Research Skills 6 : Introduction to analysing data

Question 1

Inspecting and Plotting your data

Answer 1

• ALWAYS start by looking at your raw data before calculating statistics.
• Look at the actual numbers.
• Check for obvious mistakes, missing values and outliers.
• Think about the best graphical representation for your data
• Graph the results and look at them.

Statistics only represent your data and describe your data. They do not substitute the results

Question 2

Summarising Data: Descriptive Statistics

Answer 2

You can use descriptive statistics (e.g. average) to simplify your data

MEASURES OF “AVERAGE“ (“Measures of central tendency”)

-Mean
“Common average”, “arithmetic mean”

-Median
The middle value. Put all the observations in order of size. Find the middle value- the value which has the same number of observations larger than it, as smaller than it.

Question 3

Disadvantages of descriptive stats

Answer 3

The mean is strongly affected by outliers

The median is insensitive to outliers and to skewed distributions

Question 4

Name two measures of spread

Answer 4

1. Range

2. Standard Deviation

Question 5

What is the Range?

Answer 5

• Smallest to largest value

- But only tells you about the largest and smallest value, nothing about the spread of all the other observations.

Question 6

What is Standard Deviation?

Answer 6

• A mathematical measure of the spread of data around the mean.
• Notice that SD is a measure of the spread
• It does not show the actual spread or range
• ± 1 SD around the mean will include a lot of the data
• ± 2 SD around the mean will include most of the data
• But some results will be even further out

Question 7

What is Variance?

Answer 7

The average of the squared differences from the Mean, or the square of the Standard Deviation (SD2)

Question 8

What is Interquartile Range ?

Answer 8

Divide the data into the 
top 25%
next 25%
next 25% 
bottom 25%

Interquartile range covers the middle two groups. Used by population scientists with large datasets. Not useful with small numbers of observations.

Question 9

Graphing Data: what are the two types of data?

Answer 9

1. Numerical (quantitative) data

2. Categorical Data

Question 10

What is Standard Error of the Mean (sem) ?

Answer 10

This does not measure the spread of the data. It measures our confidence in the estimate of the mean.

Question 11

Standard Deviation vs SEM

Answer 11

• Standard deviation is a measure of the spread in your data. As you get more data the spread will stay about the same- the s.d. will change only slightly.
• S.e.m. is a confidence interval , a measure of the uncertainty in your estimate of the mean..

Question 12

What is a disadvantage of SEM?

Answer 12

• this only works for large numbers of observations (>20-30)
• For small numbers of observations, the s.e.m. is too optimistic
• You could find the true confidence intervals using a t-test

Question 13

What are properties of Normal Distribution?

Answer 13

Among the properties of 
- the normal distribution:
it is symmetrical about the mean
- it extends to + and to – infinity
- however ~ 95% of observations lie within   ± 2 standard deviations of the mean

Question 14

What is Normal Distribution?

Answer 14

The “normal distribution” is a particular mathematical distribution with two parameters, the mean and the standard deviation.

Question 15

What is the Central Limit Theorem?

Answer 15

• If a variable is affected by a lot of different random factors
• Each has a small effect
• And their effects are additive
• The distribution will approximate to a normal distribution

Question 16

Summary I - Own your data

Answer 16

1. Look at the raw data
2. Plot the raw data
3. Think about what the data it means

Question 17

Summary II - Descriptive Statistics

Answer 17

1. Measures of average

• Mean: works best for mathematicians
• Median: sometimes gives a more sensible answer when there are outliers, or a skewed distribution

2. Measures of spread

• Range(only tells you about smallest and largest observation)
• Standard deviation (s.d.) (more useful measure of overall spread)
• Variance (=s.d.2)
• Interquartile range (only useful if large number of observations)

Question 18

Summary III - Error Bars

Answer 18

1. Could mean anything
2. So must be defined in the figure legend
3. S.D. error bars are a measure of the spread of the data
4. S.E.M. error bars are an indication of your confidence in the estimate of the mean

Question 19

Summary IV - Standard Error of the Mean

Answer 19

1. S.e.m. is a confidence interval

• We can be ~60% confident that the “true” mean is ± 1 s.e.m. distant from the experimental mean
• And 95% confident that the “true” mean is approx. ± 2 s.e.m. distant from the experimental mean

2. As the number of observations gets larger the s.e.m. gets smaller
3. Our confidence in the estimate of the mean is higher