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Main content

Current time:0:00Total duration:4:41

AP.STATS:

DAT‑3 (EU)

, DAT‑3.A (LO)

, DAT‑3.A.1 (EK)

, DAT‑3.A.2 (EK)

, DAT‑3.B (LO)

, DAT‑3.B.1 (EK)

, DAT‑3.B.2 (EK)

, DAT‑3.B.3 (EK)

, VAR‑6 (EU)

, VAR‑6.G.4 (EK)

what we're going to do in this video is talk about significance levels which are denoted by the Greek letter alpha and we're gonna talk about two things the different conclusions you might make based on the different significance levels that you might set and also why it's important to set your significance levels ahead of time before you conduct an experiment and calculate the p values for frankly ethical purposes so to help us get this let's look at a scenario right over here which tells us raheem heard that spinning rather than flipping a penny raises the probability above 50% that the penny lands showing heads that's actually quite fascinating if if that's true he tested this by spinning 10 different pennies ten times each so that would be a total of 100 spins his hypotheses were his null hypothesis is that by spinning your proportion doesn't change rather versus flipping it's still 50% and his alternative hypothesis is that by spinning your proportion of heads is greater than 50% where P is the true proportion of spins that a penny would land showing heads it is 100 spins the penny landed showing heads in 59 spins raheem calculated that the statistic so this is the sample proportion here it's 59 out of 100 were heads so that's zero point five nine or 59 hundredths and he calculated had an Associated p-value of approximately zero point zero three six so based on this scenario if ahead of time Rahim had set his significance level at 0.05 what conclusions would he now make and while you're pausing it think about how that may or may not have been different if he set his significance levels ahead of time at 0.01 pause the video and try to figure that out so let's first of all remind ourselves what a p-value even is you could view it as the probability of getting a sample proportion at least this large if you assume that the null hypothesis is true and if that is low enough if it is some if it's below some threshold which is our significance level then we will reject the null hypothesis and so in this scenario we do see that 0.036 our p-value is indeed less than alpha it is indeed less than 0.05 and because of that we would reject reject the null hypothesis and in everyday language rejecting the null hypothesis is rejecting the notion that the true proportion of spins that a penny would land showing heads is 50% and if you reject your null hypothesis you could also say that suggests that suggests our alternative hypothesis that the true proportion of spins that a penny would land showing heads is greater than 50% now what about the situation where a significance level was lower well in this situation our p-value our probability of getting that sample statistic if we assumed our null hypothesis were true in this situation it's greater than or equal to and it's greater than in this particular situation then our threshold then our significance level and so here we would say that we fail fail to reject our null hypothesis so we're failing to reject this this right over here and it will not help us suggest our alternative hypothesis and so because of the difference between what you would conclude given this change in significance levels that's why it's really important to set these levels ahead of time because you would you could imagine it's human nature if you're a researcher of some kind you want to have an interesting result you want to discover something you want to be able to tell your friends hey my alternative hypothesis it actually is suggested we can reject the the assumption the status quo I found something that actually makes a difference and so it's very tempting for a researcher to calculate your p-values and then say oh well maybe no one will notice if I then set my significance values so that it's just high enough so that I can reject my null hypothesis if you did that that would be very unethical in future video we'll start thinking about the question of okay if I'm doing it ahead of time if I'm setting my significance level ahead of time how do I decide to set the threshold when should it be 100th when should it be 500s when should it be ten hundredths or one should it be something else