Statistical Tests

Question 1

What graph would you use with Spearman’s Rank

Answer 1

Scatter-graph - Both help to show a relationship between two variables

Question 2

Advantages of Spearman’s Rank

Answer 2

Spearman’s Rank brings a level of objectivity (or confidence to a 95/99%) that a graph may not allow.
It does not assume that each variable is normally distributed.
It is quick and easy to complete compared to Pearson’s Product.
Further analysis can be achieved by using scatter-graphs and lines of best fit.
Indicates the direction and trend between comparative variables within a data set and whether it is a positive or negative relationship.
It requires data that can be ranked (ordinal data).

Question 3

Disadvantages of Spearman’s Rank

Answer 3

It requires at least 10 observations.
Spearman’s Rank tests the ranking and not the actual values.
Detection of a correlation does not imply that there actually is a relationship.

Question 4

What graph would you use with Pearson’s Product

Answer 4

Scatter-graph - Both help to show a relationship between two variables

Question 5

Advantages of Pearson’s Product

Answer 5

Used with interval and ratio data.
It must be used with data that comes from a normally distributed population.
Indicated the direction and trend between comparative variables within a data set and whether it is a positive or a negative relationship.
Pearson’s uses actual values instead of ranked values so the true magnitude of the data is not lost.

Question 6

Disadvantages of Pearson’s Product

Answer 6

It requires at least 10 observations.
It is longer and more time consuming than Spearman’s Rank so more mistakes can be made.
Detection of a correlation does not imply that there actually is a relationship.

Question 7

What graph would you use with Linear Regression

Answer 7

Scatter-graph and linear regression (best line of fit)

Question 8

Advantages of Linear Regression

Answer 8

More accurate than a line of best-fit because it is mathematically derived and not estimated.
Useful in predicting a correlation.

Question 9

Disadvantages of Linear Regression

Answer 9

The equation is only valid within or close to the measured data.
We cannot say what happens outside of the provided range of numbers.

Question 10

What graph would you use with Chi-Squared

Answer 10

Box-plot graphs will show the mean, range, upper and lower quartile

Question 11

Advantages of Chi-Squared

Answer 11

Test is used to measure the differences between what is observed and what is expected.
Measures to a 95/99% confidence level that a graph does not allow

Question 12

Disadvantages of Chi-Squared

Answer 12

Data must be in the form of frequencies.
The expected frequency in any one cell of the table must be greater than 5.
The total number of observations must be greater than 20.
The data must have a precise numerical value and must be organised into categories of groups.

Question 13

What graph is used with Nearest Neighbour

Answer 13

Dot map - shows the specific location of set sites eg hotels in Glasgow CBD

Question 14

Advantages of Nearest Neighbour

Answer 14

Nearest Neighbour allows us to test how clustered, uniform or random the distribution of sites are.
Tests to a 95/99% confidence level.

Question 15

Disadvantages of Nearest Neighbour

Answer 15

It cannot distinguish between a single and a multi-clustered pattern of sites.
An index of 1.0 doesn’t always mean that the distribution is random - might be a reason for the location of sites.

Question 16

What graph would you use with Standard Deviation

Answer 16

Box-plot

Question 17

Advantages of Standard Deviation

Answer 17

A clear indication of how the data is clustered around the mean.
You can compare the spread of data between 2 or more data sets.
You can evaluate the reliability of the mean by showing whether data has a 68% or 95% chance of being clustered around the mean.
Does not over represent extremes of data that might be anomalies.