0@Loc: Person/c17.cha1@PID: 11312/t-00015819-12@Begin3@Languages: eng4@Participants: TS Teacher, SS Student5@ID: eng|Person|TS|||||Teacher|||6@ID: eng|Person|SS|||||Student|||7@Media: c17, video8@Comment: C-17 STATISTICS9*TS: read it out loud [= T hands S example]. ▶10*SS: oh, ok. ▶11*SS: topic (.) statistics (.) type one and type two error, decision12matrix, Pless than point zero five t_test. ▶13*TS: ok, that's fine. ▶14*TS: ok, there's kind of a lot of material. ▶15*TS: were there any particular questions you can think of? ▶16*SS: um. ▶17*TS: I thought we might start with those to make sure we covered18everything that you had trouble about. ▶19*SS: well, there's one thing in here that I don't know how important it20is, it kind of, I remember it from statistics and I don't know if I21need to understand it, but I don't [= flips through text]. ▶22*TS: ok. ▶23*SS: and it says that. ▶24*TS: what page? ▶25*SS: page one hundred thirty eight. ▶26*SS: it says, that if you conclude that you have not sampled from the27sampling distribution specified by the null hypothesis. ▶28*TS: where are you? ▶29*TS: oh yeah, right there [= student points to place in text]. ▶30*TS: ok, alright, that is you conclude that you have not sampled from31the sampling distribution specified by the null hypothesis. ▶32*SS: and instead you decide that your data are from a different sampling33distribution. ▶34*TS: ok. ▶35*SS: I don't really understand that. ▶36*TS: ok, what that's saying is when you are testing a t_test or an37F_test or something like that, what you're looking at is to see if38your means are different. ▶39*SS: uh huh. ▶40*TS: if your means are different, what does that mean? ▶41*TS: that means your samples are different. ▶42*TS: well, what does that mean? ▶43*TS: that your samples come from different populations. ▶44*TS: ok, um, when it talks about the sampling distribution, the sampling45distribution is that set of values based on the null hypothesis. ▶46*TS: it tells you the probability of obtaining any particular results. ▶47*TS: say you got a score of three, well you can look and see what the48probability of having obtained a three. ▶49*TS: ok, so what this is saying is that's just another way of saying50that there is a difference. ▶51*TS: so when it says that when your obtained results you conclude that52you have not sampled from the sampling distribution specified by the53null. ▶54*TS: in other words, your sample didn't come from the population55governed by the null. ▶56*TS: in other words. ▶57*SS: yeah, that's what. ▶58*SS: in other words, every score comes from some theoretical normal59curve that's floating out in space somewhere. ▶60*TS: it can be but the sampling distribution that's where we get the61probabilities, like when you look up the critical value, the t or62something like that; come from hypothetical sampling distributions63of which theoretically a number of samples have been drawn and put64out. ▶65*TS: you know? ▶66*SS: uh huh. ▶67*TS: there is such a thing as having a sampling distribution of ten68means or any observed number of statistics or whatever, but the ones69that we get these critical values for come from the full gamet. ▶70*TS: and so that's just a fancy way of saying, in other words, the null71wasn't an effect. ▶72*SS: uh huh. ▶73*TS: there was a difference, so to me that's a confusing way to put it74when you say that two groups are statistically different, in other75words their samples are from different populations. ▶76*SS: uh huh, uh huh. ▶77*TS: which is a funny way to think about it that you know the two78different groups came from different populations. ▶79*SS: well, you get their scores. ▶80*SS: I guess the whole concept of population like one guy over here is81from some mythical population over there, but he actually got in82with our sample. ▶83*SS: I mean to me there are just a bunch of people out there. ▶84*TS: uh huh. ▶85*SS: and they all have different scores. ▶86*TS: well, we group them into populations according to what87characteristic we're looking at +/. ▶88*SS: so in other words if you get something way out in the o@l one range89of what we're looking at then conceivably that would be a normal90score in somebody else's population? ▶91*TS: well, possibly. ▶92*TS: but yeah, sure, if you look at it in a limited sense you'll get93less confused. ▶94*TS: if you just say different populations i_e they're different because95they have different amounts of this characteristic that you're96studying. ▶97*TS: then that kinda of limits it. ▶98*SS: yeah, it just. ▶99*TS: it kind of brings it out of the realm of the flowing stuff just a100little. ▶101*SS: I just thought it meant that this one particular person had an102extremely high score or a different score not that they came from a103different population. ▶104*SS: it's like he's a Martian or something. ▶105*TS: it doesn't mean that. ▶106*TS: well, right, right it's not talking that these are people and these107are un (.) people. ▶108*SS: yeah right. ▶109*TS: it means that they're different populations as per what you're110looking at. ▶111*TS: ok, alright, anything else? ▶112*TS: we can just go through it. ▶113*SS: yeah, that's fine. ▶114*TS: page by page, but if you have specific questions which you want to115cover. ▶116*SS: well, there's one other one on page one hundred and forty two117[= maybe 143]. ▶118*TS: ok. ▶119*SS: a very large sample size might enable the researcher to find the120significant difference between means, however, this difference even121though it is statistically significant might have very little122practical significance [= student reads from text]. ▶123*SS: now, that's confusing. ▶124*TS: ok, what that means is Ok when you have larger and larger samples,125that means that you're getting more and more accurate picture. ▶126*SS: right. ▶127*TS: of what's going on. ▶128*SS: right. ▶129*TS: as you get close and closer to it, accounting for every member of130the population. ▶131*TS: statistically, the way the statistics work, it is often possible to132gain significance just be collecting more and more people. ▶133*SS: uh huh. ▶134*TS: not changing anything else, but the more people you collect it's135possible that you come closer and closer to defining things properly136so that you can have better chances of finding a significant effect.137▶138*SS: right. ▶139*TS: ok, the example they use, and I think it's a pretty good one. ▶140*TS: just because something is statistically significant doesn't mean141that it means anything. ▶142*TS: it could just be so what. ▶143*TS: in other words, if an expensive new psychiatric treatment technique144significantly reduces hospital stay, in other words, they sampled145all these patients and yes that they significantly reduced their146stay from sixty days to fifty eigth days, whoopy. ▶147*SS: uh huh. ▶148*TS: two days. ▶149*TS: so what it's just that paragraph is just about statistical150significance is important, yes, but just because the relationship is151statistically significant, different. ▶152*SS: uh huh. ▶153*TS: doesn't mean it has any real world practicality or significance. ▶154*SS: ok. ▶155*TS: I was trying to think of another example. ▶156*SS: it seems like to me maybe what they were doing is not very157significant, I mean the fact that. ▶158*TS: well, they might not have been looking to see if it would reduce159it. ▶160*TS: if by just two days, they might have been thinking it would do161something else. ▶162*SS: oh, Ok, I see. ▶163*TS: maybe what they come out with was just &=mumbles. ▶164*SS: but in most cases the more samples you have, the better your165results are gonna be, right? ▶166*SS: up to a point? ▶167*TS: up to a point, there is a difference. ▶168*TS: that's what the books' saying, I mean you can almost;169theocratically it might be possible to take your results significant170just by gathering lots of things. ▶171*TS: there's a point at which, oh gosh, I have actually a very good xxx.172▶173*TS: I'm gonna put this one pause and run upstairs. ▶174*TS: I'll be right back. ▶175*SS: ok. ▶176*TS: with another book. ▶177*SS: xxx. ▶178*TS: yeah, I saw it, but it just says that; all that is meant by179statistically significant finding is that the probability of it's180occurrence is small. ▶181*TS: that means that the null hypothesis is true. ▶182*TS: but it is the substantive meaning of statistical significance if it183is to substantively meaningful? ▶184*TS: in other words, we should not feel proud when the psychologist185smiles and says the correlation is significant. ▶186*TS: perhaps, that is the most practical use. ▶187*SS: uh huh. ▶188*SS: so you can have something that's significant but it's not very189meaningful. ▶190*TS: sure, a lot of people tend to level that criticism at research in191general, say, somebody is investigating how often someone picks192their nose, I mean who cares? ▶193*SS: yeah, right. ▶194*TS: but that's a matter of some debate. ▶195*TS: ok. ▶196*TS: alright does that take care of that. ▶197*SS: yeah. ▶198*TS: for you a little bit? ▶199*TS: ok, let's go back and kind of run through it all. ▶200*TS: can you tell me about inferential statistics? ▶201*TS: kind of review from last week a little bit. ▶202*SS: well, uh, it seems like inferential statistics are just taking203information and applying it to predicting what you expect to find. ▶204*TS: ok, it's more along the lines of saying how applicable what you205found is to your; you know and in a sense yes prediction should but206a lot of it is seeing how applicable and what you found or how207likely that holds true for the population &=mumbles. ▶208*TS: ok, alright. ▶209*TS: if a researcher has made sure that he or she has equivalent groups,210you know by experimentally controlling all the extraneous variables211or by randomization, or both, or whatever. ▶212*TS: does this necessarily mean that any differences in dependent213measure must be due to the independent variable? ▶214*SS: uh, no because there would be within, are you talking about within215subjects? ▶216*TS: right, well, or there might be error or variance. ▶217*TS: you know, sure when you talk specifically about it in general218terms, no, they're gonna be; any sample is a sample. ▶219*SS: right, there's always gonna be differences. ▶220*TS: sure, major differences or whatever. ▶221*TS: ok, that's why we need inferential statistics is to see how222representative our sample is due to the kinds of variances that223occur &=mumbles. ▶224*TS: ok, so, when we're looking at our statistics obviously we have to225have our hypothesis first, Ok, so can you tell me what the two main226types of hypothesis we deal with are? ▶227*SS: well, the null hypothesis states that the mean for the population228would be no different than the sample or expected to be. ▶229*SS: um, the alternative hypothesis of a particular research project230expects there to be a difference. ▶231*TS: uh, hah, between the means. ▶232*SS: right. ▶233*TS: in other words, the means are different, therefore they come from234different populations. ▶235*TS: that's what we were talking about. ▶236*TS: ok, so, in other words, which one means that the independent237variable has no effect? ▶238*SS: the null. ▶239*TS: ok, and so the alternative says that. ▶240*SS: there is an effect. ▶241*TS: right. ▶242*SS: it does have an effect. ▶243*TS: ok, um, why do we, Ok, usually when we're formulating hypotheses,244you know, the research hypotheses is sort of defined or sort of set245against the null. ▶246*TS: in other words, we speak of the alternative in terms of the null. ▶247*TS: that the null s not the case you know we speak in terms of248accepting or rejecting the null. ▶249*TS: do you understand the logic of that? ▶250*TS: why is that so? ▶251*SS: well, because it's easier to, uh, I mean it's, ah, let's see (.) it252would be better to prove that something is not right then to prove253that something, well (.) It might be more meaningful maybe to prove254that something is, to find out if, to refute something than to255collect data to prove your point, I don't know. ▶256*TS: that's sort of. ▶257*TS: one thing you have to be careful of is proving. ▶258*SS: right. ▶259*TS: ok, we rarely can say, rarely, never can say we prove anything. ▶260*TS: we can only get to such a probability that we accept or reject. ▶261*TS: um, it's more along the lines of that if we can determine that the262null is incorrect, we can accept the research hypothesis. ▶263*TS: in other words, the independent variable probably has had an effect264on the dependent variable. ▶265*TS: but the null statement is an exact statement, perfectly precise, it266says the population means are exactly equal. ▶267*TS: so this allows us to calculate precisely the probability of the268observed outcome occurring when the null is correct. ▶269*TS: ok, such precision is possibly due to the research hypothesis, Ok,270so we think in terms of accepting or rejecting the null. ▶271*TS: ok? ▶272*SS: ok. ▶273*TS: so it allows us for that precision because we calculate an exact274statement, if we calculate the conditions of it exactly. ▶275*TS: alright, so we speak of the probability that the observed results276could occur by chance. ▶277*TS: you know the null is rejected, and that probably gets so low, that278is unlikely that it would have occurred by chance, if the null were279true. ▶280*TS: ok? ▶281*TS: so what then is statistical significance? ▶282*SS: well, statistical significance means that data was found that would283be so unlikely to occur if the null hypothesis were true. ▶284*SS: and of course you can set that with your, ah +... ▶285*TS: probability, you confidence level or alpha. ▶286*SS: confidence level, right? ▶287*SS: the &=mumbles to that is the more unlikely it is to find something288out there and yet still the null be true. ▶289*TS: right, in other words, as you're saying you can choose how much290chance you're willing to bet. ▶291*SS: that's right. ▶292*TS: xxx. ▶293*TS: ok, alright, so but again, remember, that we speak in terms of294probability because of this error it's a real life situation that295hopefully corresponds to our lovely theoretical claims. ▶296*SS: to bad. ▶297*TS: yeah, really. ▶298*TS: ok, so we already talked about it a little bit so let's see if you299can tell me about the sampling distribution, what that is. ▶300*SS: um +... ▶301*TS: one more time. ▶302*SS: the sampling distribution, well, that term, you mean a normal303distribution? ▶304*TS: a sampling distribution, just like we were talking about earlier305when we were talking about the sampling distribution with the means306and all that. ▶307*SS: ah, well, the sample distribution would be what you get from your308sample data. ▶309*TS: ok, right the distribution of say sample means. ▶310*SS: sample means. ▶311*TS: or whatever. ▶312*SS: right. ▶313*TS: remember that a sampling distribution refers to a distribution of314statistics not raw scores. ▶315*SS: right. ▶316*TS: um, the can be of two types like I was talking about earlier. ▶317*TS: you can have say literally ten observed sample means or we can say318like I was talking about earlier in hypothetical terms an infinite319number of samples. ▶320*SS: uh huh. ▶321*TS: and that allows us to; these theoretical sampling distributions322allow us to calculate our probabilities and things like that. ▶323*TS: sampling distributions based on the assumption that the null is324true, you know allows us to calculate all those things. ▶325*SS: that's from the normal distribution xxx? ▶326*TS: it's from a sampling distribution of the scores at the confidence327levels you want xxx. ▶328*SS: I don't understand. ▶329*TS: ok, so it allows us to determine the probability associated with330each possible outcome you know for each different level of331confidence you might choose, or whatever. ▶332*TS: alright, um, so we've already talked a little bit about what333happens as sample size increases. ▶334*SS: well, your variability decreases, doesn't it? ▶335*TS: well, not necessarily. ▶336*SS: I mean. ▶337*TS: but you are more likely to detect, to obtain an accurate estimate338or to be able to xxx yes, so in a way your variability might become339smaller as you got a truer picture. ▶340*SS: yeah, you would get your curve would look more. ▶341*TS: well, your line would get more accurate, you know. ▶342*SS: xxx. ▶343*TS: you might find more outliers as you <xxx> [>]. ▶344*SS: <this is true> [<]. ▶345*TS: really the important thing to remember that +/. ▶346*SS: truer picture. ▶347*TS: yep a truer picture xxx. ▶348*TS: ok. ▶349*TS: and alright so talking about testing our means looking for350significance. ▶351*TS: what were the two types we talked about? ▶352*SS: t_test and f_test. ▶353*TS: sure. ▶354*TS: when do we want to use the t_test? ▶355*SS: t_test is used when you just have two you want to find the356difference between two different xxx. ▶357*TS: means. ▶358*SS: means ok. ▶359*TS: xxx. ▶360*SS: and then the f_test is three or more when you have three or more361means you want +/. ▶362*TS: groups . ▶363*SS: right. ▶364*TS: xxx. ▶365*TS: ok. ▶366*TS: alright so it's most commonly used when xxx two groups xxx. ▶367*SS: often the type of case is when you say have two levels of one368independant variable xxx is the usual kind of senerio. ▶369*TS: okay when using any type of statistical test of your means what370sort of things do you have to decide first (.) before you do any371kind of analysis. ▶372*TS: there are a couple of things you have to assume or decide. ▶373*SS: ah let's see <before> [//] after you've done your test before you374do your xxx. ▶375*TS: before you analyse your data. ▶376*TS: xxx you have to decide some things. ▶377*TS: you have to specify your hypothesis first. ▶378*SS: oh yeah your research hypothesis and then you set your alpha level.379▶380*TS: right, exactly. ▶381*TS: ok, so, ah, can you think of an example of when a t_test might be382appropriate? ▶383*TS: xxx. ▶384*SS: ummm. ▶385*SS: well, let's see, maybe if you want to, ah, xxx. ▶386*SS: this is hard, actually figuring these things out. ▶387*SS: umm, let me think. ▶388*TS: well if you can't think of examples you can often understand a389t_test in like graphs. ▶390*SS: right, or when you want to use it. ▶391*TS: or when you want to use it. ▶392*SS: well, umm, test scores, maybe. ▶393*TS: are affected by what? ▶394*SS: the amount of study time. ▶395*TS: ok, that sounds good. ▶396*TS: alright, so for convenience sake you want to say you had two groups397obviously for our t_test, maybe x@l one. ▶398*SS: uh huh. ▶399*TS: ok, x@l one studied for how many hours? ▶400*SS: uh, five hours. ▶401%act: puts x1 on board402@Comment: pict002 (c17/image002.jpg)403*SS: you not xxx here. ▶404*SS: ok, five hours of study. ▶405*SS: this may not be per night. ▶406*TS: oh, well. ▶407%act: x@l two equals.408*SS: two hours. ▶409*TS: two hours of study. ▶410@Comment: pic004 (c17/image004.jpg)411*TS: ok. ▶412%act: puts mean on board413*TS: this then would be what, our independent or dependent measures? ▶414*SS: ahh, those would be independent measures. ▶415*TS: right. ▶416*TS: so, what do we want to call our dependent? ▶417*TS: we'll call it y@l. ▶418*SS: the dependent measure would be, ah, grades. ▶419*TS: on the test scores. ▶420*SS: yeah, on the test scores. ▶421%act: puts y on board422@Comment: pic006 (c17/image006.jpg)423*TS: ok, so what would be our null hypothesis? ▶424*SS: the null would say that x@l one minus x@l two is equal to zero, the425means would be the same. ▶426%act: puts this on board427@Comment: pic008 (c17/image008.jpg)428*TS: do you know the symbol of the null? ▶429*SS: the null is, ah, (.) xxx. ▶430*TS: come on, you remember. ▶431*SS: mmm, I can't remember. ▶432*TS: ho. ▶433*SS: oh yeah. ▶434%act: puts Ho on board435@Comment: pic010 (c17/image010.jpg)436*TS: ok, so our alternative or research hypothesis. ▶437*SS: h_y. ▶438%act: TS puts Hy on board439*TS: yeah, and if you did in these terms? ▶440*TS: 0 [= refers to equation]. ▶441*SS: it would be x@l one minus y@l one equals zero. ▶442*SS: yeah. ▶443*TS: or that means [= puts on board]. ▶444@Comment: pic012 (c17/image012.jpg)445*SS: right. ▶446*TS: ok, alright so we're gonna set up our t_test, and there are a447couple of other things we have to get, Ok. ▶448*TS: do we think that there's gonna be a difference? ▶449*TS: I mean obviously. ▶450*SS: yeah, we do. ▶451*TS: do we think there's gonna be a direction for that difference? ▶452*TS: in other words. ▶453*SS: yeah, it would be a one tailed test. ▶454*TS: ok, in other words, so what are we saying here? ▶455*SS: we're saying that the, ah, x@l one, or x@l one. ▶456*TS: is gonna be better. ▶457*SS: yeah, is gonna be better. ▶458*TS: so a one_tailed might be more appropriate. ▶459%act: puts on board460@Comment: pic014 (c17/image014.jpg)461*TS: ok, we've decided on our direction, we formulated our hypothesis,462and about our significance level we are typical psychologists and463we're gonna say alpha is. ▶464*SS: point o five. ▶465*TS: very good. ▶466%act: puts alpha level on board467@Comment: pic016 (c17/image016.jpg)468*TS: ok, alright, so we know that our t_test is to look at our to test469the difference between our means. ▶470*TS: so could you tell me what exactly is the t_test. ▶471*TS: what are it's components? ▶472*SS: well, let's see, umm, you mean the formula? ▶473*TS: ah, the formula and then how to explain it in plain English. ▶474*SS: well, I guess what you do first of all is you get gather all your475data, you get your people and then you; get the ones that study five476hours you get their scores, and then the ones that study two hours477you get their scores. ▶478*SS: then you get your average, and ah, ah +... ▶479*TS: you apply your formula. ▶480*SS: right. ▶481*TS: ok, but what does that formula consist of? ▶482*TS: it's a ratio. ▶483*SS: yeah, it's a ratio of the, um, mean difference on top. ▶484*SS: I mean actually the difference in means go on top. ▶485*TS: means of what? ▶486*SS: of both groups groups. ▶487*TS: between groups, Ok. ▶488*SS: between groups, and then on the bottom, ah, it's +... ▶489*TS: ok, you have definition between groups. ▶490%act: puts on top of ratio491@Comment: pic018 (c17/image018.jpg)492*SS: within groups. ▶493%act: puts denominator up494@Comment: pic020 (c17/image020.jpg)495*TS: ok, what does that mean? ▶496*SS: well, there's probably gonna be some variability within the group497because not every body is gonna make the same score. ▶498*TS: in other words, each raw score and x@l one is gonna deviate from499the mean of x@l one to some degree. ▶500*SS: right, so technically you figure out the distance from the mean and501then you square it that and then you get the standard deviation. ▶502*SS: is that right? ▶503*TS: right, I was just mainly looking if you understood the logic of the504ratio. ▶505*SS: well, that's true, that's sometimes more important than506remembering. ▶507*TS: the formula, you can look up. ▶508*SS: when we were talking about that, um, when I got more into509statistics and we started really doing the; getting into just on and510on and on about with this variance, and I got kind of confused, but511really there's always gonna be within group variance. ▶512*TS: sure. ▶513*SS: so that's never gonna go away? ▶514*TS: yeah. ▶515*SS: so, um, well, I'm kinda getting ahead of myself, I was trying to516remember what was actually gonna be &=mumbles. ▶517*TS: well, you know in a perfect case you would want; the important518thing to remember is that you want your between groups difference to519get larger and larger, and your within groups differences to get520smaller and smaller. ▶521*TS: that's the way. ▶522*SS: oh, right, right. ▶523*TS: that's to make it more significant. ▶524*TS: um, are you asking maybe, do you not understand why they even look525at within groups? ▶526*TS: is that what your saying? ▶527*SS: well, kind of, yeah, I mean you know there's gonna be some528variability within the people that are in the groups. ▶529*TS: ok, I can draw a little figure that may help, but if it just starts530to confuse you more, stop me. ▶531*SS: ok. ▶532*TS: I'm gonna try this xxx [= puts graph up]. ▶533@Comment: pic020 (c17/image022.jpg)534*TS: ok, here's our two groups. ▶535*TS: ok, here's our means. ▶536*TS: xxx. ▶537*TS: we'll just play with our data here. ▶538*TS: ok, alright, this is your means, Ok, this is sort of theoretical of539the whole population, Ok. ▶540*TS: if you had it all this is the way it would be. ▶541*TS: well, obviously, if I drew a sample, my sample mean might also be542here, because of the spread of the individual raw scores, 'cause my543sample mean on this one might be somewhere over there544[= referring to s@l one] even though the trend is over here545[= referring to x@l one]. ▶546*TS: over here say my sample mean might fall a little bit above, ok. ▶547*TS: so, but if you look at the within groups variability, how much548spread around the mean there's going to be around each one. ▶549*TS: then we can sort of have an idea of how far off that would be. ▶550*TS: that's what within groups variance is, you know how far each one551xxx. ▶552*TS: so if you have some idea of how far each one xxx. ▶553*TS: then we have some idea of how close to the real mean our observed554mean is. ▶555*TS: do you see that? ▶556*SS: yeah. ▶557*TS: ok. ▶558*SS: you mean in other words, if you just picked, chose a mean, one of559those is a mean. ▶560*TS: yeah, this is gonna say, but since we are ignorant, this is just a561sample, we don't really know. ▶562*SS: right. ▶563*TS: and yet if we calculate the variability within that group we can564have some idea; I mean you know if the scores vary way over we might565say well this mean may really not be close to the real mean, but if566they. ▶567*SS: uh huh. ▶568*TS: don't vary that much we can say well this is probably pretty close.569▶570*SS: oh, Ok. ▶571*TS: ok, so that when this mean that we draw can come from anywhere on572this distribution, but if we know pretty much how varied it is. ▶573*SS: uh huh. ▶574*TS: then we're closer to knowing, you know, how significant this spread575is x@l one versus x@l two in other words, this one might have come576from somewhere way over here [= referring to s@l two] but the actual577distance is only this much [= referring to x@l one to x@l two]. ▶578*SS: uh huh. ▶579*TS: if you know something about how close this spread is to this one580[= s@l one to x@l one] then we know how much this difference581actually means [= x@l one to x@l two]. ▶582*SS: uh huh. ▶583*TS: ok. ▶584*SS: ok, well wait a minute, I understand why you would want to know. ▶585*TS: how much variability? ▶586*SS: how much within one sample? ▶587*TS: one group. ▶588*SS: one group, one mean. ▶589*TS: ok, so that gives you some idea of how close to it's real mean it590is within each group. ▶591*SS: right, right. ▶592*TS: ok, so if you know how a treatment estimate of each within group it593is, then you know how real the difference between the two groups is.594▶595*TS: in other words, if you know, if you have an idea that this sample596mean might be way off because there's a lot of variability. ▶597*SS: uh huh. ▶598*TS: then you might say well, maybe the difference between these two599groups isn't so large, because this one has so much variability. ▶600*SS: oh, Ok. ▶601*TS: that's all it's saying. ▶602*TS: that's why you use both components [= points to ratio]. ▶603*SS: oh, ok, alright I think I understand let that sink in. ▶604*TS: ok, see if you can say it back to me. ▶605*SS: so, in other words, by knowing how much variability there is within606each group, ah, and just just kinda compare a score from each group607you could tell whether. ▶608*TS: if you can see how close to the real mean, the actual mean your609sample mean is for each group. ▶610*TS: ok, you have an idea of how much each group varies. ▶611*SS: uh huh. ▶612*TS: so you have an idea, you know how good an estimator your sample613mean is of the actual distribution, xxx then you have an idea of how614actually far it is from the other one. ▶615*SS: I don't understand that. ▶616*TS: ok, Ok. ▶617*SS: I mean if you already know that your two means are far apart why618would you care. ▶619*TS: well, because this is that actual distance between the two means620[= points to x@l one and x2] you know in some other worldly621hypothetical kind of way.622*TS: but if you know that this [= points to s] is not real close to that623[= points to x], and this [= points to s two] is not real close to624that [= points to x] either; then you would want to put less625reliance on what you found. ▶626*SS: oh, ok. ▶627*TS: but if you know that this [= points t s@l one] is real close to628being true, and this [= points t s@l two] is real close to being629true then it let's you know that the distance between them is real630close to being true. ▶631*SS: oh, Ok, I understand that. ▶632*TS: ok, alright, but in any case don't worry, don't lose sleep over it633because just remember that it's the ratio between the between groups634and the within groups. ▶635*TS: ok, alright so you have that. ▶636*TS: ok, so this is your ratio and you put it through your formula to637come up with a t_value. ▶638*SS: uh huh. ▶639*TS: what do you do with that value? ▶640*SS: ok, let's say that you get two point five or something. ▶641*TS: yeah. ▶642*SS: and we go to the normal distribution table. ▶643*TS: ok, xxx the normal distribution the critical value would be xxx. ▶644*SS: right, and then we find what percentage of the population fall645beyond that point, and, ah, if it's, if you've already set your646alpha level and it is not outside that alpha level then you would647say. ▶648*TS: greater than in absolute value terms. ▶649*SS: right, then you would not reject your null. ▶650*SS: but if it was outside that then you would feel like you had enough651data to show that it was not just coincidental. ▶652*TS: ok, alright. ▶653*TS: so in other words, you start off we specify our hypothesis, our654significance level, whether it'll be one_tailed or two_tailed. ▶655*TS: we calculate our value of t which is the ratio of. ▶656*SS: between groups divided by within groups. ▶657*TS: right. ▶658*TS: you get that value and you compare it to a critical value to see if659it exceeds it, but you have to try one more thing before we know660which value to look at and that is to calculate our degrees of661freedom. ▶662*SS: yeah. ▶663*TS: so what are those? ▶664*SS: I don't really understand degrees of freedom. ▶665*TS: ok. ▶666*SS: but I know what it is, it's n@l minus one. ▶667*TS: sure. ▶668*SS: usually. ▶669*TS: but it depends on the statistic, Ok. ▶670*SS: and they say that it's the number of scores that are allowed to671vary, ah. ▶672*TS: once the mean; Ok, you're confused. ▶673*TS: alright, in terms of the t_test, the degrees of freedom are the674number of scores allowed free to vary once the means are known. ▶675*TS: for example, if the mean of a group is six, Ok, we already know676that the mean of a group is six. ▶677*SS: uh huh. ▶678*TS: ok, so we already knew that, and you have five subjects in the679group, Ok, one any four scores are known than we already know the680fifth one because whatever it has to be it would have to be to add681in the make the average six. ▶682*SS: uh huh. ▶683*TS: that means that you could pick any four values, but once you had684four, the fifth one is already determined because it has to be685whatever would add those to make it six. ▶686*SS: oh, Ok. ▶687*SS: that makes sense, but then it's not gonna vary, that. ▶688*TS: I know that's why it's not free. ▶689*TS: four of 'em were free to vary, but one isn't. ▶690*SS: oh, Ok. ▶691*TS: and that's why they say degrees of freedom is the number of sample692minus one. ▶693*SS: oh, Ok, that makes sense. ▶694*TS: ok, good, and so, and of course lot's of times that's how you695define it from backward xxx. ▶696@Comment: pic024 (c17/image024.jpg)697*TS: ok, now back to a little bit more about the one and two scale698probability. ▶699*TS: pictorially, what would be the one_tail look like? ▶700%act: puts graph up701*TS: just tell me what to draw. ▶702*SS: oh, Ok, well you'd just cut off one side of your. ▶703*TS: ok, in other words, you need your t to be at some level over here,704at point zero five or whatever. ▶705*SS: uh huh. ▶706*TS: and you know this would be your critical value for t707[= indicates critical value]. ▶708@Comment: pic026 (c17/image026.jpg)709*TS: I think the book has an example of, um, the critical value say710might be one point seven or eighteen degrees of freedom. ▶711*TS: whereas in the two_tailed one what you do. ▶712*SS: you divide it. ▶713*TS: you break it up, right, so you only have half of point zero five on714that side, so it would be a little less, and half of it uphere. ▶715%act: re-does as two-tailed graph716@Comment: pic028 (c17/image028.jpg)717*TS: ok, so we had a one_tailed test so we got to pile all of our718confidence, our guessing level over one side. ▶719*TS: whereas with a two_tailed, you know if we guesses wrong we would be720in trouble, but once we put it all on one side we need a slightly721less large t_value. ▶722*TS: see how for the two_tailed here you need something to exceed two723point one, whereas for the one with all of it clustered, you only724have to get one point seven. ▶725*SS: uh huh. ▶726*TS: so , you know we're taking the chance that we're gonna have a less727high t_value by putting it on side. ▶728*SS: that seems kind of risky. ▶729*TS: but, well, if your pretty sure then you want to go ahead and do it,730but if not then maybe not break it up. ▶731*SS: uh huh. ▶732*TS: ok, F_test. ▶733*TS: when would you want to use that one? ▶734*SS: well, I know you use an F_test when you have three or more groups,735means that you want to compare, but I'm no real sure about. ▶736*TS: ok, basically, an F_test does the same sort of thing the t_test737does. ▶738*TS: the t_test is a special case, um, with only the two groups you're739talking about, the two means. ▶740*TS: the F_test you could use an F_test for just two groups, and in that741case the F_value would equal the t_value squared. ▶742*TS: ok, so that's a special case. ▶743*TS: but the F_test for, or also called, analysis of variance. ▶744*SS: oh, yeah, an anova. ▶745*TS: ok, the same thing is typically used when you have more. ▶746*TS: ok, and it's set up, the similar thing is this, the F_value is the747ratio of two types of variance, again. ▶748*TS: and the book calls those the systematic variance and the error749variance. ▶750*TS: ok? ▶751*SS: uh huh. ▶752@Comment: pic030 (c17/image030.jpg)753*TS: 0 [= writes on board]. ▶754*TS: and what does the systematic variance correspond to? ▶755*SS: well, it's between. ▶756*TS: in other words [= points to between part of previous ratio]. ▶757*SS: right. ▶758*TS: same thing. ▶759@Comment: pic032 (c17/image032.jpg)760*TS: systematic variance to error variance. ▶761%act: finishes ratio762*TS: and the error variance being? ▶763*SS: ah, between, within, within. ▶764*TS: that's right. ▶765*TS: it's the same sort of test. ▶766*TS: ok, the systematic variance is the deviation of the groups from the767grand. ▶768*TS: in other words, it is between group variance, but this time we have769more than one group. ▶770*SS: uh huh. ▶771*TS: so, this time we might have five, two, and one hour of study, or772something like that. ▶773*TS: but in any event, (.) we have three groups; x@l one, x@l two, x@l774three. ▶775*TS: alright. ▶776*TS: we take a mean of each of those. ▶777*TS: and then we get a grand mean which is the mean of every single778score in the study. ▶779%act: puts on board780*TS: ok, the systematic variation is the deviation of each one of these781[= indicated group means] from this [= Indicates grand mean]. ▶782*TS: ok, and then what would our error variance be, our within groups,783and what is it? ▶784*SS: it would be the deviation between each group. ▶785*TS: from itself, so the within stays the same. ▶786*SS: right. ▶787*TS: within group each time, the deviation of a raw score in this group788this x@l one mean. ▶789*TS: ok. ▶790*TS: so the systematic variance, the difference between each group mean791and the grand mean is smaller when the difference between the groups792is small, obviously, and it increases as the difference increases. ▶793*SS: right. ▶794*TS: ok, the larger the F_ratio then the more likely the results will be795significant since it is more likely to exceed the critical value796when you compare the two in the critical table. ▶797*SS: right. ▶798*TS: ok, so the five_point sort of summary of that is the goal is to799determine if our obtained results are reliable and apply from the800sample to the population. ▶801*TS: ok, significance level is your choice of how confident you wish to802be. ▶803*TS: ok, you are more likely to obtain significant results when you have804a large sample and xxx. ▶805*TS: um, you are more likely to obtain significant results when between806the groups is large and within the groups is small. ▶807*TS: ok, alright, um, just remember that the t is the ratio of between808groups to within groups. ▶809*TS: you have to count both types of variance is all you really need to810remember. ▶811*TS: f is the same thing, between groups is each group to the grand and812the within is the same each individual to it's respective group. ▶813*TS: alright, so that leaves us type one and type two errors. ▶814*TS: if you want to go that's fine, but I'm welcome, I don't mind. ▶815*SS: no, no, that's fine with me. ▶816*TS: you're supposed to be cut loose at quarter till if you want, but. ▶817*SS: no, that's fine, I stayed an hour last time. ▶818*SS: I need all the help I can get. ▶819*TS: ok. ▶820*SS: this stuff, I have such a weak grasp on it, you know it's kind of821like I can do it to a certain point, and then. ▶822*TS: and that's such a shame because it really make sense when it can823click. ▶824*SS: maybe if we do some research in there. ▶825*TS: you sound fine. ▶826*TS: you're doing fine. ▶827*SS: sometimes I get confused. ▶828*SS: I think I understand it. ▶829*SS: I mean in theory I sort of understand it xxx. ▶830*TS: xxx. ▶831*TS: ok, talking about types of errors. ▶832*TS: so what am I putting up here? ▶833*TS: do you know what it's called? ▶834%act: puts grid up835@Comment: pic034 (c17/image034.jpg)836*SS: well, yeah. ▶837*TS: the decison matrix. ▶838*TS: it has to do with the population, and the decisions we make about839that population. ▶840*TS: ok, what two decisions can we make? ▶841*SS: well, let's see, we can fail to reject the null hypothesis. ▶842*TS: in other words, usually we just say it as fail to reject. ▶843*TS: that's what kind of confused me about that. ▶844*TS: yeah, I agree with you. ▶845@Comment: pic36 (c17/image036.jpg)846*TS: you are usually told to say failed to reject. ▶847%act: adds to matrix848*TS: ok, or we can? ▶849*SS: reject. ▶850%act: TS adds to matrix851*TS: ok, about our population we can say that either that the null is. ▶852*SS: true . ▶853%act: TS adds above854*TS: or we can say the null is? ▶855*SS: false. ▶856*TS: ok, if I reject the null hypothesis, in other words, I found a857difference between the number of hours of study and scores that they858make on the test, but there was actually no real difference, it was859only due to my measurement or sampling or some kind of error. ▶860*TS: what kind of error have I made? ▶861*SS: type one. ▶862%act: adds to matrix above863*TS: ok, in other words we rejected the null when actually the null was864true. ▶865*TS: ok, when the null is false and we reject the null, what have we866done? ▶867*SS: you've make a correct decision. ▶868%act: TS Adds to matrix869*TS: when the null is true and we have failed to reject it. ▶870*SS: correct decision. ▶871%act: TS adds to matrix above872*TS: ok, the null is false, but we have failed to. ▶873*SS: type two. ▶874%act: TS adds to matrix above875*TS: in other words, In English, type one errors occur when we reject876the null when the null was actually true. ▶877*TS: type two occurs when the null hypothesis is accepted although in878the population, the research hypothesis is true. ▶879*TS: in other words, the null is false and the h@l one is true. ▶880*TS: althought you were correct, we don't usually talk in terms of881proving the null. ▶882*TS: we usually say accept or reject. ▶883*TS: ok, can, which type of error do we usually think of as being more884serious in the context of social sciences? ▶885*SS: type I. ▶886*TS: ok, and why would that be true? ▶887*SS: well, because, um, you would always want to make sure that befor we888reject the null that we have really good data that proves that it's889not true, and we could, say something wasn't true, we found some890kind of effect that really wasn't a find. ▶891*TS: right. ▶892*SS: it has no basis at all, and I'm sure that happens all the time. ▶893*TS: well, as you set your alpha level higher and higher it becomes more894likely. ▶895*SS: true. ▶896*TS: ok, but why then is a type two error not so serious in research? ▶897*SS: well, you could always go back and test it again you know if you898decide you didn't find what you wanted to find. ▶899*TS: would you do another study? ▶900*SS: yeah, you can, ah. ▶901*TS: maybe you could do what with your sample size? ▶902*SS: you could increase it. ▶903*TS: ok, maybe you could do some other things like get some more904reliable measure, or. ▶905*SS: change you whole set up. ▶906*SS: I mean maybe you didn't do it right. ▶907*TS: sure, change the way you formulate things whatever. ▶908*TS: ok, what if I'm studying the effects of sleep deprivation on909teaching performance. ▶910*TS: one group has had twenty four hours of sleep deprivation and the911other has had sixty. ▶912*TS: I analyze the results and based on them conclude from them that the913amount of sleep deprivation does make a difference. ▶914*TS: however, in reality the amount of deprivation used in my conditions915causes no difference. ▶916*TS: again, what type of error have I made? ▶917*SS: ok, if you say that sixty hours of sleep deprivation is different918from the other. ▶919*TS: was different from the other. ▶920*SS: well that would be when you reject the null when it is true, so921that's type one. ▶922*TS: type I, right. ▶923*TS: so what happens as we decrease the chance of our type one, as we924set our alpha level higher and higher, what happens to our chance of925a type two error? ▶926*SS: it increases. ▶927*TS: right. ▶928*SS: because it makes it harder to, Ok, as you make it harder to reject929your null, you make it, um, easier to, you make it harder to reject930the null. ▶931*TS: right, you make it harder to reject the null. ▶932*TS: so. ▶933*SS: so, there might be some significant. ▶934*TS: so you might have made it so hard to reject that there might have935been an actual effect. ▶936*TS: you let something slide through xxx, too large of holes or937something. ▶938*TS: well, that's actually opposite the effect. ▶939*TS: in other words, as you make it so hard to reject the null, you run940the risk. ▶941*SS: that there's a real effect, and you don't pick it up. ▶942*TS: right, and you don't pick it up. ▶943*SS: don't people usually attempt it again in a different way, you know,944testing over. ▶945*TS: sure, sure, that's the whole point. ▶946*TS: for research purposes a type two is not so bad, but like the book947said say for surgery, that was needed to save somebody's life. ▶948*TS: you might want to run the risk of surgery that really wasn't needed949before you'd run the risk of before you would run the risk of not950doing surgery that was really needed. ▶951*SS: right, right. ▶952*TS: ok, um, ok, can we specify the probability of makin a type one953error? ▶954*TS: in other words, when we report our results can we specify what our955chances. ▶956*SS: well, our alpha level sets up. ▶957*SS: if we say that it's point o@l five then we have a ninty five958percent; well we have a five percent chance of making an error. ▶959*TS: right! ▶960*SS: and we also have a ninty five percent assurance. ▶961*TS: a type one error, in other words, yes, it is the alpha level that962sets up the probability of making a type one error, whereas you963can't do that for the type two because you never know. ▶964*TS: you can never know, because say you set a ninty five percent965confidence level you never know within that five percent what your966chance of failing to reject the null determine within that what. ▶967*SS: right. ▶968*TS: your exact probability is; by definition you set your alpha level969and you have that one probability level. ▶970*SS: uh huh. ▶971*TS: ok. ▶972*SS: xxx. ▶973*TS: ok, you mean one beta and all that kind of. ▶974*SS: yeah, that kind of confused me. ▶975*TS: if you want to go over it sometime just give me a call, but again I976think all you probably need to know for this course is xxx. ▶977*SS: xxx. ▶978*TS: I don't know, we'll see. ▶979*SS: well, I guess I should concentrate on this. ▶980*TS: yeah, which is why just as far as the t; if I what I drew helped981you understand the t fine if not just remember that xxx is the982ratio. ▶983*SS: right. ▶984*TS: of those two, and you know that between the groups the within is985the variability within each group. ▶986*SS: right. ▶987*TS: and you need both of them for your t@l. ▶988*TS: ok, alright, so, um, interpreting nonsignificant results then in989light of what we just said that nonsignificant results can be990problematic because you know in research we're looking for991relationships, we're not out to prove there is not relationship. ▶992*SS: uh huh. ▶993*TS: you know, that would be sort of silly, um, and it's problematic;994but as we said you can always just do another study, but you can995specify the probability and you could be wrong and end up accepting996the null which would be your type two. ▶997*TS: um, (.) Ok. ▶998*TS: xxx. ▶999*TS: um, and I may have said that backwards. ▶1000*TS: ok, a single study may not show significant results cause you had1001poor procedure or a small sample or whatever, but the important1002thing then is the remember is that if you got nonsignificance that1003doesn't necessarily mean that you have to give up. ▶1004*TS: now you could run six studies and say forget it. ▶1005*TS: but you know may not necessarily so serious. ▶1006*TS: ok, anything else? ▶1007*SS: I don't think so. ▶1008*TS: ok, I hope that was helpful. ▶1009*SS: it was, anytime I go over something. ▶1010@End