# 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

Mann-Whitney shows if two sets of data are significantly different. To work it out:

• Make a hypothesis and null hypothesis.