Topic 8 Analysis of Means Normally Distributed Not Normally Distributed One sample vs population One sample ttest Wilcoxon Signed Rank Two paired samples Paired ttest Difference then Signed Rank ID: 591040
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HRP 223 - 2008
Topic 8 – Analysis of MeansSlide2
Normally Distributed
Not Normally Distributed
One sample vs. populationOne sample t-testWilcoxon Signed RankTwo paired samplesPaired t-testDifference then Signed RankTwo unpaired samplesT-testWilcoxon Rank-sumThree or more unpaired samplesANOVAKruskal-WallisThree or more paired samplesMixed effectsTransform then mixed model
Normally DistributedNot Normally DistributedOne sample vs. populationDescribe > DistributionDescribe > DistributionTwo paired samplesAnalyze >ANOVA>t-testDescribe > DistributionTwo unpaired samplesAnalyze >ANOVA>t-testDescribe > DistributionThree or more unpaired samplesAnalyze >ANOVA>LinearAnalyze >ANOVA>Nonpar.Three or more paired samplesAnalyze >ANOVA>Mixed
One Categorical PredictorSlide3
Multiple Categorical Predictors
Unpaired samples
ANOVAPaired samplesMixed Effects ModelsIf data is not normally distributedThere are spcialized statistics (Friedman’s test for 2 predictors).Try to transform into normally distributed.Slide4
Mean vs. Expected BMI
It would be nice to see the actual Excel file.Slide5
Adds a link to source
Adds a link to source and runs import wizard
This gives instant access to the current state of the spreadsheet but it is bugged if you mix character and numeric data.Slide6
Take a Look at the DataSlide7
Prior to analysis, do all 3 plots.
Histograms and box plots show outliers and bimodal data but are not ideal for assessing normality.
The formal tests for normality are not great. They will not find problems with small samples and will declare problems with large samples.Slide8Slide9
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1. normal distribution
2. skewed-to-the-right distribution
3. skewed-to-the-left distribution
4. heavy-tailed distribution
5. light-tailed distribution
Image from: Statistics I: Introduction to ANOVA, Regression, and Logistic Regression: Course Notes. SAS Press 2008.Slide10
Inference 101
You only have one sample but you want to make inferences to the world.
Given what you see in this sample, you can guess what the distribution of samples looks like around the null distribution.Slide11
If the population you are sampling from has a mean of 4, you will not observe a score of 4.
How do you compare this sample vs. another with a mean of 5?
Make a histogram of the meansSlide12
.75/sqrt(1) = .75
.75/sqrt(5) = .34
.75/sqrt(25) = .15Distributions of the MeansSlide13
Precision
Think of the “+/- something” imprecision in the estimates of the political polls.
You typically end up saying you are 95% sure you chose an interval that has the true value inside the range bracketed by the confidence limits (CLs). Either the population value is or is not in the interval between the lower and upper confidence limit, and if you repeated the process on many samples, 95% of such intervals would include the population value. The 99% CI is wider (more accurate) than the more precise 95% CL.Slide14
Confidence Intervals from 10 Samples
Axis with units showing your outcome
You want to set the width of the interval so that in 95% of the experiments, the confidence interval includes the true value.In theory, you tweak the interval and increase or decrease the width.
The unobservable truthSlide15
Benefits of CLs
You have information about the estimate's precision.
The width of the CI tells you about the degree of random error which is set by the confidence interval.Wide intervals indicate poor precision. Plausible values could be across a broad range.Slide16
Estimation vs. Hypothesis Testing
P-value < .05 corresponds to a 95% CL that does not include the null hypothesis value.
CLs show uncertainty, or lack of precision, in the estimate of interest and thus convey more useful information than the p-value.Slide17
CLs vs. p-values
null value
Upper CLLowerCLConfidenceintervalP > .05 and the null value is inside of the confidence limits (CLs)null valueUpper CLLowerCL
ConfidenceintervalP < .05 and the null value is not inside of the confidence limits0 difference between groups or odds ratio of 1Slide18
null value
zone of clinical
indifferenceNot statistically significant and not clinically interesting
Not statistically significant, possibly clinically interestingStatistically significant but not clinically interestingStatistically significant and clinically interestingSlide19Slide20
Compare Two Teachers
Import the data
Describe the data Assign the method as a classification variableDo an unpaired T-testDo a one-way ANOVA with the predictor having only two levelsSlide21Slide22Slide23Slide24Slide25
SS total is the sum of the distance between each point and the overall mean line squared.
SS error is the sum of the total squared distances between each point and the group mean lines.Slide26Slide27Slide28Slide29
Psoriasis
Scores are arbitrary numbers 0 = < 0% response, 5 = 26-50% response, etc.Slide30Slide31Slide32
If and only if you work on a fast machine!Slide33
Weight GainSlide34Slide35Slide36Slide37Slide38Slide39Slide40Slide41Slide42
Postpartum DepressionSlide43
After the FormatsSlide44Slide45Slide46Slide47Slide48Slide49
DementiaSlide50Slide51Slide52Slide53Slide54
Wide to Long
You may have noticed that the data for these analyses are all set up as long, skinny files where there is a record for every observation on a patient. Some people store data as wide records with many variables with a single record for each person.
To convert from wide to long:Do data step processing with arrays. Use the Transpose option on the Data menu.Combine proc transpose and data step code.Use a macro I wrote. (It is brand new, so check it.)Slide55
Tolerance.sas7bdat is dataset from the book
Save a copy of the macro in a file after the fill in the blanks are done.Slide56
The stuff in the blah.sas file:
The stuff in the macro file:Slide57
tol
:
all variables starting with the letters tolSlide58
Narrow to Wide
Of course you can transpose back to wide from narrow.
If you download the keyboard macros today you will see that proc transpose now gives you a code template.