## Monday, 15 May 2017

### Multivariate Statistics

We have been using data squares to conduct statistical investigations. In the data square above, the person surveyed was a girl (G), who preferred the indoors to the outdoors (I), preferred dogs to cats (D) and was in year 6 (6). Investigating multiple variables allows us to explore how those variables might be related.

We created data squares like the one above for everyone in our class. We then photocopied the data squares, so each team had a full set of 21 data squares to work with.

Click on the images to see fullscreen versions, where you can read the data squares.

Does gender affect preference for dogs or cats?
All of the girls' data squares are in the top row, while all of the boys' data squares are in the bottom row.
All of those who prefer dogs are in the left column, while all of those who prefer cats are in the right column.

67% of the students in our class prefer dogs to cats. We can see this because there are 14 data squares in the dogs column, out of a total 21 data squares. (We converted the fraction 14/21 into a percentage by dividing 14 by 21, then multiplying by 100.)

It seems that gender doesn't have much affect on preference for dogs or cats. 63% of boys prefer dogs, while 69% of girls prefer dogs. Dogs are more popular with everyone and are only slightly more popular with girls than boys.

Does gender affect preference for indoors or outdoors?
The girls are in the left column and the boys are in the right column.
Those who prefer the outdoors are in the top row. Those who prefer the indoors are in the bottom row.

The girls in our maths class are more likely to prefer the outdoors than the boys. 69% (9/13) of girls  prefer the outdoors, while only 38% (3/8) of boys prefer the outdoors.

One problem with our data is that there are 13 girls and only 8 boys. The larger sample size of girls means that they are better represented than the boys. It is also a very small sample overall, with only 21 students.

We discussed the possible causes of this correlation between gender and preference for the outdoors. One possible explanation is that more of the boys liked video games, which are played indoors.

## Our Own Statistical Investigations

We discussed some potential data square questions and evaluated how effective they would be:

What's your favourite colour?
- People might have more than one favourite colour. - Ana
- There are too many possible answers. - Ollie

How tall are you?
- People might not know how tall they are. - Olivia
- Too many possible answers. We would need measuring tape or rulers. - Ashley

To make our statistical investigation manageable, we decided to:
- Give people two options. - Samantha
- Maybe give people two options for sports activities, e.g. swimming sports or cross country. - Daniel
- Choose something everyone knows or can easily figure out. - Minnie

We worked in pairs to develop our questions and generate predictions. We then gathered our data. Each team had 20 data squares because there were 20 of us in the room.

After exploring some of the other data, every team chose to focus on gender (girl or boy) and one other variable. All responses were simplified into either/or categories, so we could organise the data squares on a grid.