Choosing and applying statistical techniques

Overview

Matching a test to a data set, worked through correlation along a spit, a clustered distribution, counted shopper zones, regional dependence and a set of pebble measurements.

What you need to know

Answer each one before you reveal it.

Questions from this subtopic

Each one with the model answer underneath.

1. 1

   How do you decide which statistical technique to apply to a data set?

   Model answer

   By asking what the question is and what type of data you have. If the question is what is typical, use an average with a measure of spread. If it is whether two variables measured at the same sites are related, and both can be ranked, use Spearman's rank correlation. If it is how a set of point locations is spaced across an area, use nearest neighbour analysis. If it is whether observed frequencies in categories differ from expected ones, use chi-squared, which is an A2 technique. If it is how a region's share of an industry compares with the national share, use the location quotient, also A2. Matching the technique to the data type comes before any calculation.

2. 2

   You have measured pebble roundness and distance along a spit at fifteen sites and want to know whether they are related. Which technique, and why?

   Model answer

   Spearman's rank correlation. There are two variables measured at the same fifteen sites, giving paired data, both can be ranked, and fifteen pairs is above the practical minimum of about ten. The test will give a coefficient describing the direction and strength of any relationship, which can then be compared with the critical value in the provided table to judge significance. A scatter graph should be drawn alongside it to show the pattern and identify anomalies, but the graph alone cannot say whether the relationship could have arisen by chance.

3. 3

   You have the locations of forty petrol stations in a district and want to know whether they are clustered. Which technique, and why?

   Model answer

   Nearest neighbour analysis. The data are point locations within a defined area of known size, and the question is about spacing, which is exactly what the index measures. It returns a single figure on a scale from 0 for clustered through 1 for random to 2.15 for regular, which can be checked against the provided significance graph for forty points. The area boundary must be defined and justified before calculating, because changing it changes the result.

4. 4

   You have counted how many shoppers came from each of four zones and want to know whether they are drawn equally from all four. Which technique, and why?

   Model answer

   Chi-squared, which is an A2 technique and is not examined at AS. The data are raw frequencies in categories, which is what chi-squared requires, and the question is whether the observed counts differ significantly from the expected counts under the assumption of an even distribution. The degrees of freedom are the number of categories minus one, and the calculated value is compared with the critical value in the provided table. Spearman's would be wrong because there are no paired ranked variables.

5. 5

   You want to know whether a region depends unusually heavily on tourism compared with the country as a whole. Which technique, and why?

   Model answer

   The location quotient, which is required at A2 only. It compares the proportion of the region's workforce in tourism with the proportion nationally, producing a figure that is 1 if the region matches the national picture, above 1 if tourism is over-represented and below 1 if it is under-represented. It is the right choice because raw employment totals would simply reflect the size of the region, whereas the quotient standardises for size and so measures specialisation.

6. 6

   You have fifty measurements of beach pebble length from one site and want to summarise them. Which techniques, and why?

   Model answer

   An average together with a measure of spread. Report the median if the distribution is skewed or contains a few very large pebbles, since it is not distorted by extremes; report the mean if the values are fairly symmetrical, since it uses all the data. Add the range so the reader can see how sorted the material is, and note the modal size class if one clearly dominates. No correlation or pattern test applies here, because there is only one variable at one site and no second variable to relate it to.

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