jeopardy€¦ · jeopardy 10 assumptions 10 definitions / equations 13 test names 7 interpretation...
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JEOPARDY
10 Assumptions
10 Definitions / Equations
13 Test Names
7 Interpretation
1 Tie-Breaker
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Statistical Assumptions 1
What is the key assumption of all the nonparametric tests ?
- Random Sampling
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Statistical Assumptions 2
What does it mean to have a “random sample”? (2 criteria):
- Every sample (person / bug / quadrat) has the same (and equal) probability of being measured
-This probability of collecting one sample is independent from the probability of collecting any other sample
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Statistical Assumptions 3
What is the central assumption of all parametric tests ?
- Every sample comes from a population with a normal distribution
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Statistical Assumptions 4
How is this assumption applied to the paired t-test (dependent samples)?
- The differences between each subject’s two observations follow a normal distribution
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Statistical Assumptions 5
What other key assumption is central to the ANOVA (with independent data)?
- All the samples (populations) we are comparing have equal variances
- This is termed homoscedasticity
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Statistical Assumptions 6
How can we ensure we have equal variances before we do an ANOVA test?Hint: think rule of thumb
- Use equal sample size across all groups
- Compare the samples with the largest and the smallest variances. The ratio has to be smaller than 2: Vlarge / Vsmall < 2
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Statistical Assumptions 7
What sample size assumption underlies the contingency test (Chi-Square)?
- All expected cell counts (frequencies) > 1
- Over 80% of cell counts (frequencies) > 5
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Statistical Assumptions 8
What are the three key assumptions of the Pearson correlation ?
- Normally distributed data
- Linear relationship between x and y
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Statistical Assumptions 9
What are the three key assumptions of linear regression ?
- Normally distributed data
- Linear relationship between x and y
- Random distribution of residuals
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Statistical Assumptions 10
Why do we assume a large enough sample (or independent values) will be normally distributed ?
The Central Limit Theorem
In probability theory, the central limit theorem establishes that, when independent random variables are added, their sum tends toward a normal distribution, even if the original variables themselves are not normally distributed.
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Formulas 1
What is the Variance ?
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Formulas 2
What is the SE ?
S.E. : Standard Deviation / Sqrt (N)
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Formulas 3
What is the Z score ?
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Formulas 4
What is the covariance ?
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Formulas 5
What is the correlation coefficient ?
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Formulas 6
What is the equation of simple linear regression ?
𝑌𝑖 = 𝑏0 + 𝑏1𝑋𝑖 + 𝜀𝑖
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Formulas 7
What is the equation of b in simple linear regression ?
b =
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Formulas 8
What is the meaning and the equation of R2 ?
T
M
SS
SSR 2 =
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Formulas 9
What is the meaning and the equation of F ?
R
M
MS
MSF =
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Formulas 10
What is the meaning and the equation of the generic t –test statistic ?
t =
observed differencebetween sample
means−
expected differencebetween population means(if null hypothesis is true)
estimate of the standard error of the difference between two sample means
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Field’s Statistical Decision Tree
Name of test
Independent t test
Dependent t test
Independent Wilcoxon
Dependent Wilcoxon
One-way ANOVA
Kruskal Wallis
One Independent Variable
NOTE: there are other tests for paired data
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One Independent Variable
Field’s Statistical Decision Tree
Name oftwo tests
Pearson Correlation
Linear Regression
Spearman Correlation
Kendall’s Tau Correlation
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Statistical Decision Tree
Name of test
Two or MoreIndependentVariables
Multi-Way ANOVA
NOTE: there are other tests for paired data
Multiple Regression
Multiple Regression
ANCOVA &
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Interpretation 1
Are these data normally distributed ?What transformation would you use ?
This is a lognormal distribution.
Take the log of the data (y’ = log(y + c))
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Interpretation 2
What threshold value is needed to make skew.2SE and kurtosis.2SE significant (at alpha = 0.05) ?
skew.2SE kurtosis.2SE
P value
ABS > 0.98 < 0.05
ABS > 1 < 0.04
ABS > 1.29 < 0.01
ABS > 1.65 < 0.001
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Interpretation 3
What is wrong with these data ?
What approach will alert you of this problem ?
The relationship is not linear.
A plot of residuals will show you nonlinearities.
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Interpretation 4
What is wrong with these data ?
What approach will alert you of this problem ?
This outlier point has an excessive influence in this linear regression.
A box plot of the residuals.
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Interpretation 5
What is wrong with these data ?
What approach will alert you of this problem ?
This point has an excessive influence in this linear regression.
Cook’s distance will alert you, when values > 1.
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Interpretation 6
Is this result from a regression significant ? Why / why not?
95 percent confidence interval: 0.2 2.2
sample estimates: slope 1.0
YES: value of 0 cannot fit into the 95% CI
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Interpretation 7
Is this result from a fisher’s exact test significant ? Why / why not?
95 percent confidence interval: 0.2 2.2
sample estimates: odds ratio 1.0
NO: value of 1 fits into the 95% CI
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Tie-Breaker
How do we calculate the intercept for a linear regression equation ?
Slope = Covariance / (variance x): 4.25 / (1.67 * 1.67) = 1.52
The linear regression equation is: Y = alpha + 1.52 * x
X-mean = 5.4 and Y-mean = 11.0
alpha= 11.0 – (1.52 * 5.4)alpha = 11.0 – 8.2 = 2.8
Y = 2.8 + 1.52 * X