Data Type

A. Non-Parametric - QUALITATIVE/CATEGORICAL (sex)

B. Parametric - QUANTITATIVE/NUMERIC - DISCRETE (yes/no), RANK (grade, pain), or CONTINUOUS (age)

Paired Measurements: Change = Post - Pre 

Percent Change = ((Post - Pre)/Pre) * 100

Meaure of a 'typical value', Sum of all observations divided by total count

Measure of centrality, Order data, midpoint of all data values, low impact from outliers

How much the average data value varies from the mean? Square root of variance.

P-value

The probability of rejecting the null hypothesis when the null hypothesis is true.

Inferential - The probability that the test statistic would be equal to an extreme value than that actually observed. I.E. the smallest level alpha at which the data is significant.  

For example, if testing value is 0.507, two-sided, with p-value of 0.37 for coin toss, then the coin toss is what is expected within 95% of the time if the coin was fair (meaning probability of heads is 0.5).  We do not reject the null of 0.5  value.

The smaller the p-value, the stronger the evidence against the null hypothesis. 

PROC MULTTEST user guide, Article

Correlation

Relationship between two variables

Add the FISHER option to PROC CORR to include confidence intervals.

R-square - the coefficient of determination in a regression model, measures the proportion of variability in the response that is explained by the regressor variables.  R-square statistics also play an important indirect role in regression calculations. For example, the proportion of variability explained by regressing all other variables in a model on a particular regressor can provide insights into the interrelationship among the regressors.

Adjusted R-square - This is an adjustment of the R-squared that penalizes the addition of extraneous predictors to the model.  Adjusted R-squared is computed using the formula 1 - ((1 - Rsq)(N - 1) /( N - k - 1)) where k is the number of predictors.  See PROC REG User Guide. (Output Datasets)

Used to indicate the range of likely values for a statistic.  For example, a 95% confidence interval on the mean would indicate the upper and lower bounds that you can expect to encompass the means of many samples 95% of the time.

Level of confidence - 90%, 95%, 99% of the mean or proportion

Forest Plots show the magnitude of benefit and confidence limits of each subgroup analyzed.  Also see Forest macro for statistical plot.

PROC MEANS DATA=test NOPRINT NWAYS ALPHA=.05;
 CLASS trt; 
 VAR age;
 OUTPUT OUT=xxtmp N=n  MEAN=mean STDERR=stderr LCLM=lclm Uclm=uclm; RUN;

Proc Means, Proc Freq, Proc TTest for differences between two independent sample means, Proc GLM - General Linear Model, Proc NPar1way

SAS Paper, SAS Paper 2, SAS Paper 3

 CV = 100 * (sample standard deviation) / sample mean

Reference 1, Reference 2, Paper, 9.3 Function

 Least Squares Mean

 proc glimmix;
   class a b block;
   model y = a b a*b /  s;
   random int a / sub=block;
   lsmestimate A 'a1 vs avg(a3, a4)' 2 0 -1 -1 divisor=2;
run;

Reference 1, Paper

Hazards / Odds Ratio

Hazard Ratio (HR) is the relevant risk of experiencing an event being measured (e.g. death) between two groups. 

HR=1 means no difference

HR < 1 means there was a reduced risk in one of the treatment arms

HR > 1 means an increased risk in of the treatment arms

Odds Ratio (OR) is the ratio of an event happening compared to an event not happening in the sampled population.

 proc glimmix;
   class A;
   model y = A x A*x / dist=binary oddsratio;
 run; 

* Another example; 

ods output "Odds Ratios"=orci;
 proc logistic data=uis descending; 
  model dfree=age beck ivhx ndrugtx race treat site ;
 run;
 data orci;

 set orci;
 effect=upcase(effect);
 run;

Reference 1, Paper, Paper 2, Paper 3

Cox Regression model provides us with estimates of the effect that different factors event (eg. age, weight, sex, etc.) have on the time until the end.

Build a multiple regression model to predict the cost of a car.

PROC REG DATA = cars ;
MODEL invoice = Cylinders EngineSize Horsepower Length MPG_City
MPG_Highway Weight Wheelbase dummy: / SELECTION=stepwise;
RUN ;

Descriptive vs. Inferential

Descriptive Statistics

Inferential Statistics

Inferential Statistics 

Inferential Statistics 

(Modeling)

One, Two vs. Three or More Samples, Parametric vs. Non-Parametric, Mean/Proportion/ Standard Deviation

Single Measurement

Difference Between Two Measurements

Relationship Between Two Measurements

Difference Between Three Measurements w/wo Covariates(ANOVA)

PARAMETRIC (Normal Distribution)

Mean (numeric)

T-Test (One Sample vs. Fixed value)

PROC TTEST

(Example) 

(Annotate)

T-Test (Paird, Un-Paired)

PROC TTEST 

(Example)

Pearson R (Two Samples)

PROC FREQ

(Annotate)

F-Test (Three or more Samples)

PROC ANOVA (balanced)

(Annotate)

PROC GLM (unbalanced)

(Annotate)

PROC MIXED

PROC REG

(Annotated)

Proportion (category)

 Z-Test (One Sample vs. Fixed value)

 Chi-Square/ Fisher's Exact (Two Samples)

PROC FREQ

 Chi-Square/ Fisher's Exact (Two Samples with 2 levels)

PROC FREQ

Cochran–Mantel–Haenszel statistics (CMH) (Two Samples with > 2 levels) 

PROC FREQ

Standard Deviation (numeric)

 Chi-Square/ Fisher's Exact (One Sample vs. Equal values)

PROC FREQ

 F-Test (Two Samples)

PROC ANOVA

 NONPARAMETRIC (Non-Normal Distribution)

Mean (numeric)

Wilcox/Mann-Whitney U (One Sample vs. Fixed value)

PROC NPAR1WAY

Sign Test (Two Samples) 

PROC NPAR1WAY

(Annotate)

Spearman r (Two Samples)

PROC CORR

(Annotate)

Proportion (category)

Mann-Whitney U (Two Samples)

Standard Deviation (numeric)

Kruskal-Wallis (One Sample vs. Fixed value)

PROC NPAR1WAY

Kruskal-Wallis (Two Samples)

PROC  NPAR1WAY

COMPARE PRODUCT DISTRIBUTION: Which products accounted for the largest share of total company sales? 

COMPARE PRODUCT SALES: Which products were top performers based on total sales?

COMPARE PRODUCT GROUP SALES: When comparing shoes and slipper sales, which customer had higher sales?

When comparing shoes and slipper sales for selected customers, which customers had high sales?

What is the relationship between sales and expense?

Horizontal Bars

  Vertical Bars 

  Scatter Plot  

COMPARE TIME PERIODS: How much have sales risen this year?

Across time, how do shoe sales compare with slipper sales?

Kaplan-Meier curve is a graphical representation of a time to event analysis showing when a patient reaches a trials survival endpoint. 

How do survival times compare between two treatment groups - Alive/Dead/Withdrawn? In general survival analysis is based on one Event such as Death.

Censor observations means that the patient did not reach the event, or is still alive and the exact failure time is unknown. If patient is still alive, then patient is censor=0.  The days is based on the last follow-up date.  The alternative is setting censor=1;

Non-censored observations means that the patient reached the event or died.  The censor=1 and the days is their death date.  The alternative is setting it in reverse, censor=0; Note that it is possible to have several non-censor values to indicate different events such as 0=death, 1=completed study, 2=adverse event, 3=lost to follow-up.

For each censor=1 value over time, the 100% survival from time 0 is reduced. 

  Vertical Bars

        Line

Survival Analysis

(Annotate)

 Beginner SAS Programmer

 Advanced SAS Programmer

 Macro SAS Programmer