This article discusses a heart rate t-test analysis using MS Excel Analysis ToolPak add-in. This is based on real data obtained in a personally applied aerobics training program.
Do you know that there is a powerful statistical software residing in the common spreadsheet software that you use everyday or most of the time? If you have installed Microsoft Excel in your computer, chances are, you have not activated a very useful add-in: the Data Analysis ToolPak.
See how MS Excel’s data analysis function was used in analyzing real data on the effect of aerobics on the author’s heart rate.
Statistical Analysis Function of MS Excel
Many students, and even teachers or professors, are not aware that there is a powerful statistical software at their disposal in their everyday interaction with Microsoft Excel. In order to make use of this nifty tool that the not-so-discerning fail to discover, you will need to install it as an Add-in to your existing MS Excel installation. Make sure you have placed your original MS Office DVD in your DVD drive when you do the next steps.
You can activate the Data Analysis ToolPak by following the procedure below (this could vary between versions of MS Excel; this one’s for MS Office 2007):
- Open MS Excel,
- Click on the Office Button (that round thing at the uppermost left of the spreadsheet),
- Look for the Excel Options menu at the bottom right of the box and click it,
- Choose Add-ins at the left menu,
- Click on the line Analysis ToolPak,
- Choose Excel Add-in in the Manage field below left, then hit Go, and
- Check the Analysis ToolPak box then click Ok.
You should now see the Data Analysis function at the extreme right of your Data menu in your spreadsheet. You are now ready to use it.
Using the Data Analysis ToolPak to Analyze Heart Rate Data
The aim of this statistical analysis is to test whether there’s really a significant difference in my heart rate eight months ago and last week. This is because in my earlier post titled How to Slow Down Your Heart Rate Through Aerobics, I mentioned that my heart rate is getting slower through time because of aerobics training. But I used the graphical method to plot a trend line. I did not test whether there is a significant difference in my heart rate or not, from the time I started measuring my heart rate compared to the last six weeks’ data.
Now, I would like to answer the question is: “Is there a significant difference in heart rate eight months ago and last six week’s record?”
Student’s t-test will be used to analyze 18 readings taken eight months ago and the last six weeks as data for comparison. I measured my heart rate upon waking up (that ensures I am rested) during each of my three-times a week aerobics sessions.
Why 18? According to Dr. Cooper, the training effect accorded by aerobics could be achieved within six weeks, so I thought my heart rate within six weeks should not change significantly. So that’s six weeks times three equals 18 readings.
Eight months would be a sufficient time to effect a change in my heart rate since I started aerobic running eight months ago. And the trend line in the graph I previously presented shows that my heart rate slows down through time.
These are the assumptions of this t-test analysis and the reason for choosing the sample size.
The Importance of an F-test
Before applying the t-test, the first test you should do to avoid a spurious or false conclusion is to test whether the two groups of data have a different variance. Does one group of data vary more than the other? If they do, then you should not use the t-test. Nonparametric methods such as Mann-Whitney U test should be used instead.
How do you make sure that this may not be the case, that is, that one group of data varies more than the other? The common test to use is an F-test. If no significant difference is detected, then you can go ahead with the t-test.
Here’s an output of the F-test using the Analysis ToolPak of MS Excel:
Notice that the p-value for the test is 0.36 [from P(F<=f) one-tail]. This means that one group of data does not vary more than the other.
How do you know that the difference in variance in the two groups of data using the F-test analysis is not significant? Just look at the p-value of the data analysis output and see whether it is equal to or below 0.05. If it is 0.06 or higher, then the difference in variance is not significant and t-test could now be used.
This result signals me to go on with the t-test analysis. Notice that the mean heart rate during the last six weeks (i.e., 50.28) is lower than that obtained six months ago (i.e. 53.78). Is this really significant?
Result of the t-test
I had run a consistent 30-points per week last August and September 2013 but now I accumulate at least a 50-point week for the last six weeks. This means that I almost doubled my capacity to run. And I should have a significantly lower heart rate than before. In fact, I felt that I can run more than my usual 4 miles and I did run more than 6 miles once a week for the last six weeks.
Below is the output of the t-test analysis using the Analysis ToolPak of MS Excel:
The data shows that there is a significant difference between my heart rate eight months ago and the last three weeks. Why? That’s because the p-value is lower than 0.05 [i.e., P(T<=t) two-tail = 0.0073]. There’s a remote possibility that there is no difference in heart rate 8 months ago and the last six weeks.
I ignored the other p-value because it is one-tail. I just tested whether there is a significant difference or not. But because the p-value in one-tail is also significant, I can confidently say that indeed I have obtained sufficient evidence that aerobics training had slowed down my heart rate, from 54 to 50. Four beats in eight months? That’s amazing. I wonder what will be the lowest heart rate I could achieve with constant training.
This analysis is only true for my case as I used my set of data; but it is possible that the same results could be obtained for a greater number of people.
© 2014 April 28 P. A. Regoniel