Find statistical dferences between days

[jonatan_velarde]

I have this dataset:

data have;
length day$ 20;
input week day$ sell_item;
format sell_item sell_item_.;
datalines;
1 Monday 6
1 Tuesday 51
1 Wednesday 69
1 Thursday 68
1 Friday 28
1 Saturday 16
1 Sunday 94
;
proc freq data=have;
tables day / nopercent norow nocol deviation expected chisq;
weight sell_item;
run;

here i see information of selling items in a store. Regarding chi squared test, can be found statistical significance (p<0.01), but i would like to estimate individual difference of selling between each day.

thanks in advance

[sbxkoenk]

The Chi-Square Test you do is testing for Equal Proportions.

Here's how to compare two proportions in SAS (between two days if you want):

• https://blogs.sas.com/content/iml/2017/07/05/test-equality-two-proportions-sas.html
• https://support.sas.com/kb/22/561.html

I haven't read above blog and usage note myself (I'm in a hurry) but it may be that you still have to correct for an inflation of the TYPE-I error when doing multiple comparisons (like a BONFERRONI correction).

Cheers,

Koen

[PaigeMiller]

You can't find a statistical difference between days unless you have replicates of Monday, and replicates of Tuesday, and so on.

[jonatan_velarde]

I thought the same my friend, later i posted current question.

What can be done with this code:
data have;
length day$ 20;
input week day$ sell_item;
format sell_item sell_item_.;
datalines;
1 Monday 6
1 Tuesday 51
1 Wednesday 69
1 Thursday 68
1 Friday 28
1 Saturday 16
1 Sunday 94
2 Monday 16
2 Tuesday 41
2 Wednesday 29
2 Thursday 28
2 Friday 78
2 Saturday 6
2 Sunday 4
3 Monday 16
3 Tuesday 71
3 Wednesday 19
3 Thursday 18
3 Friday 18
3 Saturday 36
3 Sunday 64

;
proc freq data=have;
tables day / nopercent norow nocol deviation expected chisq;
weight sell_item;
run;

[PaigeMiller]

Okay, what hypothesis do you want to test to determine if the difference between days is statistically significant?

[jonatan_velarde]

Hypothesis: At least 1 day has better sells at week.

[StatDave · Accepted solution]

For that hypothesis you only need the Type 3 test for DAY from this code:

proc genmod data=have;
class day;
model sell_item=day/dist=poisson type3;
run;

[Ksharp]

Also could try TESTP= option:
proc freq data=have;
tables day / testp=(.....);
weight sell_item;
run;

[StatDave]

If there is only the one predictor, then you can fit a Poisson model. Note that in this case, the model is saturated, so the predicted values are exactly the observed values.

proc genmod;
class day;
model sell_item=day/dist=poisson;
lsmeans day / diff ilink; 
run;

If there is a second categorical predictor, resulting in a 2-way table with your SELL_ITEM variable giving the cell counts, then this note shows ways you can proceed, including analyzing subtables or fitting a model.