What are statistical norms?
introduction
Statistical norms in sport enable individual performance to be compared with other athletes in the same target group. The statistical norms consist of mean values and their scatter information and only apply to a corresponding group.
Statistical norms thus mathematically indicate the average characteristic value.
Group membership
The comparison of average characteristics only makes sense, of course, for test persons who belong to the same group.
Example:
- Average time for 3000 meters male high school graduates.
- Average speed on the anaerobic threshold for footballers in the 1st Bundesliga
- Average result for one Fitness test for 60 year old women
For the corresponding service areas, the data should be sent to representative samples be determined. Statistical norms cannot simply be transferred to every individual and only apply to the individual athlete if they behave in accordance with the norms.
How are statistical norms determined?
Two methods are available for determining statistical norms:
- Determination of the arithmetic mean values
- regression analysis determination
1. Determination of arithmetic mean values
The determination of arithmetic mean values is particularly useful when comparing groups. Average values for individual years in schools provide an overview of whether individual students are better or worse than the average.
Calculation:
The individual values are added up and divided by the number of participants.
The sample should / must be sufficiently large and representative of the population.
Problems with arithmetic mean values:
Arithmetic mean values are unsuitable for the high-performance area, as only a few test subjects can achieve the athletic performance.
2. Regression analysis determination
In the regression analysis determination the data are obtained from the so-called extrapolation of the regression line. It is important that the extrapolation can be allowed.
The data can be read from this straight line.
E.g. The shot put performance is correlated with the bench press performance.
The regression line shows what bench press performance a shot putter should have if it hits the ball 20 meters
Statistical norms and confidence limits
In order to be able to read data from the statistical norms, certain confidence limits are necessary.
The preferred confidence limits are:
- The standard error of estimate
- The hyperbolic confidence limit
- (The standard error of the estimate)
1. Standard error of the regression line
Se = ± s? 1-r2
r = Correlation between (e.g. bench press and shot put) / 0.86
s = Scatter values
The standard error of estimation indicates the range in which the true value is with an error probability of (1% = p <0.01 or 5% p <0.05).
2. Hyperbolic Confidence Limits
= Confidence intervals
The estimates are particularly precise in areas where a lot of data can be collected (in the range of the mean).
The further the measured value deviates from the mean value, the less precise the estimate becomes. (lower and upper performance range).
