Elaborate Concepts On The T-test Using Calculations And Spss (Statistics Project Sample)

Statistical Interpretation
Name
Institution
Exercise 1
A t-test was conducted to test whether there was a significant difference between the baselines and post LDL measurements of 15 participants after a nurse-based intervention. The mean difference between the two measurements was -8.2. The test was significant at t(14)=0.0036. This implies there was a statistically significant difference between the Baseline and Pre LDL values. A non-parametric test, the sign test was also used to determine whether a significant difference between the two measures exists. The probability that the median value was less than 0= (0.0461) was significant at alpha=0.05. Similar results were obtained using the Wilcoxon Signed Rank test where the absolute value of the test statistics was significant at 0.0044<0.005 and the one –sided test significant at 0.0022<0.005. The normal Q-Q plot shows that the data was close to normal since most of the points lie close to the slope line. All the tests give a similar outcome; the nurse-based intervention method improved the LDL cholesterol levels for the patients. However parametric tests are much easier to conduct, do not require a lot of data and can be used on various shapes of data. Non-parametric tests require large sample sizes, for example in the sign test, each of the paired samples should be present. These tests do not depend on the distribution of a sample, and the results tend to be invalid.
Exercise 2
An ACOVA analysis was conducted to determine whether LDL pre was a significant predictor of LDL post. A summary of the model fit shows that 51.68% of the variation was accounted for by the model while the rest was due to chance while the F-value=13.9014 was significant at 0.0025<0.005. A look at the parameter estimates revealed that LDL Pre was a significant predictor of LDL post at 0.0025<0.005. Finally, the normal quartile plot shows the data was normal since most of the values lie on and close to the slope line. The regression equation obtained was:
LDL Post=-74.1888+1.4779489*LDL Pre
* Predict the POST LDL and gain using the average Pre LDL
LDL Post= -74.1888+1.4779489*138.067
LDL Post= 129.8672
Gain= -8.1998; -8.2 in exercise 1
* Predictions for pre LDL of 130 and 145
LDL Post= -74.1888+1.4779489*130
=117.9446
Gain= -12.0554; -15 in exercise 1
LDL Post= -74.1888+1.4779489*145
=140.1138
Gain = - 4.8862; 0 in exercise 1
The results from exercise 2 seem more accurate since they are not rounded off to whole numbers. Furthermore, while getting the average between the Pre and Post LDL values, data accuracy may be lost due to truncation errors and rounding off. The ANCOVA method seems more appropriate and accurate.
Exercise 3

POST


<130

>=130

Totals

Pre

<130

2

8

10


>=130

13

7

20


Totals

15

15

30

Estimated proportion with LDL less than 130 pre and post;
Expected frequency=230*100=6.6667%
McNemar’s statistic
χ2=(8-13)28+13=1.1905
The p-value using excel;
CHISQ.DIST.RT(1.1905,1)= 0.275229
The McNemar’s test is used to determine whether there is an association between paired dichotomous variables. In this case, the p-value 0.275229<0.05. This implies the proportions less than 130 pre is not equal to the proportion less than 130 Post. We conclude that there was no association between the case and control variables.
Exercise 4
Data Analysis Using SPSS
A 95% confidence interval was used for all the tests
T-Test
Paired Samples Statistics


Mean

N

Std. Deviation

Std. Error Mean

Pair 1

LDL PRE

138.07

15

6.041

1.560


LDL POST

129.87

15

12.420

3.207

Paired Samples Correlations


N

Correlation

Sig.

Pair 1

LDL PRE & LDL POST

15

.719

.003

Paired Samples Test


Paired Differences

t

df

Sig. (2-tailed)


Mean

Std. Deviation

Std. Error Mean

95% Confidence Interval of the Difference








Lower

Upper




Pair 1

LDL PRE - LDL POST

8.200

9.104

2.351

3.158

13.242

3.488

14

.004

SIGN TEST
NPar Tests
Wilcoxon Signed Ranks Test
Ranks


N

Mean Rank

Sum of Ranks

LDL POST - LDL PRE

Negative Ranks

10a

8.40

84.00


Positive Ranks

3b

2.33

7.00


Ties

2c




Total

15



a. LDL POST < LDL PRE

b. LDL POST > LDL PRE