Stage 5

Question 1

What is the purpose of of descriptive statistics?

Answer 1

1. To organise, summarise and describe various measures of a sample. (Descriptive statistics do not allow you to predict anything about the population from which the sample is taken)

Question 2

What are the common forms of analysis for descriptive statistics?

Answer 2

1. Measures of central tendency (mean, median, mode) 2. Measures of dispersion (range, inter quartile range, standard deviation) 3. Comparative measures of dispersion used to compare multiple samples of the same variable

Question 3

Define the mean.

Answer 3

The sum of all the values in a data set divided by the total number of values

Question 4

What are the advantages of using the mean value?

Answer 4

1. Most widely used measure of average 2. Easy to calculate 3. Often used/needed for further statistical analysis

Question 5

What are the disadvantages of using the mean value?

Answer 5

1. Distorted by extreme values 2. Unreliable if there are only a few values used in calculation

Question 6

Define the median.

Answer 6

The middle value of a data set when the values are arranged in rank order. It is easily found if values are plotted on a dispersion graph

Question 7

What are the advantages of using the median value?

Answer 7

1. Unaffected by changes in extreme values 2. More representative of the whole data set if the data set is extremely skewed

Question 8

What are the disadvantages of using the median value?

Answer 8

1. Equal weight is given to each item in the data set regardless of the value of that item 2. Of limited use in further data analysis

Question 9

Define the mode.

Answer 9

The value that occurs most frequently in a data set

Question 10

What are advantages of using the mode value?

Answer 10

1. Simplest measure 2. Model class can be useful when data is grouped

Question 11

What are disadvantages of using the mode value?

Answer 11

1. Often more than one mode in a data set

Question 12

What is the purpose of inferential statistics?

Answer 12

1. To infer (i.e. predict) population parameters from a sample 2. Involves testing a hypothesis against the probability that a significant result has not occurred as a result of random factors (i.e. by chance)

Question 13

What are the common forms of analysis for inferential statistics?

Answer 13

1. Tests of difference between two samples 2. Tests of correlation between two samples 3. Tests of association within or between samples

Question 14

What are the 7 stages of the methodology used for inferential statistics?

Answer 14

1. State a null hypothesis 2. State an alternative hypothesis 3. State the rejection level 4. Work out the calculated statistic 5. Compare the calculated statistic with the critical statistic 6. Decision making 7. Write the conclusion

Question 15

What is Spearman’s Rank correlation coefficient?

Answer 15

• Measures the strength of the relationship between two variable. • Allows you to state the apparent trend • Varies from -1 to +1 and can be used when there are equal numbers of data in each set (at least 12)

Question 16

What are the advantages of using Spearman’s Rank?

Answer 16

1.Shows the significance of the data 2. Proves/disproves correlation 3. Allows for further analysis 4. Doesn’t assume normal distribution

Question 17

What are the disadvantages of using Spearman’s Rank?

Answer 17

1. Does not tell you the cause of the relationship 2. Does not allow you to predict one variable from another 3. Does not explain anything about anomalies in the relationship 4. Quite a complicated formula so can be difficult to work out 5. Need 2 sets of variable data so the test can be performed 6. Only looking at data in relation to one another, so doesn’t analyse the actual value.

Question 18

Name 4 examples of using inferential statistics.

Answer 18

1. Spearman’s Rank correlation coefficient 2. Best-fit lines and linear regression 3. Mann Whitney U Test 4. Chi Square

Question 19

What are best-fit lines and linear regression?

Answer 19

• Highlights the trend in the scatter graph • The steepness of best-fit line shows the rate of change in y as x changes • Best-fit lines are calculated from linear regression: line is positioned so that the distance between it and all the points is at a minimum • Calculated using the regression formula

Question 20

What are the advantages of using lines of best-fit and linear regression?

Answer 20

1. Shows the relationship between two variables
2. used for prediction = so gaps in data can be estimated
3. Identifies anomalies in the data - the bigger the residual (distance from the regression line to a value of y) the more anomalous
4. Residuals can be mapped to see if there is a spatial pattern or other explanation for anomalies

Question 21

What are the disadvantages of using lines of best-fit and linear regression?

Answer 21

1. Regression analysis can only be used for straight line relationships and sometimes relationships are non-linear
2. Only an estimate and could have a sampling error
3. Might be a extraneous (third) variable affecting the data set and x and y may be independent from each other

Question 22

What is the Mann Whitney U Test?

Answer 22

• Measures any difference between two variables • Can be used when there are unequal numbers of data in each set

Question 23

What are advantages of using the Mann Witney U Test?

Answer 23

1. Shows spread from the mean
2. Very visual
3. Indicates relaibility of data
4. Compare graphs easily and anomalies are clearly shown
5. Easy to work out mean, median, etc

Question 24

What are disadvantages of using the Mann Witney U Test?

Answer 24

1. Time consuming to construct
2. Standard deviation is easily manipulated and bias
3. Large data set needed

Question 25

What is Chi Square?

Answer 25

* Measures 'goodness of fit' (i.e. whether data are in line with theoretical predictions) * Test to compare data collected with expected values using theoretical hypothesis which is being tested • Measures the association/difference between two variables

Question 26

What are the advantages of using Chi Square?

Answer 26

1. Can test association between variables 2. Identifies differences between observed and expected values

Question 27

What are the disadvantages of using Chi Square?

Answer 27

1. Can't use percentages 2. Large number of observations needed for the test to be considered valid 3. Difficult formulae

Question 28

What are the 3 main groups of statistics?

Answer 28

1. descriptive statistics 2. inferential statistics 3. spatial statistics

Question 29

What is nearest neighbour analysis?

Answer 29

- quantifies spatial distribution of data points * Measures point patterns in space so they can be described as clustered, random or uniform * The index varies from clustered (0) to uniform (2.15) •

Question 30

What are the advantages of using nearest neighbour analysis?

Answer 30

1. Identifies clusters which can be further analysed 2. Identifies changes of distribution over time 3. Useful for comparisons in different areas

Question 31

What are the disadvantages of using nearest neighbour analysis?

Answer 31

1. Cannot be used in an irregular shaped area having rivers or relief barrier separating nearest neighbor 2. Not always valid for comparison - Size of settlements will vary in terms of population and land mass

Question 32

What is location quotient?

Answer 32

* Measures the concentration of population in a small area engaged in a particular activity in relation to the geographical area it is located * Mostly used to measure concentration of economic activity in an area or region compared to national average

Question 33

Gini Coefficient or Index of Dissimilarity

Answer 33

• A statistical measure of the degree of variation represented in a set of values • Used especially in analysing income inequality or the degree of segregation in a town or city • The closer the index is to 1 the more uneven the distribution

Question 34

When would you use descriptive statistics?

Answer 34

When you need to organise/summarise/ describe statistics. You cannot use it to predict patterns.

Question 35

When would you use inferential statistics?

Answer 35

When you need to predict population parameters. Used when testing a hypothesis against the probability of something happening, in order to prove that the result is significant and did not just occur because of random factors.

Question 36

Inferential statistics - Give 2 examples of tests of difference between two samples.

Answer 36

1. Mann Witney U test 2. Student's t-test

Question 37

Inferential statistics - Give 2 examples of tests of correlation between two samples.

Answer 37

1. Spearman's Rank Correlation Coefficient 2. Pearson's Product Moment Correlation Coefficient

Question 38

Inferential statistics - Give 2 examples of tests of association between two samples.

Answer 38

1. Chi - squared test

Question 39

Descriptive statistics - Why are comparative measures of dispersion needed?

Answer 39

Because it's unfair to compare IQRs and SDs across data sets as the value of each is strongly influenced by the size of the mean and median.

Question 40

Descriptive statistics - Name 2 examples comparative measures of dispersion.

Answer 40

1. index of variability 2. coefficient of variation

Question 41

Descriptive statistics - Comparative measures of dispersion - how does the index of variability work?

Answer 41

Index of variability expresses the quartile deviation as a % of the median of a data set.

Question 42

Descriptive statistics - Comparative measures of dispersion - how does the coefficient of variation work?

Answer 42

Coefficient of variation expresses the standard deviation as a % of the mean set of data.