# Summary statistics for two populations

I have two populations: part-time worker in the health industry (IND=17) and part-time worker in the financial industry (IND=12)

For those two populations I have several variables (demographic variables and professional variables) What would be a good table to show the different populations of part-time workers (how similar/different they are)? Should I work with percentages or means?

AGE

• 2 = 18-24 years old
• 3 = 25-29 years old
• 4 = 30-34 years old
• 5 = 35-39 years old
• 6 = 40-44 years old
• 7 = 45-49 years old
• 8 = 50-54 years old
• 9 = 55-59 years old
• 10 = 60-64 years old

SEX

• 1.00 = Male
• 2.00 = Female

EDU

• 1.00 = Pre-primary, primary and lower secondary education
• 2.00 = Apprenticeship/high school degree or equivalent
• 3.00 = College graduate
• 4.00 = Master degree
• 5.00 = PhD

SIZE

• 1 = Less than 10 employees
• 2 = 10-49 employees
• 3 = 50-99 employees
• 4 = 100-249 employees
• 5 = 250-499 employees
• 6 = 500-999 employees
• 7 = 1000 employees or more

FCT

• 1 = Marketing, sales, distribution management
• 2 = Production, manufacturing operations (purchases, process planning, storage etc.)
• 3 = Customer support (customer service, call center, counter, care)
• 4 = Infrastructure (IT operations and development, logistics)
• 5 = Research and development
• 6 = Internal services, finance/financial control, HR training
• 7 = Other

COLLAR

• 1 = Blue collar worker
• 2 = White collar worker

MGMT

• 1 = I do not manage other people
• 2 = I manage other people who are not managers
• 3 = I manage managers

SCOPE

• 1 = My company only has employees in my own country
• 2 = My company has employees in more than one but less than 10 countries
• 3 = My company has employees in more than 10 countries

TENURE

• 1 = Less than 1 year
• 2 = 1 year to less than 2 years
• 3 = 2 years to less than 5 years
• 4 = 5 years to less than 10 years
• 5 = 10 years to less than 20 years
• 6 = 20 years to less than 30 years
• 7 = 30 years and over
• How would you take a mean of your variables?
– Dave
Commented Aug 3, 2020 at 17:37
• So would you make a table with percentages of the two industries side by side?
– user283542
Commented Aug 3, 2020 at 18:08

Percentages. If your table just shows the average age of health industry workers, that doesn't seem to tell you much. This will give you the largest tables.

If you want small tables, use the means. You could also include the standard deviations (SD). For example, treat AGE as continuous. If you had a mean of 6 and a SD of two, that would say that 95% of the the ages fall between 4 and 8, or 30-34 and 50-54.

You could also use 5-number summaries. This would show the min, 1st quartile, median, 3rd quartile, and max. It shows the distribution in a different way. This would give you a mid-size tables.

• Could I use the mean ans SD for all variables?
– user283542
Commented Aug 4, 2020 at 9:27

I think of summary/descriptive statistics as a tool to communicate the nature of a set of data at a glance, whether that is through tables of means and SDs, percentages, bar charts, histograms, pie charts etc.

There isn't a one-size-fits-all approach: you need to examine your data types (continuous, ordinal, categorical) and distributions (e.g. normal, bimodal) and then choose the method that you think conveys a summary of the data in as succinct a way as possible, without being misleading.

@Dave asked you in a comment how you would take a mean of your variables - I think this was intended as a hint to get you thinking along the right lines. So let's take an example and work it through. Say half of the workers had 'Pre-primary, primary and lower secondary education' ('1) and half of them had a PhD ('5'), and you took the mean of '1' and '5', you would end up with a mean of '3', 'College graduate'. This wouldn't be a good representation of the underlying data at all (percentages would give a better summary of the data in this example). This example also demonstrates that you should be extremely cautious about taking the mean of an ordinal scale: the size of the steps between the points on your ordinal scale are not necessarily equal, in which case taking the mean doesn't make much sense.

Another one of your variables ('FCT') is categorical, and there's no scenario I can think of for this variable in which taking the mean would work at all.

I won't go through all your variables and data types as there are many examples out there on how to deal with, for example, the 'Age' variable, where you've collected categorical data about an underlying continuous variable, but I hope this helps to point you in the right direction.

Some further notes of caution - you state that you have data from two 'populations'. Note that a population is made up of all the individuals within a defined group. Is your population very small? I suspect what you in fact have is a sample from each of two populations (sample sizes n=17 and n=12). These sample sizes are not particularly large to be trying to distinguish between 7 different categories within the variable 'FCT'. If you calculate the confidence intervals on the percentages, you may be able to see this. Also, what measures did you take to make sure that your samples aren't biased in some way, e.g. that your survey didn't just reach people working in marketing? (You may want to read up on survey methods to ensure a good response rate across all parts of a population, and how to interpret your data carefully if you are not able to do so, which is a common problem).