Introduction

Question 1

What does a geographical data frame comprise?

Answer 1

Cases + geographical references + variables (attributes/measurements about the cases)

Question 2

Salary in £s per week is an example of which measurement?

Answer 2

Ratio

Question 3

What are the three broad purposes of data analysis?

Answer 3

• Description/exploration
• Probabilistic inference and confirmation
• Modelling relationships

Question 4

What measures of central tendency can be used to describe ratio data?

Answer 4

Mode, Median, arithmetic mean, geometric mean

Question 5

What measures of spread can be used to describe ordinal data, and which cannot?

Answer 5

% in the mode and IQR can both be used, but standard deviation and the coefficient of variation cannot.

Question 6

What is the varience, and why does this explain its low resistance?

Answer 6

The average of the squared deviations - therefore any outliers are made worse by squaring.

Question 7

By dividing the standard deviation by the mean, and multiplying the outcome by 100 what do I get?

Answer 7

The coefficient of variation - a dimensionless measure that gives relative spread in comparison to the mean.

Question 8

How do you standardize values?

Answer 8

Subtract the mean and then divide by the standard deviation.

Question 9

What is the coefficient of variation particularly useful for?

Answer 9

Comparing distributions with very different means and comparing variables measured in different units.

Question 10

Boxplots are good for comparing multiple batches of data, but what do they show about each batch?

Answer 10

The middle, extremes, IQR and identifies outliers.

Question 11

What equation(s) can be used to find outliers on a boxplot?

Answer 11

> UQ + 1.5*IQR

<LQ - 1.5*IQR

Question 12

What do stem and leaf plots enable us to see about the data?

Answer 12

The frequency distribution and overall shape of the data, the centre of the data and marked deviations.

Question 13

What is important about the sum of absolute deviations from the mean?

Answer 13

It will be less than from any other number.

Question 14

How can the arithmetic mean be applied to nominal data?

Answer 14

Binary variables can be split into categories of 0 and 1, with the mean giving us the proportion of data in the ‘1’ class.

Question 15

Describe the difference between inferential, explanatory and relational statistics.

Answer 15

Inferential - Go beyond the data to say something about a population.
Relational - why two events coincide
Explanatory - What caused an event

Question 16

How do you calculate the standard deviation?

Answer 16

The square root of the varience.

Question 17

When calculating the trimmed mean, what is g? And how can g:0 and g:1 be otherwise described?

Answer 17

g = robustness factor.

g:0 is the arithmetic mean (no values trimmed) whilst g:1 represents guarding against 2 outliers.

Question 18

For data with a positive skew, the median, mode and mean occur in which order?

Answer 18

Mode<Mean

Question 19

Starting with x^3 as a transformation for negatively skewed data, write out the ladder of power.

Answer 19

x^3…..x^2…….x…….sqrtx……ln(x)…..-1/sqrtx……-1/x…….-1/x^2

Question 20

What skew is found in most distributions and what transformation is used to correct this?

Answer 20

Positive - log scale corrects this.

Question 21

If an outlier is a mistake, you can correct or omit it. If not, what two steps should you follow?

Answer 21

Try a transformation. If there is still no apparent reason, do a with/without analysis.

Question 22

What does the multiplication theorem state?

Answer 22

That for independent events, the probability of them occurring together is given by the product of their individual probabilities.

Question 23

A permutation is a set of objects in a given order, whereas in a combination the order matters. How can we find the number of possible combinations of a sample?

Answer 23

c(population size, sample size) = c(3,2) = 3!/2!(3-2)!

Question 24

What is probabilistic inference?

Answer 24

Making an inference from a sample to a population and calculating the chances of this being wrong.

Question 25

After stating H1, collecting representative data and stating H0, what are stages 4,5 and 6 in hypothesis testing?

Answer 25

4 - specify significance level
5 - choose statistical test
6 - calculate test statistic

Question 26

What does a p value tell you?

Answer 26

the chance of getting an observed value by chance if H0 is true.

Question 27

Under what circumstance can we reject H0 for a given p value?

Answer 27

When p<alpha

Question 28

What does a sampling distribution show?

Answer 28

All possible results that can be obtained under H0

Question 29

Linear association between two variables is measured by what unit free indicator of both strength and direction?

Answer 29

Pearsons correlation coefficient - r. Where r = -1 there is very strong negative correlation. Where r=0 there is no linear correlation and where r=1, there is very strong positive correlation.

Question 30

What is ‘error’?

Answer 30

The deviation of points from their expected value.

Question 31

To make all deviation positive, we use the sum of the squared error. How do you calculate this?

Answer 31

sum of (y-y^)^2