0@Loc: Frederiksen/f-ratio.cha1@PID: 11312/t-00015841-12@Begin3@Languages: eng4@Participants: STU Student, TUT Tutor Adult5@ID: eng|Frederiksen|STU|||||Student|||6@ID: eng|Frederiksen|TUT|||||Adult|||7@Media: f-ratio, video8@Comment: Review of one-way ANOVA9@Comment: Goes to blackboard10@Comment: Begins explanation of F-ratios11*TUT: Ok so, this. ▶12%act: erases board13*TUT: ok, F ratios, ok, can be assumed under the null hypothesis to have14a certain distribution. ▶15%act: draws axes on bb16*TUT: ok, for things like , and there's , oh let me go back a bit farther17xxx. ▶18@Comment: Systat Analysis Window (comp.jpg)19*TUT: The shape of an F ratio, the precise shape of an F ratio20[% points to F ratio in systat anaysis window], depends on the21degrees of freedom that you have here. ▶22%act: points to df on anova table in systat analysis window .23*TUT: Ok, and here we have two and sixty nine degrees of freedom. ▶24*TUT: Now <what> [/] what the F distribution specifies it's a lot like25the sampling distribution of the mean that we talked about. ▶26*TUT: The F distribution specifies what the ratio of these mean squares27[% points to mean square values in anova table] would look like28under the null hypothesis. ▶29*TUT: That is, there being no significant difference, ok, among the30means. ▶31*TUT: And it specifies what that distribution would look like <if you>32[/] if you had, uh: sets of data from nineteen seventy and nineteen33eighty and nineteen ninety, and in fact in the underlying34populations for the math achievement scores there were no35significant differences for those three decades. ▶36@Comment: Computer Screen (comp.jpg)37*TUT: And if you did continuous sampling, ok, over and over again,38alright, what you would find if you make this ratio. ▶39%act: points to screen40*TUT: ok, you'd find you'd get a distribution, ok, that looks something41like this [% draws f distribution on bb] that is it starts at zero42[% writes zero on bb], ok, and it goes up, ok? ▶43*STU: Ok. ▶44@Time Duration: 00:23:51-00:25:5345*TUT: Actually I need a stats book here because I want the exact values.46▶47%act: looks on bookshelf for stats book48*TUT: Pedhauzer. ▶49%act: takes book50*TUT: There should be an F table in here. ▶51%act: flips through book52*TUT: Oh this one. ▶53%com: finds table in book54*TUT: So here we have the degrees of freedom55[% points to degrees of freedom for the numerator column of table]56ok, for the top part of the ratio which is two. ▶57*TUT: And what we know is that we have sixty nine degrees of freedom for58the bottom part of the ratio. ▶59%act: runs finger over rows in table60*TUT: So we'll go over here and we can actually choose uh seventy, ok? ▶61*TUT: Alright, now <the ones> [//] the particular ones we are interested62in are these ones, ok? ▶63%act: circles critical f values in the 2, 70 cell in the table64*TUT: Because they allow me to scale <this> [/] this I know the65distribution is shaped like this. ▶66*TUT: It's called a J distribution, ok? ▶67%act: goes to bb and points to f curve68*TUT: You don't know that but I know it from working with these69distributions so you can accept that xxx (.) ok? ▶70*TUT: And this distribution is such that it starts at zero and goes up71[% gestures to right along x axis] and at a value of three point one72three [% writes value on bb] which you see there. ▶73*STU: Right. ▶74*TUT: Right, that's a value that cuts this distribution into two parts . ▶75%act: draws vertical line at 3.13 value76*STU: Oh, ok. ▶77*TUT: ninety five percent of the distribution78[% writes 95% and arrow on bb] is below three point one three. ▶79*STU: Right. ▶80*TUT: And five percent is above . ▶81%act: writes 5% and arrow on bb82*STU: Ok. ▶83*TUT: So that accounts for the whole distribution. ▶84@Comment: Blackboard (board.jpg)85*TUT: What that means is that five percent of the area under this86distribution lies between three point one three and infinity. ▶87%act: motions to region beyond the board88*STU: Ok. ▶89*TUT: Ok. ▶90@Time Duration: 00:25:53-00:26:2891*TUT: Now, there's another figure given there in bold face I think92[% extends lines to the right], what is that value? ▶93%act: looks at book with student94*STU: four point nine two. ▶95*TUT: four point nine two, ok. ▶96*TUT: Which lies at about here. ▶97%act: marks it on graph98*TUT: Now this is another cut line, &=draws:line ok? ▶99*STU: xxx. ▶100*TUT: What? ▶101*STU: ninety ninety. ▶102*TUT: Yeah that's the, <it's the> [/], it's the ninety ninety one, cut103line, ok? ▶104*TUT: such that105[% draws bracket from cut line to zero and writes 99% on bb] ninety106ninety percent lies below four point nine two and one percent of the107distribution . ▶108%act: writes 1% with arrow on bb109*STU: Is up there. ▶110*TUT: lies above that, ok? ▶111@Time Duration: 00:26:28-00:27:54112*TUT: Now <these are> [//] of course these are probability distributions113[% writes 'prob' on bb], right? ▶114*TUT: ok. ▶115*TUT: And what that means is that if it were the case that across these116decades [% gestures to years on flipchart page 1] there were no117differences in math achievement scores, that is <you> [/] you have118the null hypothesis situation, and you did repeated sampling sizes119of twenty four, ok, from here [% gestures to flipchart p. 1], and120then you did this analysis of variance and you formed this F ratio121[% points to f ratio on screen], ok? ▶122*TUT: That is the mean square for year [% points to ms year] over the123mean square over the residual. ▶124%act: points to ms error125*TUT: ok, you would gradually and lets say you do that thousands of126times, right? ▶127*STU: Yeah. ▶128*TUT: Ok, <if you take> [//] if you did a frequency distribution of those129F ratios, right, what you would find is that you would get a pattern130like this [% gestures to f dist on bb], ok? ▶131*TUT: Say you do it a thousand times, you would expect that, well, ninety132five percent of the F ratios that you would form133[% points to 95% cut line on f dist on bb] under this null134hypothesis situation would lie between zero and three point three135[% gestures between these values on bb], and the great bulk of them136would lie close to zero, ok? ▶137*TUT: But occasionally just because of random sampling you'd get an F138ratio that lies above that. ▶139%act: points to region above 95% cut line140*STU: ok. ▶141@Time Duration: 00:27:54-00:28:45142*TUT: So that five percent of the time you get an F ratio that lies above143three point one three. ▶144%act: points to region above 95% cut line145*STU: Yeah. ▶146*TUT: And one percent of the time, ok, if you did a sample of one147thousand, you'd expect that about ten of them to lie above four148point nine two. ▶149%act: points to region above 99% cut line150*STU: Ok. ▶151*TUT: Ok, just by chance. ▶152*TUT: Ok? ▶153*STU: Yeah. ▶154*TUT: Alright, so that's basically what the meaning of this F ratio is,155ok. ▶156%act: moves left hand over f ratio157*TUT: That is it gives you the probability of finding a particular F158value within these intervals159[% gestures to two cut lines on f dist on bb] under the null160hypothesis case, that is when there is no significant difference in161the underlying populations of achievement scores across the decades.162▶163%act: gestures to data on page 1 flipchart164*TUT: ok. ▶165*TUT: <That's what> [/] that's what the F ratio is, alright? ▶166@End