The interquartile range
The interquartile range is a measure of dispersion. The interquartile range (IQR) is the range of values covered by the middle 50% of a set of data. To find the interquartile range:
- find the median of the values to the left of the median (the lower quartile).
- Find the median of the values to the right of the median (the upper quartile).
- Subtract the median of the lower quartile from that of the upper quartile to get the interquartile range.
Spearman's rank is used to find out if two sets of numbers are correlated. To work it out:
- Rank each number - the highest is one.
- Calculate the difference (d) between the ranks and the numbers for each pair.
- Square each 'd' and add up the values.
- Work out the Spearman's Rank Correlation Coefficient (r). You will have the formula.
- The number you will end up with will be between -1 and 1.
- A positive number means that the variables are positively correlated. The closer the number is to 1, the stronger the correlation.
- Conversely, a negative number means that the two sets of variables are negatively correlated. The closer the number is to -1, the stronger the correlation.
- To prove a genuine link, you have to look at the probability of a correlation being shown by chance. To solve this, you need a graph/table of critical values.
Chi square tells you whether two variables are linked. To work it out:
- Make a hypothesis and null hypothesis about the existence of a link
- Use the null hypothesis to predict a result - the expected result (E).
- Carry out the experiment and record the result - the observed result (O).
- Work out the formula:
- Calculate O-E for each area
- Then square each of the resulting numbers
- Divide each by the expected result (E).
- Finally, add all the numbers together.
- Compare your result to the cricial value
- If the result is smaller than the critical value there is no significant difference between O&E and you accept your null hypothesis.
- If it's larger than the critical value you reject your null hypothesis.
Mann-Whitney shows if two sets of data are significantly different. To work it out:
- Make a hypothesis and null hypothesis.
- Rank the data - start with the lowest score
- If some of the values are the same, give them an average rank.
- Add up the ranks for each group.
- Put them into volumes, using the formulae.
- The result must be less than or equal to the critical value to be significant and for you to reject the null hypothesis.