Statistical Analysis to show Relationship Strength.

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Presentation transcript:

Statistical Analysis to show Relationship Strength. Spearmans Rank Statistical Analysis to show Relationship Strength.

Rank distance - Rank price Results from a survey looking investigating the price of items in relation to the shops distance from a major tourist attraction Rank distance - Rank price

SPEARMAN’S RANK CORRELATION COEFFICIENT It says … It allows us to … Compare the RANK ORDER of TWO Data Sets

This example is based on a survey looking at price & distance The total of 6 x Spearman’s Rank Correlation Coefficient The DIFFERENCES between the RANKS assigned to each ‘price’ SQUARED The Number of different ‘sites’ This example is based on a survey looking at price & distance

The Maths The top line of the equation d² (rank difference 2) = 285.5. Multiplying this by 6 gives 1713. Now for the bottom line of the equation. n (the number of sites) =10. n³ - n :1000 – 10 = 990 R = 1 - (1713/990) R: 1 - 1.73 = -0.73 What does this R value of -0.73 mean? The closer R is to +1 or -1, the stronger the likely correlation. Perfect positive correlation is +1 and a perfect negative correlation is -1. The R value of -0.73 suggests a fairly strong negative relationship.

What is it showing? rs close to -1 rs close to 1 rs close to 0 Total Agreement Overall Neither Agree or Disagree Total Disagreement rs close to -1 rs close to 1 rs close to 0

The significance of the relationship! The R value of -0.73 must be looked up on the Spearman Rank significance table. 'degrees of freedom' : This is the number of pairs in your sample minus 2 (n-2). 8 (10 - 2). Using the r value (y axis) the degrees of freedom value (x axis)plot the position of the graph (next page).

Tasks Work through the example on p.636 (Waugh), fill in the table & check that you understand how each column is calculated. Complete the tasks on the next 2 slides and

A student Surveyed the ages, in years, and the prices, in £’s, of ten second hand cars of a particular type, in a local paper and obtained the data in the table below: What can you say about the relationship between the age and price of cars … Age, years 6 2 9 5 13 4 7 8 3 10 Price, £’s 2790 5990 850 3100 650 3350 3790 1350 4590 990 Data Ranks Differences Age Price d d2 Use the graph (p.637) to determine the significance of the relationship.

What is the significance of the relationship? A student has been shown photographs of eight different people and asked to estimate their ages … The results are shown … Actual age in years 54 88 22 70 30 15 47 6 Estimated Age 45 35 62 24 19 56 11 Data Ranks Differences Actual Estimate d d2 What is the significance of the relationship?