Descriptive Statistics

Question 1

What are the scales of measurement for numerical data?

Answer 1

Nominal data
Ordinal data
Interval scales
Ratio scales

Question 2

What are the characteristics of nominal data?

Answer 2

Not really scales, more labels, names, or categories to which cases are assigned
Sometimes known as categorical data
Key characteristic: There is no implied ordering or numerical relationship between categories

Question 3

When analysis nominal data what statistic could you use? And what does the analysis look at?

Answer 3

The analysis looks at relative frequency of cases in each category

You should use chi-squared

Question 4

What are the key characteristics of ordinal data?

Answer 4

Categories to which cases can be assigned can be ranked or ordered in some way

However cannot assume that the differences between neighbouring categories are equal

Question 5

What is the key characteristic of interval scales?

Answer 5

The categories to which cases can be assigned can be ordered in some way and we can assume that the differences between neighbouring categories are equal

However there is no true zero - the point is arbitrary

Question 6

What are the key characteristics of ratio scales?

Answer 6

The categories to which cases can be assigned can be ordered in some way, we can can assume that the differences between neighbouring categories are equal, and there is a true zero

Question 7

What are descriptive statistics?

Answer 7

They summarise the distribution with a few numbers which describe:
Central tendency - the middle of the distribution (same as average -mean, median)
Dispersion - the spread of scores (standard deviation)

Question 8

What is the mode and what can it be used for?

Answer 8

It is the most common score

Only good for nominal data

Also good for summarising common incorrect answers to a test

Question 9

What is the median and what can it be used for?

Answer 9

It is the middle score when the scores are in rank order

If there is an even number of cases then the media is halfway between the too middle values

Question 10

What is the mean and what is it used for?

Answer 10

The mean is the arithmetic average - add up the scored and divide them by the number of scores

Question 11

How to measure the standard deviation?

Answer 11

Calculate the mean
Subtract the mean from each score to get deviations
Square the deviations
Total the squared deviations
Divide the total by N-1 (this is the variance)
Take the square root of the variance to get the standard deviation

Question 12

How would you work out the standard deviation when you have the Standard Deviation?

Answer 12

Once you have the mean and SD for a sample, subtract sample mean from score and divide the sample by SD

Question 13

What are characteristics of non-parametric tests?

Answer 13

Relatively easy to calculate
Assumption free
Can use nominal and ordinal data
But they are not very powerful as they do not make use of information about the variability of the data

Question 14

What is power?

Answer 14

The power of a test reflects how sensitive it is - more sensitive tests will detect a significant difference even if that different is quite small
The more powerful - the more likely to spot a significant result

Question 15

What is a type 1 error?

Answer 15

A false positive

- tests says there’s a significant effect when really there isn’t

Question 16

What is a type 2 error?

Answer 16

False negative
Tests says there’s no significant effect when really there is

Parametric tests are less likely to find one of these

Question 17

What is a parametric test?

Answer 17

Parametric tests are more complicated to calculate but are more powerful
Uses more informative interval scale, takes advantage of measure of variability and the properties of the normal distribution
But data must meet certain parameters

Question 18

What are some assumptions of parametric tests?

Answer 18

Interval or ratio scale data - interval between two measurements is meaningful
Scores must be normally distributed
Samples being compared must have similar variances
Aside- the tests are robust (can cope with some deviation from these ideal conditions)

Question 19

What does a normal distribution graph look like?

Answer 19

Bell shaped

Symmetrical around the mean

Question 20

Why study statistics?

Answer 20

People are so variable and our ways of measuring their performance are so error prone

Question 21

What is a problem of error variability?

Answer 21

People (even the same person tested twice) will give different scores - people are complicated and they will be influenced by conditions not under our control
Because we expect people who are the sass to give us different scores, it is difficult to judge when it is meaningful or down to error variability

Question 22

What is the main problem with error variability?

Answer 22

We need to be able to distinguish between error differences (variability) and meaningful differences
We only consider meaningful differences to be significant

Question 23

How do you deal with error variability?

Answer 23

Try to eliminate it - good experimental design, matching participants, controlled environment, accurate measurement techniques, control confounding variables (leads to reduction in error)

Try to account for it - work out how big it is and take it into account

Question 24

Error variability and the logic of statistical tests:

Answer 24

If we find a difference between groups or conditions, we need to know if this difference is an error or it’s a real difference so you would use the variability in a particular condition to estimate the size of error variability. Since everyone in the same condition should be the same, the variability must be due to error. We compare the variability between conditions (total variability) with within conditions (error variability) to decide if the difference is more than can be explained by error variability

Question 25

What is variability is variability within a condition?

Answer 25

Error variability

Question 26

What variability is variability between conditions?

Answer 26

Error variability and any effect of treatment

Question 27

What does variability tell us?

Answer 27

How much scores in a distribution are spread out or clustered together

Question 28

Estimating variability:

Answer 28

Standard deviation - the average amount that scores differ from the mean
SD gives a good indication of the shape of the distribution of the scores in the sample