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Representing data numerically: Difference between revisions
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The central tendency of a data set is commonly described either by the [[wikipedia:mean|mean]], the [[wikipedia:median|median]], or the [[wikipedia:mode|mode]]. | The central tendency of a data set is commonly described either by the [[wikipedia:mean|mean]], the [[wikipedia:median|median]], or the [[wikipedia:mode|mode]]. | ||
Take these numbers | Take these numbers for example: 1, 3, 3, 4, 6, 7, 18; | ||
* The mean is adversely affected by outliers. Here the mean is 6. | * The mean is adversely affected by outliers, like 18. Here the mean is 6. | ||
* The median ignores the values and just represents the middle position in an ordered series. Here the median is 4. | * The median ignores the values and just represents the middle position in an ordered series. Here the median is 4. | ||
* The mode is only useful for integers or categories. Here the mode is 3. | * The mode is only useful for integers or categories. Here the mode is 3. | ||
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The [[wikipedia:standard error (statistics)|standard error of the mean]], on the other hand, is an easy way to represent the precision of the measured mean. This is probably what you want to do most of the time, unless you are interested in describing the breadth of spread. The standard error is often abbreviated as SE, SEM, or S<sub>E</sub>. | The [[wikipedia:standard error (statistics)|standard error of the mean]], on the other hand, is an easy way to represent the precision of the measured mean. This is probably what you want to do most of the time, unless you are interested in describing the breadth of spread. The standard error is often abbreviated as SE, SEM, or S<sub>E</sub>. | ||
Both concepts are interconnected. The standard deviation is in fact in the numerator of the formulae to calculate the standard error of the mean. But the latter is further reduced by sample size N. | Both concepts are interconnected. The standard deviation is in fact in the numerator of the formulae to calculate the standard error of the mean. But the latter is further reduced by sample size N and thus smaller than the standard deviation. | ||
== Notation == | == Notation == | ||
Typically, you will state the calculated mean to represent your data. Accompany this with the most appropriate measure of dispersion - either the standard deviation or the standard error of the mean. For the numerical example above this would look like this: | Typically, you will state the calculated mean to represent your data. Accompany this with the most appropriate measure of dispersion - either the standard deviation or the standard error of the mean. For the numerical example above this would look like this: | ||
* mean & standard deviation: 6 (SD=5.7) or 6 +/- 5.7 (SD, n=7) | * mean & standard deviation: mean=6 (SD=5.7, n=7) or mean = 6 +/- 5.7 (SD, n=7) | ||
* mean & standard error: 6 (SEM=2.1) or 6 +/- 2.1 (SEM, n=7) | * mean & standard error: mean=6 (SEM=2.1, n=7) or mean = 6 +/- 2.1 (SEM, n=7) | ||
Don't forget to state which method you used. This is forgotten in every 7th publication on average [http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=pubmed&cmd=Retrieve&dopt=AbstractPlus&list_uids=16223828 (Altman & Bland 2005)]. Also, state | Don't forget to state which method you used. This is forgotten in every 7th publication on average [http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=pubmed&cmd=Retrieve&dopt=AbstractPlus&list_uids=16223828 (Altman & Bland 2005)]. Also, state the sample number n to give readers an impression of how many measurements you took. | ||
== References == | == References == | ||
