Statistical Skills

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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.
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Spearman's Rank

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.
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Chi Square

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.
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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.
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