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Comment: Ok, because there is viratully no where else to vent, and I doubt anyone is reading this forum at this point, here I go:I think I hate quilting. I'm not sure if it's the exacting fiddliness of it all
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  = A note about unequal group sizes in ANOVA =

Howell (1992) pp 410-417 and 542-549 illustrates and recommends the use of the (default) Type III sums of squares (termed Method I by Howell) for looking at sources of variation in an anova where the group sizes differ. This is ''provided the differences in group sizes are independent of the groups''.

The computations for these may be done using either a least squares approach based upon formulating the anova in terms of a linear regression (to generate Type III sums of squarres) or by using the formulae associated with equal groups as given, for example, [:FAQ/ss: here] but replacing the i-th group sample size ($$n_text{i}$$) with its harmonic mean, $$\bar{n}_text{i}$$:

$$\bar{n}_text{i}$$ = Harmonic mean of k means = $$ \frac{k}{\frac{1}{n_text{1}} + ... \frac{1}{n_text{k}}} $$

Howell (1997) states (e.g. on p.582 of his fourth edition) that using harmonic means of sample sizes to compute sums of squares in anovas in cases where group sizes are unequal gives sums of squares for sources of variation which closely approximate the type III sums of squares.

Using harmonic means, or Type III sums of squares, in an anova gives an ''unweighted'' means analysis which is an ''equally weighted'' analysis of group means because group means are treated equally irrespective of the size of the group upon which they are based. An example is [:FAQ/equalwts: here.]

Tabachnick and Fidell pp 217-218 also discuss sums of squares. They, like Howell, recommend Type III sums of squares for use for equally weighted groups and type II sums of squares when the sample sizes reflect the importance of the groups, e.g. when it is desired to consider the relative frequency of their occurrence in the general population (giving rise to a ''weighted'' means approach).

Harmonic means are also useful for averaging rates - see this [:FAQ/hmeg:example.]

__References__

Howell DC (1992) Statistical Methods for Psychology. Third Edition. Duxbury Press:Belmont, CA. (Fourth Edition is as above but published in 1997)

Tabachnick BG and Fidell LS (2007) Using Multivariate Statistics. Fifth Edition. Pearson:Boston.
Ok, because there is viratully no where else to vent, and I doubt anyone is reading this forum at this point, here I go:I think I hate quilting. I'm not sure if it's the exacting fiddliness of it all or if I am just not that into sewing machines (hand sewing? Hell yes!) but today was a total piss off in every way.1. On the bus to the work room a woman with her headphones on whistled all the way from Bloor to Queen St West, along Lansdowne. But not along with the music she was listening to, oh no, that would make too much sense, just one note over and over again, toot toot toot toot toot toot toot toot 2. I couldn't get the zig zag correct on the machine I always use and had to get help twice. It makes me feel totally stupid and I hate that. Then the tension was wrong and my fabric was bunching up in an ugly, hateful way, so I needed help again. 3. And then ironing and did I mention I hate ironing?4. Then the sewing machine I always use died. Literally. It was smelling funny, burny maybe, but I thought that maybe it had been freshly oiled, it was working fine, chugging along and then nothing. Motor gonzo, sorry Karyn. That's a $1300.00 Bernina, if you were wondering.5. Switched to a fancier machine ($3000.00 Bernina, fucking EEK!)that is all computerized and it was a clusterfuck for a bit, fiddling fiddling fiddling and then it was working and boy howdy, I want THAT machine, srsly, but sadly, I ran out of time. I got about a third of what needed to be done finished. Not one block is done completely. And I work tomorrow, training a new employee and again on Thursday (which I don't normally work) and then directly to my class Thursday night where I will have the complete lack of joy announcing my complete lack of doneness. This from the woman who only works 7 hours a week. Ugh.I suck.
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Ok, because there is viratully no where else to vent, and I doubt anyone is reading this forum at this point, here I go:I think I hate quilting. I'm not sure if it's the exacting fiddliness of it all or if I am just not that into sewing machines (hand sewing? Hell yes!) but today was a total piss off in every way.1. On the bus to the work room a woman with her headphones on whistled all the way from Bloor to Queen St West, along Lansdowne. But not along with the music she was listening to, oh no, that would make too much sense, just one note over and over again, toot toot toot toot toot toot toot toot 2. I couldn't get the zig zag correct on the machine I always use and had to get help twice. It makes me feel totally stupid and I hate that. Then the tension was wrong and my fabric was bunching up in an ugly, hateful way, so I needed help again. 3. And then ironing and did I mention I hate ironing?4. Then the sewing machine I always use died. Literally. It was smelling funny, burny maybe, but I thought that maybe it had been freshly oiled, it was working fine, chugging along and then nothing. Motor gonzo, sorry Karyn. That's a $1300.00 Bernina, if you were wondering.5. Switched to a fancier machine ($3000.00 Bernina, fucking EEK!)that is all computerized and it was a clusterfuck for a bit, fiddling fiddling fiddling and then it was working and boy howdy, I want THAT machine, srsly, but sadly, I ran out of time. I got about a third of what needed to be done finished. Not one block is done completely. And I work tomorrow, training a new employee and again on Thursday (which I don't normally work) and then directly to my class Thursday night where I will have the complete lack of joy announcing my complete lack of doneness. This from the woman who only works 7 hours a week. Ugh.I suck.


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None: FAQ/wmeans (last edited 2014-04-30 13:49:02 by PeterWatson)