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CCSS.Math: in an experiment aimed at studying the effect of advertising on eating behavior in children a group of 500 children 7 to 11 years old were randomly assigned to two different groups after randomization each child was asked to watch the cartoon in a private room containing a bowl a large bowl of goldfish crackers the cartoon included two commercial breaks the first group watched food commercials mostly sacks while the second group watched non-food commercials games and entertainment products once the child finished watching the cartoon the conductors of the experiment weighed the cracker bowls to measure how many grams of crackers the child ate they found that the mean amount of crackers eaten by the children who watched food commercials is 10 grams greater than the mean amount of crackers eaten by the children who watched non-food commercials so let's just think about what happens up up to this point so they took 500 they took 500 children and then they randomly assign them to two different groups so you have Group 1 over here and you have group 2 so let's say that this right over here is the first group the first group watched food commercials so this is group number 1 so they watched food commercials we could call this the treatment group we're trying to see what's the effect of watching food commercials and then they tell us the second group the second group watched non-food commercials so this is the control group so number two this is non-food commercials so this is the control right over here once the child finished watching the cartoon they weighed how much the meet they for each child they weighed how much of the crackers they ate and then they took the the mean of it and they found that the mean here that the kids ate 10 grams greater on average then this group right over here which just looking at that data makes you believe that okay well something maybe happened over here that then maybe the treatment from watching the food commercials made the students eat more of the of the goldfish crackers but the question that you always have to ask yourself in a situation like this well is it there's some probability that this would have happened by chance that even if you did if you didn't make them watch the commercials if this if these were just two random groups and you didn't make either group watch a commercial you made them all watch the same commercials there's some chance that the mean of one group could be dramatically different than the other one it just happened to be in this experiment that the mean here that it looks like the kids ate 10 grams more so how do you figure out what's the probability that this could have happened that this could have that that the that the 10 grams greater and mean amount eaten here that that could have just happened by chance well the way you do it is what they do right over here using a simulator they re randomized they re randomized the results into two new groups and measure the difference between the means of the new groups they repeated the simulation 150 times and plotted the differences given the results the resulting differences as given below so what they did is they said okay they have 500 kids and each kid they had 500 children so number 1 2 3 all the way up to 500 all the way up to 500 and for each child they measured how much was the weight of the crackers that they ate so maybe child 1 8 2 grams and child 2 8 4 grams and child 3 8 I don't know 8 12 grams all the way to child number 508 I don't know maybe they didn't eat anything at all 8 0 grams and we already know let's say you know the first time around 1 1 through 201 through I guess we should you know the the first half was in the treatment group when they were when we're just ranking them like this and then the second they were randomly assigned into these groups and then the second half was in the control group but what they're doing now is they're taking the same results and their rear and amaizing it so now they're saying ok let's maybe put this person in then group number 2 put and this person in group number 2 and this person stays in group number 2 and this person stays in group number 1 and this person stays in group number 1 so now they're completely mixing up all of the results that they had so it's completely random of whether the student had watched the food commercial or the non-food commercial and then they're testing what's the mean what's the mean of the new number one group and the new number two group and then they're saying well what what is the distribution of the differences in means so they see when they did it this way when they're essentially just completely randomly taking these results and putting them into two new buckets you have a bunch of cases where you get no difference in the mean so out of the 100 out of the hundred 50 times that they repeated the simulation doing this little exercise here 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 tribal counting this is see 1 2 3 4 5 6 7 8 9 10 11 12 oh I don't want to keep it so small I'm having them aging but it looks like there's about you know I don't know high teens about 20 times when there was actually no noticeable difference in the means of the groups where you just randomly when you just randomly allocate the results amongst the two groups so when you look at this if it was just you know if you just randomly put people into two groups the probability or the the situations where you get a 10 a 10 gram difference is are actually very unlikely so this is let's see is this the difference the difference between the means of the new groups so it's not clear whether this is group 1 minus group 2 or group 2 minus group 1 but in either case the situations where you have a 10 where you have a 10 gram difference in mean it's only two out of the hundred and fifty times so when you do it randomly when you you know when you just randomly put these results into two groups the probability of the means being this different it only happens to out of the hundred and fifty times there's 150 dots here so that is on the order of of two percent or actually it's less than two percent it's between one and two percent and if you know that you know this is group let's say let's say that the situation we're talking about let's say that this is Group 1 minus group 2 in terms of how much was eaten and so you're looking at this situation right over here then that's only one out of 150 times so it's it happened less than what it happened it happened less frequently than one in a hundred times it happened only one in a hundred and fifty times so if you look at that you say well the probability of this was just random the probability of getting the results that you got is less than one percent so to me and then to most statisticians that tells us that our experiment was significant that the probability of getting the results that you got so the children who watched food commercials being 10 grams greater than the mean amount of crackers eaten by the children who watched non-food commercials if you just randomly put 500 kids into two different buckets based on the simulation results it looks like there's only there's there's only if you'd run the simulation 150 times that only happened one out of 150 times so it seems like this was very it's very unlikely that this was purely due to chance if there's this if this was just a chance event this would only happen what roughly one in 150 times but the fact that this happened in your experiment makes you feel pretty confident that your experiment is significant in most in most studies and most experiments the threshold that they think about is the probability of significant if the probability of that happening by chance is less than five percent so this is less than one percent so I would definitely say that the experiment is significant