Expected mean squares
Expected mean squares are a way of figuring out how much of the differences between groups in an experiment can be attributed to the things you’re trying to investigate, and how much is just random chance.
For example, let’s say you’re trying to figure out whether different types of fertilizer make plants grow better. You have three groups of plants that you’re treating with three different types of fertilizer. You want to know whether the differences in the plant’s growth are due to the different fertilizer types, or just because the plants were a bit different to begin with.
To figure this out, you look at the expected mean squares. This is like looking at how big the differences were between the groups, and then seeing if they were bigger than what you would expect from random chance.
You take the differences in growth within each group, and then look at how much those differences contribute to the overall differences between the groups. If the differences within each group are pretty small compared to the differences between the groups, then you can say that the differences between the groups are probably due to the fertilizer treatments, rather than just random chance.
It’s like if you had three piles of blocks, and you wanted to know if one pile had more blocks than the others. You would count up how many blocks were in each pile, and then see if the differences between the piles were bigger than what you would expect if you just picked blocks randomly from a big box. If the differences were bigger than what you would expect from chance, then you would say that one pile really did have more blocks than the others.
So in summary, expected mean squares are a way of figuring out if differences between groups in an experiment are meaningful or just random chance.
For example, let’s say you’re trying to figure out whether different types of fertilizer make plants grow better. You have three groups of plants that you’re treating with three different types of fertilizer. You want to know whether the differences in the plant’s growth are due to the different fertilizer types, or just because the plants were a bit different to begin with.
To figure this out, you look at the expected mean squares. This is like looking at how big the differences were between the groups, and then seeing if they were bigger than what you would expect from random chance.
You take the differences in growth within each group, and then look at how much those differences contribute to the overall differences between the groups. If the differences within each group are pretty small compared to the differences between the groups, then you can say that the differences between the groups are probably due to the fertilizer treatments, rather than just random chance.
It’s like if you had three piles of blocks, and you wanted to know if one pile had more blocks than the others. You would count up how many blocks were in each pile, and then see if the differences between the piles were bigger than what you would expect if you just picked blocks randomly from a big box. If the differences were bigger than what you would expect from chance, then you would say that one pile really did have more blocks than the others.
So in summary, expected mean squares are a way of figuring out if differences between groups in an experiment are meaningful or just random chance.