Preliminaries and Descriptive Statistics

Question 1

What is a variable?

Answer 1

Something that can vary

Question 2

What are the three types of variable?

Answer 2

• Categorical: non-numerical
• Continuous: numerical but doesn’t have to be a whole number
• Discrete: numerical and a whole number

Question 3

What does a population consist of?

Answer 3

people or items that share a particular characteristic (or set of characteristics)

Question 4

What does a sample refer to?

Answer 4

to a selection of individual people or items from a population

Question 5

In statistics what are we trying to do in regard to populations and samples?

Answer 5

draw inferences about a population from a sample

Question 6

What is a population parameter?

Answer 6

a quantity that describes some characteristics of a population with respect to a specific variable (needs to be worked out with the entire population)

Question 7

What is a sample statistic?

Answer 7

A quantity that describes some characteristic of a sample with respect to a specific variable

Question 8

Why is it usually hard to calculate population parameters?

Answer 8

We don’t have access to the entire group

Question 9

Why is it important to summarise data?

Answer 9

It can be very complex and there can be lots of it

Question 10

What should a measure of central tendency provide?

Answer 10

An indication of a ‘typical’ score in the data set

Question 11

What are the three measures of central tendency?

Answer 11

• Mean
• Median
• Mode

Question 12

How do you work out the mean?

Answer 12

Add all scores together and divide by number of scores (N)

Question 13

What are the pros and cons of using the mean?

Answer 13

• Pro: provides an estimate of the average score of the data-set
• Con: is affected by extreme data points

Question 14

What is the mean?

Answer 14

The average

Question 15

What is the median?

Answer 15

Value that lies in the middle of the data

Question 16

How do you find the median?

Answer 16

• order (rank) the data
• find the score in the middle
• if working with an even set find the average of the two scores in the middle

Question 17

What are the pros and cons of using the median?

Answer 17

• Pro: Insensitive to extreme scores in the data set

- Con: Doesn’t reflect the shape of the scores

Question 18

What is the mode?

Answer 18

Indication of the ‘typical’ score in the data set.

Question 19

How do you find the mode?

Answer 19

Find the most frequently occurring value

Question 20

What’s the pro and con of using the mode?

Answer 20

• Pro: very easy to calculate from a histogram and easy to understand
• Con: data set might have more than 1 mode or no mode at all

Question 21

What is the range and what is the problem with it?

Answer 21

• Difference between the maximum and minimum scores in your data
• Range doesn’t always change for distributions with different shapes

Question 22

What is the deviation?

Answer 22

The (signed) distance of a score from the mean

Question 23

How do you calculate the average deviation?

Answer 23

1. Calculate the mean
2. Calculate the deviation of each score from the mean
3. Calculate the average deviation (add up all the deviations and divide by the number of deviations)

Question 24

Why don’t we usually use the average deviation as a measure of spread?

Answer 24

Deviations often cancel each other out

Question 25

How do you calculate the average squared deviation (we don’t usually use this)

Answer 25

1. Calculate the mean
2. Calculate the deviation of each score from the mean
3. Square the deviation (doesn’t affect ordering of the largest deviation)
4. Calculate the average squared deviation (by dividing by number of deviations)

Question 26

How do you work out the sample variance? Why don’t we usually use this?

Answer 26

1. Work out the mean
2. Calculate deviation of each score from mean
3. Square deviation
4. Calculate a slightly adjusted average squared deviation (divide by n (number of scores) – 1)
   - When N is big this won’t make much of a difference
   - However the units are in measure^2 which is a bit weird

Question 27

How do we calculate the standard deviation?

Answer 27

1. Calculate mean
2. Calculate deviation of each score from mean
3. Square deviation
4. Calculate sample Variance (divide by n-1)
5. Calculate standard deviation by taking square root
   - This number is in original units

Question 28

Will more concentrated data have a larger or smaller standard deviation?

Answer 28

Smaller and more spread out data will have a larger SD

Question 29

What are the four different types of data plot?

Answer 29

• histogram
• box plot
• scatter plot
• data summary

Question 30

Why is using a histogram useful?

Answer 30

• easy to spot mode
• easy to see outlying data
• easy to see range and shape of data

Question 31

Why is using a box plot useful?

Answer 31

• easy to identify median
• easy to see lower and upper hinge
• easy to see hinge spread
• easy to see adjacent values (lowest and highest values falling within the inner fence

Question 32

What is a scatter plot?

Answer 32

A correlational research design

Question 33

Where’s a data summary graph often found?

Answer 33

in data research where you have manipulated variable and see what effect it has on the DV - the standard deviation is plotted

Question 34

What’s the difference between a numerical and categorical data summary graph?

Answer 34

• numerical data summary graph has a line connecting the data points
• categorical usually uses bars