1. Finding Geometric Means Using SAS
Better Than Average
Finding Geometric Means Using SAS

2. What are we trying to say with an “average”?
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Expected Value

3. Common Types of “Averages”
Median: Middle element of ordered data
Mode: Value most often seen in a data set
Main advantages: not influenced by extreme values, can be used for any type of distribution
Main disadvantage: Insensitive, gives no information about your distribution
Images: source

4. Common Types of “Averages”
Arithmetic Mean: Calculated from the sum of values divided by the number of values in a data set
Main advantages: Easy to understand and uses all observations, can give information about your distribution
Main disadvantages: Easily skewed by outliers and inaccurate if working with non-Normal data
Image: source

5. What is a geometric mean?
Geometric Mean: Calculated by taking the nth root of the product of n positive observations in a data set
Main advantages: Precise, but not influenced by extreme values
Main disadvantages: More difficult to understand, all
values must be non-zero and positive
Image: source

6. Geometric Series: Each number increases by the same proportion (3)
(3, 9, 27, 81, 243)

7. When should I use the geometric mean?
Non-Normal/skewed data
Ratios or proportions/scaled data
Small sample sizes
Source

8. Bioassays/dose-response curves Population growth
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Compounding interest
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Decay rates
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Scaled bioequivalence
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Survival analysis
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9. ..but data is messy! Use your judgement in selecting your “average.”
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10. What if my data contains zeroes?
0 ×𝑛=0
Adjust your scale so that you add 1 to every number in the data set, and then subtract 1 from the resulting geometric mean.
Ignore zeros or missing data in your calculations.
Convert zeros to a very small number (often called “below the detection limit”) that is less than the next smallest number in the data set.

11. What if my data contains negative numbers? −1 =𝑖
If all values are negative, simply convert all values to positive numbers before calculating the geometric mean. Then assign the resulting geometric mean a negative value.
If your data set contains both positive and negative values, you will have to separate them and find the geometric means for each group, and you can then find the weighted average of their individual geometric means to find the total geometric mean for the full data set.

12. How can I use SAS to compute geometric means?
Geomean() or Geomeanz() functions
PROC SURVEYMEANS
Manual calculations
Source

13. Finding the geometric mean for an observation/row: Geomean() or Geomeanz() Functions
Returns the geometric mean of a numeric constant, variable, or expression
If any arguments are negative, result is a missing value
If any arguments are zero, result is zero
Fuzzes the values of arguments that are extremely small and approximately zero—if you do not want this, use the geomeanz() function
Skips missing values

14. input studyid var1 var2 var3 var4 var5;
DATA my_data;
input studyid var1 var2 var3 var4 var5;
geometric_mean = geomean(of var1-var5); *Calculates geometric mean;
datalines; ;
run;
PROC PRINT data=my_data;
id studyid;
Note that you can use “OF” for a list of variables

15. Finding the geometric mean for a population/column: PROC SURVEYMEANS
The geomean option within PROC SURVEYMEANS returns the geometric mean of the specified variables.
*Values must be non-zero and positive
You can also request confidence limits for the geometric mean
GMCLM requests the 2-sided confidence limits
LGMCLM requests the 1-sided lower confidence limit
UGMCLM requests the 1-sided upper confidence limit

16. PROC SURVEYMEANS data=my_data geomean;
var var1 var2 var3 var4 var5;
run;

17. Which measure of variation should I use?
Standard error: how precise is the calculation of the geometric mean
Standard deviation: how spread out is the data around the geometric mean
Coefficient of variation: how does the variation for this geometric mean compare with another data set

18. Geometric Standard Error
Output by default in PROC SURVEYMEANS

19. Geometric Standard Deviation
Find the natural log of your variable using the log() function in the DATA step:
DATA my_data2;
set my_data;
ln_var1 = log(var1); *Calculates the natural log of variable 1;
run;

20. Geometric Standard Deviation
2. Use PROC MEANS to find the arithmetic mean and standard deviation of your newly log-transformed variable:
PROC MEANS data=my_data2 mean stddev; *Specifies output;
var ln_var1;
output out=meansout mean=a_mean stddev=a_stddev; *Creates new data set;
run;

21. Geometric Standard Deviation
3. Exponentiate the arithmetic mean and standard deviation to find the geometric mean and geometric standard deviation, using the EXP() function in the DATA step:
DATA my_data3;
set meansout;
geo_mean = exp(a_mean); *Converts to geometric mean;
geo_stddev = exp(a_stddev); *Converts to geometric standard deviation;
run;
PROC PRINT data=my_data3 noobs;
var geo_mean geo_stddev;

22. Applying the Geometric Standard Deviation
Geometric Mean ± Geometric Standard Deviation =INCORRECT!

23. Applying the Geometric Standard Deviation
The geometric standard deviation is multiplicative, NOT additive:
Lower bound = geometric mean ÷ geometric standard deviation
= ÷ =
Upper bound = geometric mean x geometric standard deviation
= x =
Resulting range for one geometric standard deviation
is (91.24, )

24. Geometric Coefficient of Variation
𝐺𝑒𝑜𝑚𝑒𝑡𝑟𝑖𝑐 𝐶𝑉= 𝐺𝑒𝑜𝑚𝑒𝑡𝑟𝑖𝑐 𝑆𝐷 1 𝐺𝑒𝑜𝑚𝑒𝑡𝑟𝑖𝑐 𝑀𝑒𝑎𝑛
Reduce the geometric standard deviation to the power of the reciprocal of the geometric mean in the DATA step:
DATA my_data4;
set my_data3;
geo_cv = geo_stddev**(1/geo_mean); *Calculates geometric CV;
run;
PROC PRINT data=my_data4 noobs;
var geo_cv;

25. To sum up:
Use geometric means for data that is lognormal or uses ratios or proportions
Make sure your values are non-zero and positive
Use your judgement in choosing the mean to express your expected values when working with messy data
Source

26. Questions?

27. Contact Information
Name:Kimberly Roenfeldt Company: Henry M Jackson Foundation for the Advancement of Military Medicine City/State: San Diego, CA Phone: (619)