Tech Library: A Model for Tomorrow
Appendix AA: Statistical Analysis of Survey Results
From the responses obtained from the second survey, several basic statistics were calculated on the amount of time that students currently spend at Tech Library and on the amount of time they would spend at Tech Library if it were renovated.
The statistics for the amount students currently spend at Tech Library are as follow:
Descriptive Statistics: Initial |
||||||
Variable Initial
|
N | Mean | Median | TrMean | StDev | SE Mean |
132 |
2.269 |
1.500 |
2.123 |
2.283 |
0.199 |
|
| VariableInitial | Minimum |
Maximum |
Q1 |
Q3 |
||
| 0.000 | 7.000 | 0.000 | 3.500 | |||
These values show a sample of size 132, with a mean of 2.269 hours per week and a standard deviation of 2.283.
The statistics for the amount of time per week that students imagined they would spend at Tech Library after the proposed renovation are listed below:
Descriptive
Statistics: After_Renovation
|
||||||
Variable After_Renovation |
N |
Mean |
Median |
TrMean |
StDev |
SE Mean |
132 |
3.990 |
3.500 |
4.048 |
2.197 |
0.191 |
|
Variable After_Renovation |
Minimum |
Maximum |
Q1 |
Q3 |
||
0.000 |
7.000 |
1.750 |
5.500 |
|||
These values show another sample of 132, with a new mean of 3.990 hours per week and a slightly lower standard deviation of 2.197.
Now the important question is whether the difference between these two means is statically significant or not. If the difference is significant, then it can be stated with confidence that the average student usage of Tech Library per week will increase after the renovation. If the difference is not significant, there are two possibilities, either the sample size was not large enough or there is really not a significant increase in the number of hours students would spend at Tech Library.
There are two ways of conducting this analysis. The first way is to run a two-sample t-test. In that case, a basic or null hypothesis is formulated stating that the true difference between the means of these two populations equals zero (“Initial” mean – “After_Renovation” mean = 0). The alternative hypothesis states that the difference between the “Initial” mean and the “After_Renovation” mean is not zero (“Initial” mean – “After_Renovation” mean < 0), because we believe the second mean is higher than the first. The calculations for that analysis follow below:
H0: m1-m2 = D0
H1:
m1-m2 < D0
The t-statistic is calculate with the following equation:
The inputs to the equation are given above with = 2.269, = 3.990, = 0, = 2.283, = 2.197, and = = 132. This gives us a t-value of -6.24 for the samples considered. The t-distribution value ta,n1+n2-2, with a = .05 and n1 = n2 = 132 is -1.645 for the population distribution. Since -6.24 < -1.645, the null hypothesis can be rejected and it can be drawn that the difference between the means of these two samples is statistically significant. This means that the survey results confirm that people will increase their usage of the library if the renovation is completed.
Another way of conducting this analysis is to perform a confidence interval test:
This equation has the same inputs as the t-test, and gives an upper bound on what the true difference between the two means is. Running this test shows:
-1.266
Since this value is below zero, the confidence interval confirms that the value of the “Initial” mean minus the “After” mean isn’t zero, and is in fact negative (meaning the usage of the library will be higher after the renovation). This data can be confirmed by the printout below.
Two-Sample T-Test and CI: Initial, After_Renovation
Two-sample
T for Initial vs After_Renovation
|
||||||
Variable
|
N
|
Mean
|
StDev
|
SE Mean
|
||
Initial |
132 | 2.27 |
2.28 |
0.20 |
||
| After_Renovation | 132
|
3.99
|
2.20 |
0.19
|
||
Difference = mu Initial - mu After_Renovation
Estimate for difference: -1.721
95% upper bound for difference: -1.266
T-Test of difference = 0 (vs <): T-Value = -6.24 P-Value = 0.000 DF = 261
A final helpful comparison of the two sets of data can be seen by looking at side by side boxplots of their distributions.
This
shows that the mean, median, first quartile, and third quartile
are all significantly higher for the “After Renovation” data.
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