Test significant difference in mean across values of categorical variable using summary dataset

[annisann]

/* 

I have a dataset that contains summarized data on a group of people who received 

healthcare services. The data is summarized by several characteristics of the people,

such as race, gender, marital status, etc. In my example below, I have created a

fake dataset of the summary race data.

Race is a character variable with different values of race (race A, race B, etc.).

Population_total is the number of individuals (n)  in the particular race category. 

Service_min is the number of healthcare service minutes summed across all individuals in the race category.

Min_per_pop is the average number of service minutes per individual in the race category:

min_per_pop = service_min / population_total

What is the best way to determine whether there is a significant difference in service

minutes across the categories of race, using this summary data? 

*/

data summarydata;
length race $6 population_total 8 service_min 8 min_per_pop 8;
input race $ population_total service_min min_per_pop;
infile datalines dsd dlm='|' ;
datalines;
race_A|42188|94961594|2250.9148
race_B|13820|32049662|2319.0783
race_C|7062|9109865|1289.9837
race_D|350|516013|1474.3229
;
run;

/* I have tried a one-way ANOVA using both proc glm and proc anova per the following code, 

but they do not return any p-value or significance test results. The F value and p-value are blank.

*/

proc glm data=summarydata;
class race;
model min_per_pop = race;
run;
quit;

proc anova data=summarydata;
class race;
model min_per_pop = race;
run;
quit;

/* I have also tried proc logistic, using the counts instead, but it creates this error:

ERROR: No valid observations due either to missing values in the response,

       explanatory, frequency, or weight variable, or to nonpositive frequency or

       weight values.

*/

proc logistic data=summarydata;
class race;
model service_min/population_total =race;
run;

/* What am I doing wrong? Or what is a better way to test for significant differences?

I also know there is a macro %SUM_GLM that can be used for a one-way ANOVA on summary

data, but it requires the standard deviation, which I do not have. I only have the 3 numeric measures above.

*/

[PaigeMiller · Accepted solution]

If you don't have a standard deviation of the minutes (or the raw data), then you cannot perform a statistical test.

[annisann]

thank you!

[Ksharp]

You need MEANS statement of PROC GLM to do ANOVA h-test and LSMEANS statment  to "Test significant difference in mean across values of categorical varia".

I also noticed that there are only one obs for one race in your dataset,
You need include 'Population_total ' variable in PROC GLM via FREQ statement.

proc glm data=have ;
class race;
model min_per_pop = race;
means race / hovtest=levene(type=abs) tukey;
freq Population_total ;
quit;

And LSMEANS statement.

data have;
length race $6 population_total 8 service_min 8 min_per_pop 8;
input race $ population_total service_min min_per_pop;
infile datalines dsd dlm='|' ;
datalines;
race_A|42188|94961594|2250.9148
race_B|13820|32049662|2319.0783
race_C|7062|9109865|1289.9837
race_D|350|516013|1474.3229
;
run;
proc glm data=have ;
class race;
model min_per_pop  = race;
means race / hovtest=levene(type=abs) tukey;
lsmeans race/adjust=tukey;
freq Population_total ;
quit;