Some measurements can be difficult to work with and understand. In these cases, it can be useful to transform them to another function. Linear and logarithm transformations are two possible ways of accomplishing this. The transformation does not change the information, but rather displays it in a way that makes it easier to analyse and interpret the results.
Linear functions have limited uses. However, they are useful in changing the range of the data to one that it easier to work with and understand. One instance would be if you were looking at the number of short-handed goals scored by a team during one season. Suppose a team scores 238 goals in a season with 12 of them being short-handed goals. Dividing 238 by 12 gives us the proportion of 0.0504. Small numbers like this are trickier to work with, making accurate analysis more difficult. However, if a linear relation is used to transform the data to a percentage the number becomes 5.04, which is definitely easier to understand and compare to other teams’ numbers of short-handed goals.
A logarithm, more commonly known as logs, is another frequently used transformation. Logs are used when you want to look at the proportional differences between the variables. This is often useful when looking at the earnings of players. If Player A is making 8.4 million, player B is making 5.4 million and player C is making 2.4 million it would appear that player B’s performance is halfway between that of players A and C as their earnings are all 3 million dollars apart. However, if you want to look at the difference in proportion between the players it would be better to use a log transformation. The result would be 15.94 for player A, 15.50 for player B and 14.69 for player C. It is now easier to see that player B’s performance is actually closer to that of player A than to player C. One caution to note when using log-transformed values; as most people are not familiar with log data it is often interpreted incorrectly. If this were the case, it would be more appropriate to use the original data.
In order to determine which type of transformation may be appropriate for a set of variables you need to look at the distribution of the transformed data. If the resulting data forms close to a normal distribution, in other words a bell curve, the transformation is a useful tool. If the resulting histogram is skewed with the peak towards the left or right side of the graph, then the transformation is not appropriate for use with this data.
Using a linear, log or other type of transformation allows analysts and coaches to easily detect patterns within a data set. Predictions will be more accurate, which would result in better responses by the teams involved.
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