(10): In short, how many participants are there? That is the 'number of rows'.

Let's use HAD

In the 'Psychological Statistics' exam, this is, in a sense, the most representative problem for this subject. It is a problem where you have to choose the F-value (approximate value) of an analysis of variance from the options, but it is quite difficult to arrive at the answer by calculating the numbers with a calculator. It is not impossible. You can do it with a calculator if you really want to. It is just that it is quite tedious, so I do not want to do it.

So, you might think, 'Can't I just use Excel?' but no, you cannot. Well, you can do it if it is 'between-subjects', but you cannot do it if it is 'within-subjects'. Even so, you cannot just say, 'Please don't give us within-subjects problems.' Therefore, let's just quietly use HAD. Oh, R is also fine.

Let's enter the data

Now, let's open HAD and enter the data into the [Data] sheet. There are two points that are particularly easy to get wrong. These are familiar points for those who have been using HAD while studying the textbook.

You need an ID in column B, right?

This is a specification of HAD. For now, there is no problem if you just enter a sequential number starting from 1 (1, 2, 3, ...). This sequential number will not be the subject of analysis. However, if you enter the data you 'want to analyze' in column B, it will not work well. Some of you may have failed a few times when you first started using it.

Does the number of participants match the ID?

Here, the number of participants refers to the number of people who participated in the experiment when the data for the analysis of variance was collected. If 12 people participated, there should be data for 12 people, so the ID should go up to 12. You understand, right?

For those who don't get it

(The numbers are completely arbitrary, so please do not pay any attention to them at all!)

We had people evaluate their preference for three types of soup flavors. How many people's worth of data is this?

• Data for 12 people, it can be considered. For example, the '2' in the yellow cell means that a participant happened to participate in a survey to taste 'Soup A' and rated the flavor preference as '2'.

• Data for 4 people, it can be considered. For example, the data '4, 6, 8' in the green cell means that one participant participated in a survey to taste three types of soup, 'Soup A, B, and C', and rated the flavor preferences as '4, 6, 8' respectively.

'Between' or 'Within'

Don't get angry and ask, 'Which one is it!' You cannot clearly distinguish it with this data alone. To make it clearly distinguishable, it is assumed that, for example, the following explanation would be added to the problem.

• 'Between-participantsdesign': This means it is data for 12 people. 'Soup A', 'Soup B', and 'Soup C' differ 'between' participants, meaning different participants are evaluating different soups.

• 'Within-participantsdesign': This means it is data for 4 people. 'Soup A', 'Soup B', and 'Soup C' differ 'within' participants, meaning the same person is comparing three types of flavors.

In reality, there are some problems where neither is explicitly stated, and I speculate that they were likely presented as a 'between-participants design'. Also, there was one where participant numbers '1-4' were shown to the left of 'Soup A', indicating that there were 4 participants, that is, it was a 'between-participants design'.

This is how to enter the data

So, how do you actually enter the data? You do it like this. A within-participants design (4 participants) is simple. You can just enter it exactly in the format of the table shown.

For a between-participants design (12 participants), you do it as follows. Now, there are 12 people.

When you enter and compare data like this, it becomes clear that the experimental methods are obviously different. In the case of 'taste evaluation' as shown in the example, it is often conducted by randomizing the tasting order and hiding whether the sample is A, B, or C, while being careful not to let the flavors of the three soup bases mix (so as not to be influenced by what was tasted previously). This is because doing so can, to a significant degree, exclude individual differences—which might exist infinitely—in 'taste preference' from the analysis. As a result, only the differences in the taste of the soup bases are extracted as differences in evaluation scores. Well, I suppose it often isn't that simple, though.

This time, I ended up writing quite properly, even including how to use HAD. I feel like I've almost provided the answer, but I wonder if that's okay.