Calculating SEM using Analysis of Variance (ANOVA)

I hope that the approach outlined above has persuaded you that the SEM is really simple concept, particularly if you think of it as the within-subject standard deviation. I hope you will also see that it is an extremely simple calculation to make if you format the data appropriately in a simple table.

You will, however, often see the SEM calculated using a technique called the analysis of variance or ANOVA for short. If you take the table of measurements from the 2 person data and perform an ANOVA you will obtain a table that looks something like this (depending on the spreadsheet or statistical package that you use, this analysis is included in the Excel spreadsheet that you could have downloaded earlier).

You can ignore everything else on this table apart from the value of 9.8 highlighted in green. This is the within groups mean square (MS) value and the SEM is the square root of this (which equals 3.1 just as calculated in the section above).

If you regularly perform ANOVA this may be a quicker way of calculating the SEM than I’ve suggested above. If you have a really good understanding of ANOVA then this might help you understand what the SEM represents. If neither of these apply to you then it is generally easier just to calculate the SEM as suggested above. (It should be noted that using ANOVA to calculate SEM can be particularly cumbersome for the time series data commonly encountered in gait analysis).