Running Stats with R | A Full Analysis

-

I have only completed 2 full marathons so far in my life, and many halves. I love running and enjoy all the benefits that come with it. I was just recently cleared by my doctor to start running again after a long wait on some back issues I was experiencing. So I set a goal of getting back on the road in September. The thing is, I spent half of the month down in Brazil and I noticed a difference in my running pace. While Brazil's temperatures are definitely warmer than Canada in September (average of 26.8 C in Brazil versus 17 C in Canada), I also ran through a neighbourhood that has a lot of hills while down South. So, I decided to run some plots (no pun intended) and some statistical tests on the data using R for everything as a way of sharing with you all the cool things you can do for your Six Sigma projects using this incredible statistical program.

Here's a quick look at the dataset:



And here's my research question: "is there a statistically significant difference in my running pace considering the two countries I ran in September?". 

To answer this question, the first thing I wanted to see was a set of different visualizations of the data I have available. To start off, these are the comparative boxplots between the two countries.



I noticed right away that my overall pace in Brazil was slower (more minutes to cover one km), and there's also more variation in my running pace down there.

Moving on, using the same dataset of course, I explored other visualizations such as these comparative density plots:

These violin plots:


And these dot plots:



All of these plots are showing the same slower pace and higher variation in Brazil, each in a slightly different type of visualization. 

Then I decided to create I-MR control charts that would distinguish my running pace in both countries, in a more time-wise continuous manner. Here they are:


 


From these I-MR control charts I noticed a clear "jump" in the central tendency (average time in minutes per km) of my running in Brazil as well as more variation in the data when compared to my running in Canada.

I then performed a 2-sample t test to see if indeed there was a statistically significant difference in my running pace between the two countries. Here's the output from R:


With an extremely low p-value at a 95% confidence level and therefore alpha risk of 5%, I confirmed that there is a statistically significant difference between my running pace in Canada and Brazil (Brazil, from the various previous plots being a slower pace with higher minutes per km measurements).

Finally, and although temperature was not the only factor in my running performance in Brazil, I did look into the relationship between temperature in Celsius and my running pace. Here's the Scatter diagram for it:


And here's the single-predictor linear regression on the data:


Generically speaking, the higher the temperature the slower I was (or said differently, the more minutes I spent to run one km). With a R-square of 0.5704 the relationship is positively moderate and the equation of the best fitted line is Minutes per km = 5.44338 + 0.03949 x Temperature.

The bottom line is: running in Brazil proved to be a lot harder than back home in Canada. I guess with all the Brazilian BBQ, the hills, the higher temperatures, and some nice local brews at the end of the work day I could not have expected anything different.

Comments

Post a Comment

Popular posts from this blog

The Mathematical Significance of Wisdom Over Time

-
Image
My oldest daughter Maya turned 15 yesterday, Aug 21, 2022. I took some time and went to see her at the end of her special day. Amongst other things, we were discussing wisdom, and how we mature over time. Indeed, a natural process for all of us. I was telling Maya that as she grows older, she will learn things. She will learn things in school, and she will learn things in life. Perhaps more in life than in school. Then we caught ourselves discussing a more numerical type of analysis (Maya has always been amazing with numbers). We realized that, when she was at her year zero (of course, this is a figure of speech) I was 30. She was a baby whom only knew how to cry for food while I knew a little bit about life and things. Now she is 15, she knows a little bit more than what she knew when she was 0, or 5, or 10. I'm 45, I also know a little bit more than what I knew when I was 30 (or 0, or 5, or 10). We decided to graph the data, looking into the "wisdom rate of growth" over...
Read more

Binary Logistic Regression for Raccoon Visits to My Backyard

-
Image
It's that time of the year! No, I don't mean April showers bring May flowers, I mean the time when our fellow wild life animals like to visit our backyards often in search for food. Our raccoon friends have become a bit of an annoyance though since they like to sometimes use our deck as latrine. So, I've been collecting some data and have decided to run a binary logistic regression with the help of SigmaXL statistical package to predict the probability that these masked bandits may (or may not) show up. For that, I've been using a safe and natural repellent (I won't broadcast but, it's coyote urine) to help me in discouraging the presence of the poopy animals around our property. The Data Here's a snapshot of the data I've been collecting. As you can see, the outcome (Y: Raccoon Appearance) expected is a binary (dichotomous) variable. I'm trying to figure out if Mr. Coon and friends will show up or not given certain predictors. I've been trackin...
Read more

Gage R & R Full Example with ProcessMA

-
Image
Gage R&R (Repeatability & Reproducibility) is a Measurement Systems Analysis (MSA) technique that uses ANOVA to assess the accuracy of measurements given variation found in parts and operators measuring parts. We start by looking into the setup of the example. The data contains: Three operators: 1, 2, and 3. Three trials: 1, 2, and 3. Ten parts: 1 through 10. This means 90 responses: each operator measures each part 3 times (3 operators x 10 parts x 3 times = 90 responses). Here's a snapshot of the dataset (first 30 rows): To perform a Gage R&R in ProcessMA, select GageRnR (Crossed) under the option Gage RnR  as shown in the screenshot below. The following fields should be selected accordingly for the study: Study variation: 6 * the standard deviations of each source of variation Hit OK. The first table of results showcases the ANOVA output. Recall from the ANOVA significance tests that we are looking into two or more factors and their interactions; in this example: pa...
Read more