ANOVAs

anovas

• let me learn you a thing about tests, my lass
• pull up a chair
• get comfy
• cause i still haven't really figured out what i'm gonna say

variation within conditions

• so you're in psychology. and that means you're dealing with PEOPLE. ick. kind of. not really. at all.
• so people vary. you can have the same person do the same test a hundred times and get all kinds of data points. and when you have MULTIPLE people doing the same test a bunch of times, you'll get even MORE variability.
• because people aren't consistent. and that's okay. it's just really annoying. you know, for analysis.

between conditions

• so you have people being all wibbly wobbly inconsistent within their own condition. but you're also CHANGING conditions too, right, because this is an experiment. so people are going to be wibbly wobbly inconsistent in that condition, also, just in a different way.

two kinds of variation

• let's say in one condition, they're all skirting around the number 6, and in the other condition they're all skirting around the number 9. The fact that they're skirting around in each condition is going to make variation - you know, since they're not ALL either 6 or 9 - and the difference between 6 and 9 is variation, too.
• so skirting around makes variation WITHIN conditions
• and you manipulating the independent variable between the conditions will make variation in BETWEEN conditions.

so what of it

• but if you wanna show the world that you found some way of altering people's behaviour, and that your experiment was successful, you have to prove that you're causing variation BETWEEN conditions. that means that you have to figure out how much variation WITHIN conditions there is, and get rid of it in your analysis, so you can look at JUST the kind of variation you actually care about.
• and that's what the ANOVA does!

so like remember

• in order for you to reject the null and say that you're causing significant variation between conditions, the variation between conditions has to EXCEED variation within conditions. or else your results are just due to chance, or people being wibbly wobbly.

also another cool thing

• ANOVAs can also let you analyse data that has multiple IVs
• so you can have like a zillion conditions and use an ANOVA to make sense of it
• BUT remember the more tests you do, the more of a dick you are, so you have to use the Bonferroni correction:
• p value/# of conditions

ok so how do you do an ANOVA??

• goddamn you impatient
• make sure it meets the assumptions first course:
• - all your conditions show normal distributions
• - " " " have about the same variance
• - random variance is also normally distributed (when you find it)
• - everyone did the task on their own

it's simple i promise

• so you end up using a lot of subscripts when you're talking about means and values that are specific to a person and their condition. it's all just descriptive, everything means something and it's all just to tell you where the number came from
• course i can't do subscripts in this program so i'll make things capitalised and the lower case stuff is what's in the subscript, aight?

we're building a formula is all

• so if you wanted to describe how to go from the mean of all your data (we're calling this the grand mean) to the specific value of one participant, how would we do it?
• pretty simply actually. you just have to remember the two different kinds of variances that i was talking about before: WITHIN condition and BETWEEN conditions.
• if you added them together + the grand mean, you got it.

example

• so let's say you have participant i who was in condition j, and got the score x.
• we'll call the grand mean (mean across conditions) n.
• so Xij = the score that participant i got in condition j
• we're just naming things so far really

between condition variance

• so we were talking about two different kinds of variance. if we were going to figure out how to determine the variance BETWEEN conditions, how would we do it?
• we'd take the mean of the condition (which we'll call m) and subtract it from the grand mean (n), yeah. and that difference, we'll call t.
• so n - m = t, and t is the general effect of the condition.

within condition variance

• so in the same way, if you were to take a person's score (x) and subtract it from their condition's mean (m), you'd get their 'unique contribution', or basically how wibbly wobbly they are. we're calling that difference e.
• so m - x = e

so let's look at all of it together

• we've just labeled:
• N = the grand mean
• T = the difference caused by the condition (BETWEEN condition variance)
• E = the difference caused by the person (WITHIN condition variance)
• if we were to take all this into account, we'd get...
• X = the specific score of a person within their condition
• so let's do that

stirring occasionally

• so we throw it all together and add the labels
• N + Tj + Eij = Xij
• the grand mean + the difference caused by condition j + the difference caused by person i in condition j = the score of person i in condition j
• or
• grand mean + BWTN var + WTHN var = pps' score

JUST DONT FORGET

• BONFERRONI'S CORRECTION
• p value/# of conditions
• VERY IMPORTANT PLEASE AND THANK YOU <3