What are the types of statistical tests/analysis which I can do here ?

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Slim Jim

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Dear All,

I am writing my Master Thesis on the concept of 4-day work week...this is about how employees instead of working 5 days a week...work only for 4 days a week...since the concept is relatively new..mine is an exploratory study...

In this study there are three parts -

Part 1 - I cover the advantages and disadvantages of the concept..
Part 1 has its own separate research question...

Part 2 - I discuss about the two real-world trials which were carried out on the concept...
Part 2 has its own separate research question...

Part 3 - Since the concept is new and not widely used..in this part I try to judge the employee's perception about the concept of four-day work week...that is how they view working as per a four day work week..

Part 3 again has a separate question which is " How do employees in Australia perceive the concept of 4 day work week ?"

There are no other hypotheses in my Project...only the above Research Questions...which are different for each of the 3 parts

I have to answer the research question of Part 3 with an online survey whose questionnaire I have already prepared.. I have not started passing the survey around.. just in case I need to change anything in it.. that is make some questions mandatory or not...Although I am not sure how many qualified responses would be enough..but I plan to gather closely 130-140 responses(a qualified response is a response in which it is established that the person is currently an employee in Australia or has previously been an employee in Australia)..i will check this later...at this stage i need to be little bit clear about the analysis part...

The overall objective of my Thesis/study is to develop set of general guidelines for employers who are trying to implement this concept in order to help them understand whether if it makes sense to implement the concept of 4 day work week or not and if they want to implement it what are the factors that they need to consider..
For my Survey, I have established that there are 6-7 independent variables and there is only a single dependent variable.

To explain what I need to do and for sake of simplicity, I list only 2 Independent variables and the 1 Dependent variable as below -

Independent Variable 1 - Category under which the respondent's employer can be categorized into ?
Option 1 - Government
Option 2 - Private
Option 3 - Other

Independent variable 2 - Respondent's gender ?
Option 1 - Male
Option 2 - Female
Option 3 - Other

Dependent Variable - Willingness of the employee to work as per a Four day work week ?
Option 1 - Yes
Option 2 - No
Option 3 - Maybe

I will take the survey only once and after I have all the responses I will start analysis and developing my guidelines

Depending on the responses of the survey and the analysis I would like to see for eg. -

If there are people who have selected their employer type as "Government" and said that they are not willing to work as per a 4-day work week..
Then my guideline would include something like - Employers who are Government entities need to be vary of adopting a four-day work week as employees do not seem to like it..

Similarly if the respondents select "Government" as their employer type and for willingness to work as per four-day work week ..select "Yes".. then my guidelines would be Employers who are Government entities need to consider implementing a four-day work week as the study shows that the employees are in favour of it...

Similarly for Employer type "Other" and when they select willingness - Yes or No ..then a recommendation accordingly...

So ..

Government v/s. Yes
Government v/s. No
Government v/s. Other

Hence, whichever option stands out I can give out a recommendation accordingly...

Similar type of analysis for the Gender variable against the willingness variable...

Additionally similar analysis for all the other independent variables against the dependent variables of Willingness..

My professor has told me that I need to do statistical analysis..what exact type he did not specify..and I cannot ask him at this moment...i need to present him something and then maybe he gives me a feedback...However, in my case considering the stage I am currently in...my Research Objective and my Research Questions and the Survey Questionnaire will not change..so i think for Part 3 - doing analysis as above will be most appropriate and in line with my Research Question and the Research Objective -

Hence, in my case can anyone tell me what type of Statistical Analysis or Tests i need to do in order to check the variables as described above ?

If you require any additional information, please let me know.

Thanks,
 
Basically, your professor wants you to test whether the variable is statistically significant in predicting the response.
1) The chi-squared test can be used to select categorial features for classification problems.
2) You can check the correlation plots between the variables
3) You can build a predictive model to eliminate the variables via some common criteria such as AIC, BIC, R^2 adjusted, p-value, etc...
 
@BigBeachBananas Thank you for your response..

I will do some more research on 2) and 3)...however what is AIC, BIC, R^2 adjusted, p-value, etc.? Sorry but i am a complete newbie wrt statistics...

Additionally, will 2) and 3) help me to derive analysis as mentioned above.. ?

I also considered the chi square test option that is one Independent variable at a time with a Dependent variable...but if understand correctly a chi square test will only tell me whether if the variables that is for e.g. Gender and Willingness are related/associated to each other..but not exact details that is for e.g. "Male" category of Gender is related/associated to "Yes" category of "Willingness"..hence i dropped the idea of chi square tests...
 
I just noticed a important detail in my Thesis Supervision Guide which I have received from the professor -

I quote the following sections from it:

"Primary data are best presented in tables and figures. You will subsequently apply the methods for data analysis described in the Research Design section to the results to gain de-rived data, such as a statistic.

However, don't use statistics unless you have a reasonable sample size. The minimal sample size is determined by the required precision and confidence interval, the population size, and the sample proportion. Recommendations for random sampling are given in Table.

Margin of Error Size of Population
-------------------------------------------------------------------------------------------------------------------
200 500 1000 5000 >5000
-------------------------------------------------------------------------------------------------------------------
± 3% 170 340 520 900 1100
± 5% 130 220 280 360 390
± 10% 65 80 90 95 100


In this case,

1) How can I know what is the margin of error for my population...that is employees in Australia ? How to calculate it ?

2) If I get for e.g. margin of error as ± 5%, does this mean that I need to collect atleast 390 responses for my survey in order to do statistical analysis ?

3) If I presume the answer for 2) as Yes...and if I do not have 390 responses for my survey...then i need to do just descriptive statistics..am i correct ?

Thanks,
 
Slim Jim said:
1) How can I know what is the margin of error for my population...that is employees in Australia ? How to calculate it ?
Click to expand...
The table shows how many you need for data. Depending on how much tolerance for error, you are required to have 3%, 5%, or 10%.
Slim Jim said:
2) If I get for e.g. margin of error as ± 5%, does this mean that I need to collect atleast 390 responses for my survey in order to do statistical analysis ?
Click to expand...
Correct, let's say you want a 5% margin error, and the population of Australia is >5000, then you need 390. If less than 390, you haven't met the requirement. Observe the table, the smaller margin of error, require more sample size.
Slim Jim said:
3) If I presume the answer for 2) as Yes...and if I do not have 390 responses for my survey...then i need to do just descriptive statistics..am i correct ?
Click to expand...
The margin of error is a statistical test. Let's say 60% of your surveyors say they prefer to work 4-days. This margin error means that now you know with 95% confidence that 55% to 65% of the total population prefer 4-days.
 
@BigBeachBananas Thank you for the clarification..

When it is said that "Recommendations for random sampling are given in Table".. doesn't it mean that if for e.g. if I collect 200 responses and the margin of error is 10% as per the table...then from my 200 responses only 180 responses will be correct that is only 180 responses are valid for my analysis ..and since this 180 is greater than 100(the criteria for 10% error rate) then then I need to do statistical analysis..

is this correct ?
 
Slim Jim said:
@BigBeachBananas Thank you for the clarification..

When it is said that "Recommendations for random sampling are given in Table".. doesn't it mean that if for e.g. if I collect 200 responses and the margin of error is 10% as per the table...then from my 200 responses only 180 responses will be correct that is only 180 responses are valid for my analysis ..and since this 180 is greater than 100(the criteria for 10% error rate) then then I need to do statistical analysis..

is this correct ?
Click to expand...
What you're supposed to do is: first decide your tolerance for error (3%, 5%, and 10%), then look at the population.
Let's say that you decided to go with a 3% margin of error, and the population >5000. From the table, you are required to have at least 1100 to satisfy the requirement. Now let's say you only have a 500 sample size, which didn't meet the requirement. However, if you look at a 5% margin with the same population, you only need 390. You don't really have to do another statistical test, you can say that your margin of error is between 3% and 5%.
 
@BigBeachBananas Thank you for your response...actually i might maximum get 150 responses..and with these number of responses..does it make sense to do analysis like regression or chi square tests... or I can analyse these 150 responses by doing simple descriptive statistics...
 
Slim Jim said:
@BigBeachBananas Thank you for your response...actually i might maximum get 150 responses..and with these number of responses..does it make sense to do analysis like regression or chi square tests... or I can analyse these 150 responses by doing simple descriptive statistics...
Click to expand...
You can go with a 10% margin of error if that is all you can obtain. It all depends on what is "acceptable" by your professor. Is your professor ok with a 90% confident vs 95% confident that x% of the people? I suspect most of your data are classification i.e. not numerical so I would recommend the Logistic Regression. You can do it easily with R-studio or python. You can see here for more info:
www.r-bloggers.com

How to perform a Logistic Regression in R | R-bloggers

Logistic regression is a model for predicting a categorical (binary) variable. Learn to fit, predict, interpret and assess a glm model in R.
www.r-bloggers.com www.r-bloggers.com
 
@BigBeachBananas Thank you for your response...i will check with my professor what is the confidence rate acceptable for him...

Additionally at this stage i think it is best if I just focus on doing the basic analysis and see how it addresses my research question and study objective...

If the basic analysis proves to be inadequate..i think then i will focus on advanced analysis like Logistic regression...

thanks for your help...:)
 
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