Statistics

Measures of central tendency

Mean

The mean is the total sum of scores, divided by the amount of scores. For example, with a set of data reading:

5, 9, 2, 3, 9, 7, 2, 9, 4, 1, 8

The sum of the data is 59 (5+9+2+3+9+7+2+9+4+1+8). There are 11 individual scores, so to find the mean, one would divide 59 by 11. In this instance, the mean is 5.36.

Median

The median is the central score in a set of data. Let us take the same data as above:

5, 9, 2, 3, 9, 7, 2, 9, 4, 1, 8

To find the median, one must first order the data:

1, 2, 2, 3, 4, 5, 6, 7, 9, 9, 9

Now we have the same eleven values, but numerically ordered. The median value is found by taking the number of values, adding one, and then dividing by two. For example, in this set there are eleven values. If we add one, we have twelve, and if we then divide by two, we have six. Thus, the sixth value in this set is the median value, which means that the median is five:

1, 2, 2, 3, 4, 5, 6, 7, 9, 9, 9

When there is an even amount of values (say, 10 or 12), the median value will fall between two numbers. For example, let us add an extra value of 9 to our set:

1, 2, 2, 3, 4, 5, 6, 7, 9, 9, 9, 9

There are now twelve values. If we follow the same rule as before, we add one to make thirteen, then divide by two to get 6.5. That means that the median value is halfway between the sixth value and the seventh value of our set:

1, 2, 2, 3, 4, 5, 6, 7, 9, 9, 9, 9

Thus, in this particular set of values, the median is 5.5.

Mode

The mode is simply the most frequent data value.

1, 2, 2, 3, 4, 5, 6, 7, 9, 9, 9

In this set, 9 occurs three times, which is more than any other value, which means that it is the mode.

In some circumstances, there will be more than one mode.

Interpretation of p-values and conclusions

p-value

The p-value serves as a measure of the probability (hence ‘p’) that the difference in the results of the experimental group and the control group was a product of chance alone. For example, a p-value of 0.05 suggests that there is a 5% (or 5 in 100) probability that the difference in results between the groups was due to chance, whilst a p-value of 0.5 suggests that there is a 50% probability that the difference was due to chance.

In general, a p-value of 0.05 or lower (0.04, 0.03 etc.) is utilised to deem whether or not results are statistically significant. That is, whether they can be trusted and generalised.

Generalising findings

If there are no extraneous variables and the results are deemed to be statistically significant (see above), generalisations can be made to the wider population based on the results of the sample used.