Analysis of One Quantitative Variable
For this project, you must find some sort of published, existing data. Possible sources include almanacs, magazine, journal articles, textbooks, web resources, athletic teams, newspapers, reference materials, campus organizations, professors with experimental data, electronic data repositories, the sports pages or collect your own data from fellow students, neighbours or friends. The dataset you select must have at least 25 cases. It also must have at least two categorical variables and at least two quantitative variables. Choose or collect a dataset that interests you!
See the description below of what analysis should be included. Use technology to automate calculations Write Your Report Cut and paste all relevant computer output with your analysis. Be sure to include both computer output and your discussion of that output in every case. As you discuss each analysis, be sure to interpret what you are finding in the context of your particular data situation. Include all of the following.
How did you find or collect your data (If you found the data, give a clear reference. If you collected the data, describe clearly the data collection process you used.) What are the cases What are the variables What population do you believe the sample might.generalize to Is the sample data from an experiment or an observational study Include a copy of the dataset.
• Analysis of One Quantitative Variable: For at least one of the quantitative variables, include summary statistics (mean, standard deviation, five number summary) and at least one graphical display. Are there any outliers Is the distribution symmetric, skewed, or some other shape
• Analysis of One Categorical Variable: For at least one of the categorical variables, include a frequency table and a relative frequency table.
• Analysis of One Relationship between Two Categorical Variables: Analyse your own data for a chisquare test for association between the two Categorical Variables. State the hypotheses of the test. Conduct the test, showing all details such as expected counts, contribution of each cell to the chisquare statistic, degrees of freedom used, and the pvalue. State a clear conclusion in context. If the results are significant, which cells contribute the most to the chisquare statistic For these cells, are the observed counts greater than or less than expected Whether or not the results are significant, describe the relationship as if you were writing an article for your campus paper. If the results are significant, can we infer a causal relationship between the variables.
• Analysis of One Relationship between a Categorical Variable and a Quantitative Variable Include a sidebyside histogram and describe it. Does there appear to be an association between the two variables If so, describe it. Also, use some summary statistics to compare the groups.
• Analysis of One Relationship between Two Quantitative Variables: For at least one pair of quantitative variables, include a scatterplot and discuss it.
• Conclusion: Briefly summarize the most interesting features of your data.
Analysis of One Quantitative Variable
This study sought to apply statistical knowledge learnt in class in analyzing real data. I obtained my dataset from the internet, the link to the dataset is given The data contains 60 observations with a total of four variables (two categorical and two numerical/quantitative variables) namely
Variable 
Type 
Prior Sexual Experience 
Categorical 
Dose of Drug 
Categorical 
Sexual Activity Index 
Numerical/Quantitative 
Age of the respondent 
Numerical/Quantitative 
Analysis of One Quantitative Variable
The first analysis done is looking at the summary statistics of one of the quantitative variable. Some of the measures analyzed include, mean, median, minimum, maximum, mode, standard deviation, skewness and kurtosis of the data.
Table 1: Descriptive statistics (Quantitative data): 

Statistic 
Sexual Activity Index 
Nbr. of observations 
60 
Minimum 
9.370 
Maximum 
23.550 
Range 
14.180 
1st Quartile 
12.405 
Median 
15.020 
3rd Quartile 
17.323 
Mean 
15.152 
Variance (n1) 
9.593 
Standard deviation (n1) 
3.097 
Variation coefficient 
0.203 
Skewness (Pearson) 
0.297 
Kurtosis (Pearson) 
0.547 
Lower bound on mean (95%) 
14.352 
Upper bound on mean (95%) 
15.952 
As we can see from the table, the average sexual activity index of the respondents is 15.152 with a median of 15.02. The maximum and minimum sexual activity index are 9.37 and 23.55 respectively. The 95% confidence interval for the sample mean showed that the range is between 14.352 (lower bound on the mean) and 15.952 (upper bound on the mean).
Also measured were the Skewness and Kurtosis; skewness measures the distribution symmetry of the dataset. The skewness and kurtosis values are close to zero implying that the data could have come from a normally distributed dataset.
Table 2 below gives the normality test. Both the KolmogorovSmirnov test and ShapiroWil test showed were insignificant (pvalue > 0.05). We thus fail to reject the null hypothesis and conclude that the data is normally distributed at % level of significance.
Table 2: Tests of Normality 

KolmogorovSmirnov^{a} 
ShapiroWilk 

Statistic 
df 
Sig. 
Statistic 
df 
Sig. 

Sexual Activity Index 
.094 
60 
.200^{*} 
.974 
60 
.226 
*. This is a lower bound of the true significance. 

a. Lilliefors Significance Correction 
Next a histogram of the sexual activity index is presented and as can be seen the data seems to be normally distributed though not perfect as is expected of the bellshaped curve.The above boxplot shows that there is no any outlier in the dataset and that the data seems to be normally distributed.
Analysis of One Categorical Variable
In analyzing one categorical variable the study considered analyzing dose of drug taken by the respondents. There were three dosage namely vehicle, 10 mg ad 15 mg. Table 3 below presents the frequency table for the categorical variable dose of drug. As can be seen in the table, equal number of respondents took the three different dosage, i.e. 33.3% (n = 20) took vehicle, another 33.3% (n = 20) took 10 mg and the remaining 33.3% (n = 20) took 15 mg.
Table 3: Dose of Drug 

Frequency 
Percent 
Valid Percent 
Cumulative Percent 

Valid 
Vehicle 
20 
33.3 
33.3 
33.3 
10 mg 
20 
33.3 
33.3 
66.7 

15 mg 
20 
33.3 
33.3 
100.0 

Total 
60 
100.0 
100.0 
The above can also be visualized in the bar chart presented below;
Analysis of One Relationship between Two Categorical Variables:
In analyzing relationship between two categorical variable, the study considered Prior Sexual Experience and Dose of Drug.
Analysis of One Categorical Variable
The following hypothesis was tested using ChiSquare test of association;
H_{0}: There is no association between Prior Sexual Experience and Dose of Drug.
H_{1}: There is association between Prior Sexual Experience and Dose of Drug.
This was tested at 5% level of significance.
To test the above hypothesis, a Pearson ChiSquared (χ^{2}) test of independence (association) was used.
Table 4: Dose of Drug * Prior Sexual Experience: Cross tabulation 

Prior Sexual Experience: 
Total 

No Sexual Experience 
Prior Sexual Experience 

Dose of Drug 
Vehicle 
Count 
10 
10 
20 
Expected Count 
10.0 
10.0 
20.0 

10 mg 
Count 
10 
10 
20 

Expected Count 
10.0 
10.0 
20.0 

15 mg 
Count 
10 
10 
20 

Expected Count 
10.0 
10.0 
20.0 

Total 
Count 
30 
30 
60 

Expected Count 
30.0 
30.0 
60.0 
As can be seen in the above table (table 4), there is no any difference in terms of prior sexual experience of respondents and the dose of drug. The count and expected counts are equal across all the columns and rows.
ChiSquare Tests 

Value 
df 
Asymp. Sig. (2sided) 

Pearson ChiSquare 
.000^{a} 
2 
1.000 
Likelihood Ratio 
.000 
2 
1.000 
LinearbyLinear Association 
.000 
1 
1.000 
N of Valid Cases 
60 

a. 0 cells (0.0%) have expected count less than 5. The minimum expected count is 10.00. 
A chisquare test of association was performed to determine whether there was association between prior sexual experience of respondents and the dose of drug taken by the respondents. There was no association between prior sexual experience of respondents and the dose of drug taken by the respondents, = 0.000, p > .05. We can conclude that prior sexual experience of the respondent does not significantly influence the dose of drug taken by the respondent.
Analysis of One Relationship between a Categorical Variable and a Quantitative Variable
This section sought to analyze One Relationship between a Categorical Variable and a Quantitative Variable. The relationship we looked at is that between prior sexual experience and sexual activity index. The hypothesis we sought to test is;
H_{0}: The mean sexual activity index for the respondents with prior sexual experience is the same as that of the respondents with no prior sexual experience
H_{1}: The mean sexual activity index for the respondents with prior sexual experience is different from that of the respondents with no prior sexual experience.
This was tested at 5% level of significance.
In testing the hypothesis, an independent ttest was used. This test is usual when comparing the two groups of data sets like in our case.
Table 6: Group Statistics 

Prior Sexual Experience: 
N 
Mean 
Std. Deviation 
Std. Error Mean 

Sexual Activity Index 
No Sexual Experience 
30 
13.8967 
2.66063 
.48576 
Prior Sexual Experience 
30 
16.4067 
3.02956 
.55312 
Table 6 above gives the group statistics. As can be seen, the average sexual activity index for the respondents with prior sexual experience is 16.41 while that of the respondents with no sexual experience is 13.90. Respondents with prior sexual experience have a much higher sexual activity index when compared to the respondents with no prior sexual experience.
Table 7: Independent Samples Test 

Levene's Test for Equality of Variances 
ttest for Equality of Means 

F 
Sig. 
t 
df 
Sig. (2tailed) 
Mean Difference 
Std. Error Difference 
95% Confidence Interval of the Difference 

Lower 
Upper 

Sexual Activity Index 
Equal variances assumed 
.194 
.661 
3.410 
58 
.001 
2.51 
.73614 
3.98 
1.036 
Equal variances not assumed 
3.410 
57.05 
.001 
2.51 
.73614 
3.98 
1.036 
An independent samples ttest was conducted so as to be able to make a comparison in the mean sexual activity index for the respondents with prior sexual experience and that of the respondents with no prior sexual experience. There was a significant difference in the sexual activity index for the respondents with prior sexual experience (M = 16.41, SD = 3.03) and respondents with no prior sexual experience (M = 13.90, SD = 2.66) conditions; t (58) = 3.41, p = 0.001 (< 0.05). These results suggest that prior sexual experience really does have an effect on the sexual activity index. Specifically, our results suggest that respondents with prior sexual experience have higher sexual activity index compared to the respondents with no prior sexual experience.
Analysis of One Relationship between Two Categorical Variables
The boxplots above further attempts to visualize the differences in the sexual activity index based on the prior sexual experience. As can be seen, the mean sexual activity index for those with prior sexual experience is much higher compared to that of the respondents with no prior sexual experience. No outliers were observed in any of the two box plots.
Analysis of One Relationship between Two Quantitative Variables
This section sought to analyze the relationship that exists between two quantitative variables. We considered age of the respondent and the sexual activity index. Pearson correlation test was done to check on the relationship that exists between the two variables based on the coefficient that exists.
Table 8: Correlations 

Sexual Activity Index 
Age of the respondents 

Sexual Activity Index 
Pearson Correlation 
1 
.460^{**} 
N 
60 
60 

Age of the respondents 
Pearson Correlation 
.460^{**} 
1 
Sig. (2tailed) 
.000 

N 
60 
60 

**. Correlation is significant at the 0.01 level (2tailed). 
As can be seen n table 8 above, the Pearson correlation coefficient is 0.460 and the relationship is significant at 5% level of significance (r = 0.460, p < 0.05). The negative coefficient means that there is a negative relationship between the two variables (sexual activity index and age of the respondents). Negative linear relationship means that an increase in the age of the respondent would result to a decrease in the sexual activity of the respondent while a decrease in the age would result to an increase in the sexual activity index.
A negative linear relationship can be observed between the two variables.
Regression model
To further understand how age of the respondent affects the sexual activity index, a regression equation model was constructed.The linear equation model is Where is the constant coefficient while is the coefficient for the independent variable “respondent’s age”.
The model summary table (table 9) presents the value of R, RSquare, adjusted RSquare and the standard error of the estimate. The value of RSquared is 0.211, this basically means that 21.1% of the variation in the sexual activity index (dependent variable) is explained by the independent variable (age of the respondent). This value is quite small, implying that the larger proportion is explained by other variables outside the model.
Table 9: Model Summary 

Model 
R 
R Square 
Adjusted R Square 
Std. Error of the Estimate 
1 
.460^{a} 
.211 
.198 
2.77418 
a. Predictors: (Constant), Age 
The regression model was found to be fit and appropriate in predicting the sexual activity index using the explanatory variable “Age of the respondent” (p < 0.05). see table 10 below.
Table 10: ANOVA^{a} 

Model 
Sum of Squares 
df 

1 
Regression 
119.587 
1 
Residual 
446.373 
58 

Total 
565.960 
59 

a. Dependent Variable: Sexual Activity Index 

b. Predictors: (Constant), Age 
Looking at table 11 presented below, we observe that the coefficient of the intercept (constant) is 18.336; this implies that when all other factors are held constant we would expect the sexual activity index to be 18.336. Lastly, the coefficient of the explanatory variable (Age of the respondent) is 0.082; this implies that a unit increase in the age of the respondent would result to a decrease in the sexual activity index of the respondent. Similarly, a unit decrease in the age of the respondent would result to an increase in the sexual activity index of the respondent by 0.082. It is important to note that the respondent was found to be significant in the model (p < 0.05).
Table 11: Coefficients^{a} 

Model 
Unstandardized Coefficients 
Standardized Coefficients 
t 
Sig. 

B 
Std. Error 
Beta 

1 
Age of the respondent 
.082 
.021 
.460 
3.942 
.000 
a. Dependent Variable: Sexual Activity Index 
Conclusion
This study utilized data on prior sexual experience and dose of an androgen. The idea was to present statistical analysis of the dataset. Summary statistics was done to identify the nature of the dataset where it was found that the data comes from a normally distributed dataset with a mean computed to be 15.152.
The maximum and minimum sexual activity index was found to be 9.37 and 23.55 respectively while the 95% confidence interval for the sample mean showed that the range is between 14.352 (lower bound on the mean) and 15.952 (upper bound on the mean). No outliers were observed. In terms relationships, we observed that age is one of the crucial factors that influence the sexual activity behavior. Prior sexual experience was also identified as a factor that influences the sexual activity index. There is however no association between Prior Sexual Experience and Dose of Drug; ChiSquare test was found to be insignificant at 5% level of significance.
References
Cook, L., & Fleming, C. (2007). Analysis of clinic attendances by under14s to sexual health clinics in Gwent. Journal of Family Planning and Reproductive Health Care, 33(1), 2326.
Hubert, M., & Vandervieren , E. (2008). An adjusted boxplot for skewed distributions . Computational Statistics and Data Analysis, 52(12), 5186–5201.
John , A. R. (2006). Mathematical Statistics and Data Analysis.
Plackett, R. L. (2003). Karl Pearson and the ChiSquared Test. International Statistical Review. International Statistical Institute (ISI), 51(1), 59–72.
Smith, A. (2009). Young people's contraception and sexual health: Report of a local needs assessment in Staveley. Journal of Family Planning and Reproductive Health Care, 27(1), 29.
Waegeman, W., & De , B. B. (2008). ROC analysis in ordinal regression learning: Pattern Recognition Letters. 29, 1–9.
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