Comparing Two or More Samples

Use these statistics when explanatory variable is categorical and response is continuous

Extension from paired data - occur when a single individual or site is tested three or more time e.g. before, during and after

Another possible use - when individual/clones of individuals divided and subjected to 3+ treatments

Tests:

• Friedman (non-parametric)
• Repeated-measures ANOVA (parametric)

Used to measure same individuals repeatedly

Non-parametric equivalent of repeated-measures ANOVA - less powerful but fewer assumptions

• No assumptions about data distributions
• Data must be ordinal
• Single observation for each combination of factor levels
• One factor must represent the repeat level
• N0 - observations in same factor level (group) have same median values
  • Null rejected = 2+ groups have different medians
  • Doesn't say which two

Special two-way ANOVA - parametric test

One of the factors defines level of repeated sampling, other individuals or sampling sites

Treat analysis as two-way ANOVA

Data should be:

• Continuous
• Normally distributed
• Equal variances in each factor combination

Occurs when a single individual or site is measured/tested only once

Three or more totally separate groups of observations

Signficant result - not say which groups are different from which

• Post-hoc test required to interpret the results

Tests:

• Kruskal-Wallis (non-parametric)
• One-way ANOVA (parametric)

Used when there are >2 groups

Assumptions:

• Continuous data
• Data within each group normally distributed
• Data within each group have equal variance

N0 - each group has same mean/variance within groups is same as variance between groups

Use to compared >2 samples

• Can include 2 if needed by Mann-Whitney U test more powerful 

Non-parametric equivalent of ANOVA

• No assumptions about homogeneity of variances or normal distributions
• Less powerful
• But less likely to find a wrong significant result i.e. lower probability of Type I error

N0 - all samples are taken from populations with same median

Occur when single individual is tested twice e.g. before and after, retesting

OR

When an individual/individuals of a clone are divided and then subjected to 2 treatments

Tests:

• Wilcoxon (non-parametric) 
• Paired t-test (parametric)

Used on paired samples of data

Assumptions:

• Continuous data
• Normally distributed data
• Homogenous variances of two data sets

N0 - no difference between two columns and they could come from same data set

Paired test - used if samples not independent from each other

Non-parametric equivalent of paired t-test - less asumptions about shape of data

• Assumption - data are on continuous scale of measurement

Minimum of 6 pairs of data required 

Pick up effects when data sample variation very high

When single individual measured or tested once

Two totally seperate groups of observations = two samples

Tests:

• Mann-Whitney U (non-parametric)
• t-test (parametric)

Compare 2 samples

Assumptions:

• Normal distribution
• Continous data
• Equal variance

N0 - two sets of data are the same

Test two groups

Non-parametric equivalent of t-test - no assumptions about homogeneity of variances or normal distrbutions but less powerful

H0 - no difference between the two samples

Rank test - line up data in numerical order and rank them (tie get mean of numbers e.g. .5) 

• Information gets lost