**Statistics for Neuroscientists**

Descriptive statistics

Inferential (inductive) statistics

Choosing & using statistical tests

**Inferential (inductive) statistics**

Statistical analysis allows you to find out the statistical significance of:

differences between groups

relationships between two conditions

associations between two or more sets of values

Assumptions of the Normal Distribution

The data are on an interval or ratio scale

The mean, median and mode are close to each other

The data is symmetrically distributed around the mean

95.5% of values lie within 2SD of the mean

**Descriptive Statistics**

Descriptive statistics allow you to:

quantify / summarize data

display data

make simple comparisons

Measures of central tendency

The mean, median and mode all are measures of central tendency

The standard error of the mean (SEM) gives the range in which the population mean is expected to lie

If data conform to the Normal Distribution, the mean, median and mode values should be very similar to each other

If data do not conform to the Normal Distribution, it is more appropriate to use the median than the mean as the measure of central tendency

Measures of spread

(dispersion)

There are many measures of spread:

range

quartiles & percentiles

absolute deviation

sum of the squares

variance

standard deviation (SD)

Two sets of data

You have collected two sets of data and want to find out if there are differences between the groups

Tests for relationships

You have collected two sets of data and want to find out if the values are related to each other

The statistical analysis can provide you with two values, R and R squared

The size of the R value tells you the extent to which the data are correlated

+1 = positive correlation

-1 = negative correlation

0 = no correlation

The R squared value tells you the strength of the relationship - that is, how much of the variation in values of Y is due to X

You have continuous data which conform to the Normal Distribution

Independent measures design = unpaired Student's t-test

Repeated measures design =

paired Student's t-test

You have continuous data which do not conform to the Normal Distribution, or you have ordinal level data

Independent measures design = Mann-Whitney U test

Repeated measures design = Wilcoxon Signed Ranks test

More than two sets of data

You have collected multiple sets of data and want to find out if there are differences between the groups

You have continuous data which conform to the Normal Distribution

1. Carry out an ANOVA

2. If the ANOVA indicates that there are significant differences, carry out post-hoc analysis

For example, Dunnett's is a post-hoc test which compares the results of the control group to the results from the test groups

You have continuous data which do not conform to the Normal Distribution, or you have ordinal level data

1. Carry out the Kruskal-Wallis test

2. If the Kruskal-Wallis indicates that there are significant differences, post-hoc analysis may be carried out using the Dunn test

You have continuous data which conform to the Normal Distribution

Use the Pearson's product moment correlation coefficient

You have continuous data which do not conform to the Normal Distribution, or you have ordinal level data

Use the Spearman's Rank correlation

Linear Regression

If two sets of data are found to be linearly correlated, linear regression can be used to show the mathematical relationship between variables:

y = mx + c

2x2 contingency tables

Use the Fisher's exact test

(this reduces the risk of Type I errors)

All other contingency tables

Use the Chi-squared test

Remember to use the Bonferroni correction for your P values if you carry out multiple comparisons

Tests for associations

**Choosing statistical tests: differences**

**Choosing statistical tests:**

relationships and associations

relationships and associations

Types of data

Nominal

The data belongs in categories

e.g eye colour; hair colour

Ordinal

The data is described in rank order

e.g. scores on a rating scale; finishing position in a race

Discrete

Data collected through counting

e.g. number of bacterial colonies; number of heart beats per minute

Continuous

Interval

Uses a scale with equal divisions

e.g. temperature; height

Ratio data

Has an absolute zero that is meaningful

e.g. exam scores

One or two tailed hypothesis?

A

one-tailed hypothesis

sets out the expected 'direction' of the difference e.g. scores obtained after treatment will be higher than scores before

A

two-tailed hypothesis

just states that there will be a difference e.g. scores obtained after treatment will be different to scores before

Independent or repeated measures design?

An

independent measures

design compares data collected from different samples e.g. male vs. female

Data obtained from an independent measures design is described as '

unpaired

'

A

repeated measures

design compares data collected from the same participant e.g. before and after treatment

Data obtained from a repeated measures design is described as '

paired

'

Different statistical tests make different assumptions about the data, experimental design and hypotheses:

1. Are your data:

nominal, ordinal, discrete, or continuous (interval or ratio)?

normally distributed?

2. Does your experiment have an independent (unpaired) or repeated (paired) measures design?

3. Is your hypothesis one or two tailed?

You have collected at least two sets of nominal data and want to find out if the values are associated with each other