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# Statistics for Neuroscientists

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## Caroline Anderson

on 14 March 2018

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#### Transcript of Statistics for Neuroscientists

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
(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

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: