means tests mare 250 dr. jason turner. type of stats test called a means test tests for differences...
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Means Tests
MARE 250Dr. Jason Turner
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Type of stats test called a means test
Tests for differences in samples based upon their average (mean) and standard deviation (variance)
Several versions from 1 sample, 2 sample, through multiple samples
Means Tests
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Response – variable of interest; variable you collect - #Fish, %Coral cover, temperature, salinity, etc
Factor – variable by which response is divided; categorical - location, Date, Gender, Species
Level – components of factor; - Location (Puako, Hilo Bay), Date (Jan, Feb), Gender (♂, ♀)
Means Tests
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2 Types:
1) Parametric Means tests – have defined assumptions including normally distributed data
2) Nonparametric Means tests – have few/no assumptions
Means Tests
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Parametric means tests – require data to be normal, etc (assumptions)
Nonparametric tests – do not require data to be normal (assumptions)
Parametric vs. Nonparametric
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Parametric means tests – include 2 sample t-test, ANOVA
Nonparametric means tests – include Mann Whitney (t-test), Kruskal Wallace (ANOVA)
Parametric vs. Nonparametric
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Parametric – has strict assumptions1-Sample t-test2-Sample t-test
Pooled t-testNon-pooled t-testPaired t-test
Non-parametric – no assumptions1-Sample Wilcoxon2 Sample t-test (Mann-Whitney)
Means Tests
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1 or 2-Sample t-test:
1. Requires large sample size (n=3)2. Requires normally distributed data3. Outliers can significantly confound
results
Parametric testing is the “gold standard” – it is the type of test we attempt first
Has very strict criteria called assumptions
When to Parametric
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Has 4 Assumptions:
1. Random Samples – collected randomly
2. Independent Samples – equal chance
3. Normal Populations (or large
samples; n=3)
4. Variances (std. dev.) are equal
When to Parametric
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How do we assess these 4 Assumptions:
1. Random Samples – Sampling design
2. Independent Samples – Sampling Design
3. Normal Populations - Normality
test*
4. Variances - Equal Variance test*
When to Parametric
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Non-parametric 1 Sample t-test (Wilcoxon) or 2 Sample t-test (Mann-Whitney):
1. Small sample size ok2. Does not require normally distributed
data3. Outliers do not confound results
When to Nonparametric
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Non-parametric test are used heavily in some disciplines – although not typically in the natural sciences
Used when data are not normal, or low sample size, low “power”
When to Nonparametric
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When do we run Nonparametric tests?
1) Sample size is too small for parametric2) Fail assumptions tests (Normality,
Equal Variance)3) Fail to transform (rescale) data to meet
assumptions
When to Nonparametric
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Tests with One MeanParametric 1-Sample t-test
3 assumptions (not equal variance)
NonparametricWilcoxon test
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Also called 1 mean t-tests
Compare collected dataset with a value
For example:
The FDA has issued fish consumption advisories for populations containing Hg levels greater than 1.0 ppm.
Tests with One Mean
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0 1 2 3 4
Blue marlin
Mako shark
Little tunny
Warsaw grouper
Greater amberjack
Blackfin tuna
Yellowfin tuna
Dolphin
5 10 15
8.3
Key
Mean
FDA(1.0)
Wahoo
King mackerel
Cobia
Gag grouper
Hg (ppm)
SD
Want to test whether Yellowfin tuna have levels of Hg below 1.0 ppm
Tests with One Mean
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H0: μAhi Hg = 1.0ppm
H0: μAhi Hg ≠ 1.0ppm
Tests with One Mean
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Tests with One MeanParametric 1-Sample t-test – uses the mean and variance (std. dev.) of raw data
NonparametricWilcoxon test – uses the median of the raw data
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Tests with Two MeansParametric - require 4 assumptions 2-Sample t-test
PooledUnpooledPaired
NonparametricMann-Whitney test
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How do we assess these 4 Assumptions:
1. Random Samples – Sampling design
2. Independent Samples – Sampling Design
3. Normal Populations - Normality
test*
4. Variances - Equal Variance test*
When to Parametric
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Tests with Two MeansCompare means from two groups of raw data H0: μurchins deep = μurchins shallow
Ha: μurchins deep ≠ μurchins shallow
Most widely applied statistical tests
Variety of Parametric tests (3)
Single Nonparametric test
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How do we assess these 4 Assumptions:
1. Random Samples – Sampling design
2. Independent Samples – Sampling Design
3. Normal Populations - Normality
test*
4. Variances - Equal Variance test*
Which Test to Run
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Paired T-testParametric t-tests – data not independentPaired t-test
For example:
Growth study on mark-recaptured ahi
July 2011 July 2012
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Paired T-testParametric t-testsPaired t-test
Conduct a paired t-test - If the samples are not independent
Used when there is a natural pairing of the members of two populations
Calculates difference between the two paired samples
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How do we assess these 4 Assumptions:
1. Random Samples – Sampling design
2. Independent Samples – Sampling Design
3. Normal Populations - Normality
test*
4. Variances - Equal Variance test*
Which Test to Run
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Normality Test
Weight
Perc
ent
6005004003002001000-100-200
99.9
99
95
90
80706050403020
10
5
1
0.1
Mean
<0.010
192.2StDev 110.5N 143RJ 0.955P-Value
Probability Plot of WeightNormal
H0 hypothesis: data normally distributed
If p value is less than α, then reject H0
Data does not follow a normal distribution
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Mann-Whitney T-testNonparametric t-testsMann-WhitneyCompare medians from two groups of raw data
H0: μurchins deep = μurchins shallow
Ha: μurchins deep ≠ μurchins shallow
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How do we assess these 4 Assumptions:
1. Random Samples – Sampling design
2. Independent Samples – Sampling Design
3. Normal Populations - Normality
test*
4. Variances - Equal Variance test*
Which Test to Run
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Parametric t-testsNon-pooled t-test
Conduct a Non-pooled t-test - you cannot “pool” the samples because the variances are not equal
In Minitab – do not check box – “Assume Equal Variances” when running 2-sample t-test
Which Test to Run
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Parametric t-testsPooled t-test
Conduct a pooled t-test - you can “pool” the samples because the variances are assumed to be equal
In Minitab - check box – “Assume Equal Variances” when running 2-sample t-test
Which Test to Run
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When Do I Do The What Now?
If all 4 assumptions are met:Conduct a pooled t-test - you can “pool” the samples because the variances are assumed to be equal
If the samples are not independent:Conduct a paired t-test
“Well, whenever I'm confused, I just check my underwear. It holds the answer to all the important questions.” – Grandpa Simpson
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When Do I Do The What Now?
If the variances (std. dev.) are not equal:Conduct a non-pooled t-test
If the data is not normal or has small sample size:Conduct a non-parametric t-test (Mann-Whitney)
“Well, whenever I'm confused, I just check my underwear. It holds the answer to all the important questions.” – Grandpa Simpson