whether Y(employees injured) variation is due to X1(job function) or X2(population)

[Zznn]

Here is the actual question-
There are 1000 employees in a firm, and the firm has four departments namely D1, D2, D3 and D4 with 100, 200, 300, 400 employees respectively.
Now, each employee is explained about what constitutes an injury(for this experiment). Then, each employee is asked whether they were injured in last year. Their responses grouped according to the departments they are in -
D1= 10, D2= 20, D3= 30, D4=40,

It is to be noted that each department has different job function like for example D1 is HR department, and D4 is machining department.

Now, we have to determine whether no. of employees injured in each department (variation) is due to- Job function of the departments OR Population of the department?

PS- I'm new to statistics, so this question can be very easy or trivial, it would definitely help me a lot if any could guide me on this. Thanks in advance.
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This has been my thought process-
Y= No. of employees injured last year.
X1= Population (of employees) in department
X2= Job function of the department

both Y and X1 are numerical variables and X2 is categorical.
If we find correlation coefficient of Y with X1 and Y with X2, it will be same. So we have to think of other way.
Also, I think in this case there is collinearity between X1 and X2, which may cause one of the variable to be redundant or rather both X1 and X2 imply same thing.

So, I'm kind of stuck with here. Any help regarding this question would be deeply appreciated.

 

[Miner]

Re: whether Y(employees injured) variation is due to X1(job function) or X2(populatio

Hint: to separate the effect of population from job function, try converting counts to percentages.

 

[Zznn]

Re: whether Y(employees injured) variation is due to X1(job function) or X2(populatio

but the counts of injured will be same as percentage of injured in a department with total injured, as total no. of injured = 100

 

[Miner]

Re: whether Y(employees injured) variation is due to X1(job function) or X2(populatio

D1 = 10/100 = 10%
D2 = 20/200 = 10%
D3 = 300/300 = 100%
D4 = 40/400 = 10%

Even without performing the statistical tests, it appears that D3 has a serious issue.

 

[Zznn]

Re: whether Y(employees injured) variation is due to X1(job function) or X2(populatio

Sorry there is a typo actually D3 has 30 injured not 300, I have corrected it now in question

 

[Miner]

Re: whether Y(employees injured) variation is due to X1(job function) or X2(populatio

In that case:

D1 = 10/100 = 10%
D2 = 20/200 = 10%
D3 = 30/300 = 10%
D4 = 40/400 = 10%

There is zero difference by function (based on percentages). All differences are driven by population (based on counts).

 

[Zznn]

Re: whether Y(employees injured) variation is due to X1(job function) or X2(populatio

can you please explain why you have considered job function to be represented by percentages and population by counts.
It was mentioned in the question that the job function are distinct with different level of stress/risk.

 

[Dason]

Re: whether Y(employees injured) variation is due to X1(job function) or X2(populatio

It was mentioned in the question that the job function are distinct with different level of stress/risk.

And yet regardless of the job there was only 10% injured in each department. Think about that for a second. If you're trying to see which department is most dangerous and you go to each of them and are like "what's the chance that an employee in this department is injured this year" and they all answer 10% is there really a different "risk" of injury for each department?

 

[rogojel]

Re: whether Y(employees injured) variation is due to X1(job function) or X2(populatio

hi,
are the numbers correct? It seems a bit suspicious that the number of injuries is a multiple of 10 in each department. Is there anything special about the 10% value for instance - like a requirement that one needs to do something extra if the percentage is above 10%?

regards
rogojel

 

[Zznn]

Re: whether Y(employees injured) variation is due to X1(job function) or X2(populatio

And yet regardless of the job there was only 10% injured in each department. Think about that for a second. If you're trying to see which department is most dangerous and you go to each of them and are like "what's the chance that an employee in this department is injured this year" and they all answer 10%
is there really a different "risk" of injury for each department?

Actually, it was an interview question asked to me and interviewer specifically said that each job function has different STRESS level(RISK was my interpretation of this) with examples like Machining department and HR department.
However, I duly concur with your explanation but I think the answer should be somewhat "less straightforward", and probably require some concepts of statistics, because at one point of time in interview I was asked several statistics question and this was one of them.
It may be the case that interviewer might have thought of this question instantaneously, which can explains such loose definition of question.

 

[Zznn]

Re: whether Y(employees injured) variation is due to X1(job function) or X2(populatio

hi,
are the numbers correct? It seems a bit suspicious that the number of injuries is a multiple of 10 in each department. Is there anything special about the 10% value for instance - like a requirement that one needs to do something extra if the percentage is above 10%?

regards
rogojel

Hi,
Yes , the numbers are correct according to me, as mentioned in other post- interviewer might have thought of this question instantaneously and nothing specific was mentioned about this 10% values.