Interpreting Data

Question 1

What are the two main types of data?

Answer 1

Qualitative and quantitative

Question 2

What are the two types of quantitative data?

Answer 2

Discrete and continuous

Question 3

What are the two types of qualitative data?

Answer 3

Nominal (unordered) and ordinal (ordered)

Question 4

What is nominal data split into?

Answer 4

Binary and categorical

Question 5

What is the median?

Answer 5

Middle value when values ordered from smallest to largest

Question 6

What is the median?

2, 3, 6, 7, 10, 11, 14

Answer 6

7

Question 7

What is the mode?

Answer 7

Most common value

Question 8

What is the mean?

Answer 8

The average. It is the sum of all the values divided by the number of values.

Question 9

Calculate the mean.

2, 3, 4, 7, 8, 8, 11

Answer 9

6.1

Question 10

What does standard deviation mean?

Answer 10

The average distance from the mean

Question 11

How is standard deviation calculated?

Answer 11

The sum of (each individual value - mean) squared, then divided by the number of values. Then you square root this answer.

Question 12

What centile is the median?

Answer 12

50th

Question 13

What is the interquartile range?

Answer 13

25th to 75th centile

Question 14

When is it better to use a median rather than a mean?

Answer 14

To avoid the influence of outliers, i.e. if there is an outlier that is very different to the rest of the data.

Question 15

When is it better to use IQR rather than the standard deviation?

Answer 15

To avoid the influence of outliers

Question 16

What is the Gaussian distribution determined by?

Answer 16

Mean and standard deviation

Question 17

If the mean is reduced from 120 to 110, what happens to the Gaussian distribution?

Answer 17

It shifts to the left.

Question 18

If the mean is increased from 120 to 130, what happens to the Gaussian distribution?

Answer 18

It shifts to the right.

Question 19

What happens to the Gaussian distribution if the standard deviation is decreased from 15 to 10?

Answer 19

The curve becomes narrower and taller

Question 20

What happens to the Gaussian distribution if the standard deviation is increased from 15 to 20?

Answer 20

The curve becomes wider and flatter

Question 21

What is a useful property of Gaussian distributions?

Answer 21

A constant proportion of values will lie within any specified number of Standard Deviations above or below the mean (reference ranges).

Question 22

If you go one standard deviation away from the mean, how many % does this represent?

Answer 22

68%

Question 23

If you go 1.64 standard deviations away from the mean, how many % does this represent?

Answer 23

90%

Question 24

If you go 1.96 standard deviations away from the mean, how many % does this represent?

Answer 24

95%

Question 25

What is the 99% range? How is it calculated?

Answer 25

0.5th centile to 99.5th centile | Mean +/- 2.58 SDs

Question 26

What is the 95% range? How is it calculated?

Answer 26

2.5th centile to 97.5th centile | Mean +/- 1.96 SDs

Question 27

What is the 90% range? How is it calculated?

Answer 27

5th centile to 95th centile | Mean +/- 1.64 SDs

Question 28

If the sample size isn't too small then the distribution of the sample mean will be...?

Answer 28

Gaussian

Question 29

What is the standard error?

Answer 29

The standard deviation of this distribution (Gaussian) is called the standard error. It is a measure of the statistical accuracy of an estimate.

Question 30

What is the standard error of the mean?

Answer 30

The standard deviation of the distribution of all possible sample means – can’t do this in practice, so it is estimated.

Question 31

How is standard error of the mean estimated?

Answer 31

Standard deviation divided by the square root of the sample size.

Question 32

How is the 95% confidence interval of a sample mean calculated?

Answer 32

95% CI = sample mean +/- (1.96 x standard error)

Question 33

What does the 95% confidence interval mean?

Answer 33

We would expect 95% of samples of the same size to have a mean between the two values calculated. In the population we are 95% sure that the mean could be as low as ___ or as high as ___.

Question 34

When calculating confidence intervals and ranges, what should be used for each?

Answer 34

Standard deviation for ranges | Standard error for intervals

Question 35

When the sample size increases, the 95% range…

Answer 35

Stays the same

Question 36

When the sample size increases, the 95% confidence interval…

Answer 36

Gets narrower

Question 37

What is ‘r’? What two values is it always between?

Answer 37

Correlation coefficient | -1 and 1

Question 38

What does r=1 tell you?

Answer 38

Perfect positive correlation

Question 39

What does r=-1 tell you?

Answer 39

Perfect negative correlation

Question 40

What does r=0 tell you?

Answer 40

No correlation

Question 41

What is the equation for a linear regression?

Answer 41

y = a + bx, | where y is the outcome and x is the predictor

Question 42

What does the line of best fit do?

Answer 42

Minimises square of vertical distances

Question 43

Regression - whatever we are predicting, should it be on the vertical or horizontal axis?

Answer 43

Vertical

Question 44

Statistical significance - what does this mean and how is it determined?

Answer 44

An observed sample difference between groups might be due to chance. Statistically significant means the result is unlikely to be due to chance. Use confidence intervals and p-values

Question 45

What does a p-value mean?

Answer 45

A p-value for a result is the probability of observing a result as or more extreme than the sample result if the underlying assumption in the population is true.

Question 46

What does the p-value have to be less than to be statistically significant?

Answer 46

<0.05

Question 47

When can p-values be calculated?

Answer 47

When there is a comparison: 2 means – are they different i.e. is their difference different from 0? Association – are the observed results different from those expected Regression – is the slope different from 0?

Question 48

How are p-values calculated?

Answer 48

Using chi-squared test

Question 49

If the 95% CI for a difference excludes 0 then what can be said about the p-value?

Answer 49

p<0.05

Question 50

If the 95% CI for a difference contains 0 then what can be said about the p-value?

Answer 50

p≥0.05