Playing with statistics part 4

In the last part I did analysis of the test using standard score. Now I am going to analyze re-test. Here are the test score for both test and re-test.

		TEST			RE-TEST
		January 14th, 2012.			February 25th, 2012.
Player		v30-15IFT	Z-Score		v30-15IFT	Z-Score
1		19,5	-0,89		20	-1,44
2		19	-1,57		20	-1,44
3		19,5	-0,89		20,5	-0,78
4		20,5	0,45		21	-0,11
5		19,5	-0,89		21,5	0,56
6		20	-0,22		21	-0,11
7		21	1,12		22	1,22
8		21,5	1,79		22	1,22
9		21	1,12		22,5	1,89
10		19,5	-0,89		20,5	-0,78
11		19,5	-0,89		21	-0,11
12		19,5	-0,89		20,5	-0,78
13		20,5	0,45		21	-0,11
14		20	-0,22		21,5	0,56
15		21,5	1,79		22,5	1,89
16		20	-0,22		20,5	-0,78
17		21	1,12		21	-0,11
18		20	-0,22		20,5	-0,78
Mean		20,17	0,00		21,08	0,00
SD		0,75	1,00		0,75	1,00
Min		19,00	-1,57		20,00	-1,44
Max		21,50	1,79		22,50	1,89

Here is the histogram of the two tests. 

Now, there are two methods to calculate change (or improvement) between test and re-test IMHO. One is absolute where one just does the (re-test)-(test) (e.g. 21km/h – 19.5km/h, which is 1.5km/h) or relative which is this difference divided by the test [(re-test)-(test)]/(test) and that could be expressed as percentage (e.g. (21km/h – 19.5 km/h)/19.5, which is 7.69%. Honestly I don’t know which one is better, so I will utilize both. In the next table there is absolute change and relative change and their z-scores. 

We see that the team improved for 4,58% on average (relative change) or for 0,92 km/h on average (absolute change). 

The next thing I did is to create correlation table between these 4 data sets (test, re-test, absolute change, relative change). 

r	Test	Re-test	Absolute	Relative
Test	1
Re-test	0,80	1
Absolute	-0,31	0,33	1
Relative	-0,37	0,27	0,997	1

At the moment I don’t know how to measure significance and/or Student T test to test hypothesis, so I will only use Pearson’s correlation coefficient. (Someone please correct me if the thing I just said is plain gibberish)  

As we can see test and re-test have strong correlation (0,8) as well as relative and absolute change (0,997). We can also see the negative correlation between test and relative and absolute change (-0,31 and -0,37) which basically means that someone with higher test result will tend to show lower change. This is  a common occurrence with almost all qualities – the more advanced you are the less (and harder) you improve over time. The correlation in this case is moderate (-0,37). 

Here is the scatter of test and relative scores with the trend line.  

 

What is also interesting to do is to calculate the Z-score of the changes, which I did in the table. Using this we can identify outliers – those who are non-responders and those who are maybe on some form of AAS. Kidding aside, this is a useful tool.

 

From the graph above we can see that athlete number 5 improved for 10,26% with Z-score of 2,33. In this example he should be red flagged. This doesn’t mean anything, but rather necessities for  more analysis. Maybe he did not push on the first test. Maybe there is an error in measurement. Maybe he took Ephedrine. Same with the guy number 17. He didn’t improve at all. He should be red flagged as well. Maybe he did not push in the re-test. Maybe he is non responder. Maybe the training was not enough for him (undertrained) or even too much (under-recovered), so he didn’t show any improvement. Basically, we don’t know thus he is a suspect for further analysis.

If you are more interested about responders and non-responder make sure to check this article and this one, and make sure to check mentioned papers within them (like Vollard et al., and  Timmons et al.).

Going back to my four quadrant analysis – here is how the data looks with these athletes:

 

To be honest I got this idea WHILE I was writing this blog posts. This is why I actually like writing and reflecting – I got more ideas or they somehow emerge along the way. Anyway, I think that this idea of quadrants is very interesting. I can red-flag players and I can create different workouts based on their trainability and level of the certain tested quality. We can also identify potential talents, or non-responders. This might be interesting (especially if it could be applied to skills as well, like on the ball skills and decision making in the game) to identify strengths~weaknesses of the players and put them at certain playing positions (if they are non-responders) or modify training to get them more fit for different positions suited to coach style of play. IMHO it is interesting tool. 

For example in the quadrant analysis above athletes 9  (higher initial score, higher responsiveness) and 1 (lower initial score, lower responsiveness) would probably demand different approach to training. It is beyond the scope of this article to go into how to utilize this quadrant analysis. It is also beyond my current knowledge as well – I am just starting to experiment with it. 

That is for now folks. In the next installment I will cover how to do analysis for more frequent tests like sRPE, HRV and others we use for monitoring (this deals with comparing players baseline and his variability to himself rather than team average and variability). Stay tuned…

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Playing with statistics part 3

After a general rant in part 1 and part 2 I am about to start actually doing some stats.

Ok, the first 30-15IFT test we did was in January and here are the scores.

		TEST
		January 14th, 2012.
Player		v30-15IFT	Z-Score
1		19,5	-0,89
2		19	-1,57
3		19,5	-0,89
4		20,5	0,45
5		19,5	-0,89
6		20	-0,22
7		21	1,12
8		21,5	1,79
9		21	1,12
10		19,5	-0,89
11		19,5	-0,89
12		19,5	-0,89
13		20,5	0,45
14		20	-0,22
15		21,5	1,79
16		20	-0,22
17		21	1,12
18		20	-0,22
Mean		20,17	0,00
SD		0,75	1,00
Min		19,00	-1,57
Max		21,50	1,79

As you can see from the table I have calculated Mean and Standard Deviation. Z-score (or standard score) for each athlete is the number that shows how many standard deviations players score is above/below mean value. Having 0 in z-score is equal to mean value of the group. Standard score is great because it take variability of the group scores into account, yet again this might present a problem since some outliers can skew the score by shifting the distribution. This skewness stuff can be calculated too and it deals with normal distribution. Again I am not an expert on this. Anyway, here are the histogram and scatter gram of the scores. 

Standard score is great for comparing the athletes and creating the rankings. Here is the graph of Z-scores of the player.

 

Now it is easier to identify outliers or guys who are above/below 1SD or 2SD or whatever (which one to choose is beyond my statistic knowledge at the moment). This might guide training prescriptions for certain athletes. For example guys with Z-Score below -1 can/should do more conditioning volume (and less intensive due their lower v30-15 score which I use to determine running intensity in the intervals). After some time we can see how they respond to training (this will be covered later) and identify responders vs. non-responders and thus give some feedback to planning/programming process and individualization of training loads in general. 

Basically we can group those players in four major groups: 

Low initial score, low training response	Low initial score, high training response
High initial score, low training response	High initial score, high training response

Based on this we can judge on talent of certain players regarding certain quality. But we still lack one parameter that it is hard to measure and that is the ceiling, but this is beyond this article. 

It would be interesting to see the distribution of the athletes in these 4 quadrants over time. Again this might help with the training prescription and individualization within team sport.

If we create z-scores for more than one physical quality (like sprint time, broad jump, % of body fat, etc) we can create spider graph for each player. Here is an example of spider chart from Marco Cardinale’s blog.

The spider graph can be based on Z-score if we want to compare the player to the team average, or it could be based on absolute values if we want to compare it to a certain model of player or certain test standards (make sure to check BioForce by Joel Jamieson). Again, this can guide us with training prescription and individualization.

Another interesting graph could be equalizer. I got this idea from Marco’s blog.

 

To summarize. In this part I covered some basic descriptive statistics of static score (one test). In the next installment I will cover re-test and the statistical analysis of the change and will probably create a 4 quadrant’s graph. Until then check the links posted. Stay tuned….

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