Variability is the extent to which data points in a statistical distribution or data set diverge from the average, or mean, value as well as the extent to which these data points differ from each ...
The uncontrolled manifold hypothesis offers a statistical method to measure movement variability when performing an action, such as throwing a ball. Importantly, it offers a way to measure whether movement variability is “good” or if variability is “bad”.
In other words, variability in the shoulder joint is counteracted by variability in the elbow and wrist joints, and vice versa. This coupling of joints – which produces (good) variability in movements – allows precision in execution. It also allows the body to adapt to different scenarios, which is also a hallmark of skilful performers.
It is basically a fairly simple concept. When you're talking about variability, you're talking about how scattered or dispersed or spread out the data is. The concept basically has to do with the width of a distribution . In general, other things being equal, the wider the distribution, the more the variability (see Figure 2.5 below).
Why do you need to know about measures of variability? You need to be able to understand how the degree to which data values are spread out in a distribution can be assessed using simple measures to best represent the variability in the data. Why? Because, measures of variability also occur very frequently in the medical research literature. Again, as was the case with measures of central tendency , you cannot understand, let alone critically evaluate medical research studies unless you understand the appropriate usage of such measures.
In the medical research literature some of the most frequently used measures are the standard deviation , interquartile range , and the range (see Figure 2.5).
To get the standard deviation, as you can see in the formula, first you square the distances values are from the mean. Then you sum those squared differences. Then you divide that sum by the number of differences. Finally, you take the square root of that quotient. The reaon that you subtract and square is pretty clear.
The range is simply the difference between the highest and lowest value in the sample (see the figure below). It's a simple measure to compute and to understand. Unfortunately, it is particulary sensitive to extreme scores on the one hand and lacks sensitive to varying values between those extremes. Still you come across it fairly frequently in the literature.
If all data values are the same, then, of course, there is zero variability. The graph of the distribution would have zero width. If all the values lie very close to each other there is little variability and the distribution's graph would be quite narrow.
You should recall that the median is the point in the distribution that 50% of the sample is below and 50% is above. In other words the median is at the 50th percentile. Quartiles can also be defined. The 1st quartile is at the 25th percentile. The 2nd quartile is at the 50th percentile. The 3rd quartile is at the 75th percentile. And, the 4th quartile is at the 100th percentile.
It is basically a fairly simple concept. When you're talking about variability, you're talking about how scattered or dispersed or spread out the data is. The concept basically has to do with the width of a distribution . In general, other things being equal, the wider the distribution, the more the variability (see Figure 2.5 below).
Why do you need to know about measures of variability? You need to be able to understand how the degree to which data values are spread out in a distribution can be assessed using simple measures to best represent the variability in the data. Why? Because, measures of variability also occur very frequently in the medical research literature. Again, as was the case with measures of central tendency , you cannot understand, let alone critically evaluate medical research studies unless you understand the appropriate usage of such measures.
In the medical research literature some of the most frequently used measures are the standard deviation , interquartile range , and the range (see Figure 2.5).
To get the standard deviation, as you can see in the formula, first you square the distances values are from the mean. Then you sum those squared differences. Then you divide that sum by the number of differences. Finally, you take the square root of that quotient. The reaon that you subtract and square is pretty clear.
The range is simply the difference between the highest and lowest value in the sample (see the figure below). It's a simple measure to compute and to understand. Unfortunately, it is particulary sensitive to extreme scores on the one hand and lacks sensitive to varying values between those extremes. Still you come across it fairly frequently in the literature.
If all data values are the same, then, of course, there is zero variability. The graph of the distribution would have zero width. If all the values lie very close to each other there is little variability and the distribution's graph would be quite narrow.
You should recall that the median is the point in the distribution that 50% of the sample is below and 50% is above. In other words the median is at the 50th percentile. Quartiles can also be defined. The 1st quartile is at the 25th percentile. The 2nd quartile is at the 50th percentile. The 3rd quartile is at the 75th percentile. And, the 4th quartile is at the 100th percentile.