p-value is higher than significance level we fail to reject the null hypothesis. The p-value generated by the two sample t-test was 0.207 which is higher than the significance value of 0.05. Therefore, we fail to reject the null hypothesis that the difference between the population mean GPA of male students and the mean GPA of female students is equal to zero. Therefore, the difference between the population mean GPA of male students and the mean GPA of female students is equal to zero. the In other words, we are 95 per cent certain that the population mean GPA of male students is the same as the population mean GPA of female students.
Mathematically it can be represented as follows;
P-value = 0.207
At 95% confidence level the significance level (α) is 0.05
Decision rule
If p ≤ α :reject H0.
0.207 > α (0.05)
Therefore:
we fail to reject Ho : µ1 -µ2 = 0
and
reject Ho : µ1 -µ2 ≠ 0
Descriptive Statistics
There are several measures of center that are used to describe data including; mean, median and mode. Mode is the value that occurs the most frequent in a given data set. In the study, the mode would be the GPA score that is shared by the highest number of students. Mean is the average value which is obtained by summing up the values of each element and dividing it by the sample size. In the study, it is the sum of the GPA of each student divided by 25 which is the sample size. The mean GPA for male students was 3.06 while the mean GPA for female students was 2.936.Median is the value that occurs at the centre when the values are arranged in a descending of ascending manner. In this case, the GPA for the students is arranged from the lowest to highest or vice-versa. The median would be the 13th value starting from either side since it occurs at the middle. The median GPA for male students was 3.1 while the median GPA for female students was 3
Measures of spread are used to determine how data is spread. There are several measures of spread including; range, standard deviation and variance. Range is the difference between the largest value and the smallest value in the sample. In the study, the range would be the difference between the highest GPA obtained by the student and the lowest GPA obtained by the student. The range for male students’ GPA was 1.6 while that for female students was 1.7. Standard deviation is the square root of the variance. Variance obtained by averaging the sum of the square of the difference between the mean and the each data value.The standard deviation male students’ GPA was 0.33276618 while that of female students was 0.35237291
Median was the most appropriate measure of centre because it is not affected by outliers. Therefore, it gives an accurate picture of the centre of the data. The mean maybe be misleading in case there are extreme values in the data set which are way above or below other data values. Standard deviation is the most appropriate measure of spread because it incorporates all values. In addition, it is not affected by outliers. Range can be misleading if there are outliers since it considers the highest and the lowest values in the data set. Besides, it only considers two values in the entire data set.
Data Outliers
Data outliers are values that are far removed from where most of the data values are concentrated. Data outliers often leads to misleading results since it distorts some measures of center and some measures of spread. The data set for the GPA of male students, and female students have outliers. They are evident from the histogram and plot box.The outliers can be evidenced by histogram bars that are separated from the other histogram bars at the of the graph. The male GPA histogram has one bar at the 2.0 mark which is separated from the other bars. All the bars are bewteen 2.5 and 4.0 apart from one bar which represents the GPA of 1 student because it has a frequency of one that is isolated at 2.0. Similarly, the female GPA histogram has two bars that indicate data outliers; a bar at both extremes at 2.0 mark and past the 3.5 mark. All the bars are bewteen 2.5 and 3.5 apart from two bars which represents the GPA of 1 student on either sides because they have a frequency of one that are isolated at 2.0 past the 3.5 mark. Plot box can also evidence outliers if the whiskers are long. This is because a long whisker indicates that there are data points that fall far away from where most of the data points are concentrated. In this case, both the male GPA plot box and female GPA plot box are long. Therefore, male students GPA and female students GPA have outliers as evidenced by the plot box.
Sample Center
The centre of sample 1 is different from the centre of sample 2. This is clear from the measures of centre. The mean GPA for male students was 3.06 while the mean GPA for female students was 2.936. Therefore, the mean of sample 1 is higher than the mean of sample 2. The median GPA for male students was 3.1 while the median GPA for female students was 3. Therefore, the median of sample 1 is higher than the median of sample 2. However, when we consider the plot box we can conclude that there is the centre for sample 1 is not different from the centre of sample 2 because they overlap.
Conclusion
The study compared the academic performance of male students and female students. The variable for measuring performance was the GPA of individual students. The populations of interest were the males students in the school and female students in the school. A sample of 25 students from each population was used. The samples were selected randomly. Two sample t-tests were used to determine wether the mean of the two populations. The study revealed that Therefore, the difference between the population mean GPA of male students and the mean GPA of female students is equal to zero. the In other words, we are 95 per cent certain that the population mean GPA of male students is the same as the population mean GPA of female students. However, the measures of center reveal that the sample means of the 2 samples were different. Descriptive statistics obtained used mean and median to measure center of the data. It used standard deviation and range to describe the spread of data for the two samples. The data sets contained outliers. This was evident from analysis of the plot box graphs and histogram graphs. The histogram contained bars that were seperated from the other bars at the extremes of the graphs. The plot diagrams contained long whiskers.
