Tables of proportion: How to read them. Or: Men and women in Austrian households
It can be a drag. Both doing household chores and learning about boring tables. But what I found is that a lot of people have problems with making sense and reading tables of proportions. Tables of proportions simply show the distribution regarding one or more dimensions. So if there are two males in a household and also two females in the same household this household consists of 4 people, 50% male and 50% female. But this is only one dimension. Let’s say we add a second one and now we know that one man is actually a child. Then there are still 50% male and 50% female in the same household but there are 25% kids who are male, 25% grown men and 50% grown women. But there are also 25% kids and 75% grown ups. It’s all about how you look at the same household. That’s almost everything you have to know about tables of proportions. But let’s start fresh with some actual data:
Total number of cases and distribution
In 2016 there was a survey conducted in Austria called Social Survey Austria. You can see the full documentation and get the data itself at the Austrian Social Science Data Archive. The survey asks a lot of questions about attitudes, values and living conditions of people in Austria.
When it comes to household chorse: You do… (totals)
|way more than my fair share||135|
|a little more than my fair share||244|
|about my fair share||491|
|a littles less than my fair share||153|
|way less than my fair share||51|
The above table shows the answers after people were asked about the share of household chorse they do compared to their partner. Only people who live with their partner were asked. 1.105 people answered this question and 135 said that they do way more than their fair share. 244 answered with “a little more than my fair share” and so on. So this table shows the number of real people and how they answered this question. In statistics n usually stands for the sample size. Here I use it to mark the column that contains the total number of people (also called cases). This will be important shortly.
Next we have a table where we show the *distribution of the answers to that question *. That means that we no longer look at the individual cases in every cell – a cell is one specific value in a table – but at how many percent of all people gave which answer:
When it comes to household chorse: You do… (percent)
|way more than my fair share||12.2%|
|a little more than my fair share||22.1%|
|about my fair share||44.4%|
|a littles less than my fair share||13.8%|
|way less than my fair share||4.6%|
We can see that the 135 people who said that they do way more than their fair share translate to 12.2% of all participants that answered this question. In other words, 12.2% of 1.105 people are 135 people. Here we only have one column, so we are dealing with column percentages. Column percentages show us the proportion of each cell in relation to all cases in this column. This is fairly easy when we only have one column. So let’s jump to the next example.
The differnce between men, women, columns and rows
When it comes to household chorse: You do… (column percentages by gender)
|way more than my fair share||2.4%||21.6%||135|
|a little more than my fair share||5.4%||38.1%||244|
|about my fair share||54.0%||35.3%||491|
|a littles less than my fair share||25.1%||3.0%||153|
|way less than my fair share||8.7%||0.7%||51|
We are still looking at the same question. But now we have two columns. The first one shows how men answerd the question about household chorse and the second column shows how women answerd the question. We can see that there are 541 men and 564 women that answerd this question. I also added a third column that shows how many people in total gave which answer. Now, the column percentages tell us a lot about the difference between men and women. Keep in mind that this table is based on self-report and the answers might be relativley subjective. But nonetheless we can see pretty big differences in how the question was answered. About 22% of all women say that they do way more than their fair share when it comes to household chorse. This is a lot when we compare it to the 2% of men who gave the same answer. Keep in mind that this table shows us the column percentages. The other way to show the results to this question is to look at the row percentages:
When it comes to household chorse: You do… (row percentages by gender)
|way more than my fair share||9.6%||90.4%||135|
|a little more than my fair share||11.9%||88.1%||244|
|about my fair share||59.5%||40.5%||491|
|a littles less than my fair share||88.9%||11.1%||153|
|way less than my fair share||92.2%||7.8%||51|
You can see that the row named n, as well as the column named n, show the same numbers as in the table before. Of course they do, because we still have the same amount of each answer and the same amount of men and women. But the percentages in the Male and Female columns changed because now they show the row percentages. What this tells us, for example, is, that of the 135 people who said that they do way more than their fair share of household chorse, 90% are female and 10% are male. Also the next answers – “I do a little more than my fair share” – is predominated by women (88%). So women report way more often than men that they do more household chorse than their partner.
Before we look at other differences between men and women, let’s summarize what we have so far regarding tables:
Whenever you see a table just keep in mind that every cell conatins real people. Don’t let the percentages confuse you. If the table is made by someone who takes his work seriously you will find somewhere (maybe in tiny font at the bottom) the sample size (n). This is all you need to remember that we are dealing with real people. For example, I can tell you that 122 women said that they do way more than their fair share of household chorse. How? We know that 135 people in total said that they do way more than their fair share. We also know that 90.4% of these people are women. That’s how we can pretty easily calculate that 90.4% of 135 are 122. To cross check that: We know that there are 564 women who answerd this question and that 21.6% of these 564 women said that they do way more than their fair share. And 21.6% of 564 is also 122. So the only difference between column and row percentages is the reference the percent relate to. If it relates to all the real people in a row, we have row percentages. If it relates to all the real people in a column, we have column percentages. If you are not sure with what you are dealing, just sum up the percentages. If you start summing up the first row and it equals 100%, then you know you are dealing with row percentages. If the sum of one column equals 100%, then this is a sign that you are dealing with column percentages. That’s really all there is to it.
But since we already started to look into the data of the Social Survey Austria. Let’s look further.
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We were able to see that men and women feel differently about how much work they do in the household. We can more or less assume that women who say that they do way more than their fair share of household chorse would demand from men that they man up and help out more. When we look at the statement “Men should take over more household chores than right now” this assumption is confirmed:
Men should take over more household chores than right now (column percentages by gender)
About 63% of women at least somewhat agree to the above statement. This is almost the same percentage (60%) of women who said that they do at least a little more than their fair share of household chorse. That makes sense. But when we look at the men, 34% say that they do less or way less than their fair share but 41% of men say that men should help out more. How can this be? Maybe men who already help out their fair share demand from other men to also do so. Or maybe not. Who knows? This is a great example of where one would start an explorative analysis of the data. If it wouldn’t be too much for this little blog post we could look at the correlation between the two questions and how the men in the survey answered it.
But now it gets kind of interesting. One could assume that Austria is a modern, progressive country. But let’s just look at the next table:
Men should make money and women should look after the household and kids (column percentages by gender)
An astonishing 29% of men say that men should make money and women should stay home, handle the household and look after the kids. Seriously? What is this? The 19th century? It get’s even more amazing when we look at the women. 19% of women also agree that men should make money and women should stay home. Well, I wasn’t expecting that. But to be fair: Also 23% of men and 34% of women fully disagree with this statement. I think you can guess how I would have answered this question.
Let’s look at one more table and then I’ll leave you alone, I promise:
Men should take over a bigger part when it comes to parenting (column percentages by gender)
Here we can see again a big difference in men and women. 60% of women say that men should play a bigger role in parenting and only 43% of men at least somewhat agree with that.
Looking at all the tables we can safely assume that women in Austrian households are burdened with more reproductive labor than men. We can also say that more women than men would like this situation to change. And although a majority of men are indifferent or agree that men should take over more responsibilites, a big part of men don’t see the “problem”. Time provided it would be interesting to delve deeper into the data to find out more about specific living and working conditions to shed more light on these findings. But for now we will leave that for another day or someone else.
What have we learned today?
Yes, tables can be boring but really there isn’t too much to them. But at the same time we can learn a lot. In this blog post for example we saw that the distribution of household work between women and men is bigger than we may have thought and that women and men feel differntly about changing this situation. Just keep in mind that there are many ways to represent data, even in a boring, flat table. Remember that a table really is made up by real people. If you are not sure if you are dealing with row or column percentages:
Is the sum of one row 100%? You are reading row percentages.
Is the sum of one column 100%? You are reading column percentages.
All the tables that compared men and women are highly significant. I will probably go into what significance is in a later blog post. For now, what this means is: The differences we found today are out there in the real world and didn’t just happen by chance.
Also, I wrote this blog post mainly with R Markdown. If you are interested in the code or want to tell me something else, just write me a short mail: bernd [at] berndschmidl.com
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