Homogeneity And Heterogeneity Puns

I’m looking for an R package or function that I can use to measure the relative homogeneity/heterogeneity of groups of character strings. There are about 50 groups, each with thousands of character strings, with each string consisting of one or two characters. There are about 100 possible character strings, and not all character strings appear in all groups. A much-abbreviated example:

group1 <- c("AA", "N", "W", "AJ", "KC", "KB", "KB") 
group2 <- c("N", "W", "W", "N", "N", "N", "W", "W", "N") 
group3 <- c("WA", "W", "NY", "AA", "KC", "AK")

Group 2 is obviously the most homogenous/least heterogenous. What's an R package or function I can use to quantify this, such that it would produce an index score for each group?

Hello all,

I have seen a lot of complaining about the homogeneity of the new fleet we saw Captain Riker bring to bear in the last episode of S1-STP.

While I think it was a huge miss by production not to more visibly throw in a couple of older models (at least as a throw back to us old fans, a few defiants would have been cool!) I thought it best to take a closer look very briefly before passing too much judgement. After all, we only got some very brief looks at the fleet.

As you can see inthis linked photo, I have circled two ships in particular that I believe to be of different design among the fleet. The one on the upper left, the nacelles seem to be much more in line with the saucer section, or even a bit below it, rather than slightly above in a similar sovereign like configuration. I would chalk this up to angle, but it also seems to have a different "dome" like structure on the saucer section (about where a bridge might be). These two features make me believe that this is a different ship design, albeit somewhat close to the Zheng He, but similar to the difference between a nebula and a galaxy maybe.
The one on the bottom right is the one I was really excited about... at first I discounted it as one ship but then realized that it would be oriented the wrong way if so....so on closer inspection I think it must be two, and in that case the one nearer to us has a much different configuration than the Zheng He- in fact, it looks very reminiscent to the profile of an intrepid class ship. The nacelles are definitely below the hull and somewhat flat compared the saucer section.

The ship design of the Zheng He seems to me a natural progression to the Akira/Sovreign classes that were emerging in the late dominion war. Indeed, even the idea of a mass produced war ship of similar design flows very naturally from a society that was involved in a huge, civilization threatening war- look at the proliferation of B52s during WW2 and how long they remained (or the airframe at least...) a staple of american military strategy. So before we all start bemoaning the idea of a homogeneous starfleet, it actually makes sense if starfleet has taken on a much more military focused role in federation society over the last 20 years. If you believe my half-baked analysis of this photo, the fleet isn't even entirely homogenous, it is just mostly made up of this new mass-produced warship class of vessels.

I will now step down from my table

Social Democrats and other Progressives everywhere turn to Scandinavia and the Nordic model, saying that they want to reform their respective countries along similar lines. I find it disingenuous as they conveniently ignore progressive European states that spent too much, such as Greece and Italy. Scandinavian countries had functioning healthcare and social welfare before they were socialized, and the only reason their welfare programs work so well in the first place is because they're highly intelligent people, in a high trust, homogeneous society.

This wouldn't even be a problem if it was an error few people make. But there is a large quantity of politicians and politically minded people that basically respond to everything with 'lets just do it like Sweden'.

Are there any benefits of having the equipment and battle strategy of your troops being the same across the board vs having every group do it's own thing? Historically how does one compare to the other?

Self-explanatory title. I'm looking to run an ANCOVA and started learning R recently. It's been going well but I've found myself really stuck on finding out how to run these assumptions.

I have 3 levels of one IV, one covariate, and one DV.

I want to see if the covariate has a linear relationship with the DV at each level. I've managed to plot the DV (y axis) against the CV (x axis) and separate them by colour for each level, but I'm pretty stuck with adding in the lines for each level to indicate a linear relationship.

Secondly, I'm unsure how to check for homogeneity of regression in R.

If anyone could help I would really appreciate it. Sorry if this isn't the right place to post.

EDIT

I was hoping for some graphical indication of the two assumptions.

At the moment for a linear relationship graphic I've got

plot(CV, DV,
    pch = c(15,15,15) [Factor], col = c("red", "blue", "green"),
    xlab = "CV", ylab = "DV"
legend("topleft", legend = c (Condition1, Condition2, Condition3,
    pch = c(15,15,15), col = c("red", "blue", "green"))

This gives me a scatter graphic with each the DV and CV plotted for each group. However, what I really need is a line of best fit for each different level to compare the linear relationship for each level to ensure the assumption is satisfied.

I have tried to find information on this extensively but with no luck

So before the patient enters the mri, passive shimming is applied to fix the in-homogeneity.

Next the patient enters and then active shimming is applied

Q. What is the size and shape of the in-homogeneity due to the patient entering? (I guess in average)

Q. How is the 2nd order shim coils designed to counter this in-homogeneity?

I understand that after the patient enter the mri, the active shimming process is done automatically by the machine.

Q. Is is done by measuring the ppm over a certain volume?

Thanks

Hi all,

I am analyzing a large dataset for my thesis and the original plan was to conduct a huge series of ANCOVAs - however, it looks like one of the assumptions (homogeneity of variance) is violated within this population. I know there are non-parametric options (like Brown Forsythe) which might be a better option in this case - however, it looks like covariates can't be included with the non-parametric options!? And that sort of upsets my analysis.

My data comes from a sample of approximately 30,000 people (with at least a few hundred if not a few thousand in every group bring compared) and so I'm hoping I can just ignore the violations and make it clear in my finished paper that this assumption was violated and so results should be interpreted cautiously. Is that at all an acceptable option? I just think that chance of large variances skewing results from a smaller group seems unlikely when all of the groups are this large.

Richard Lowery emails me this:

I saw your post about epidemiologists today.  I have a concern similar to point 4 about selection based what I have seen being used for policy in Austin.  It looks to me like the models being used for projection calibrate R_0 off of the initial doubling rate of the outbreak in an area.  But, if people who are most likely to spread to a large number of people are also more likely to get infected early in an outbreak, you end up with what looks kind of like a classic Heckman selection problem, right? In any observable group, there is going to be an unobserved distribution of contact frequency, and it would seem potentially first order to account for that.

As far as I can tell, if this criticism holds, the models are going to (1) be biased upward, predicting a far higher peak in the absence of policy intervention and (2) overstate the likely severity of an outcome without policy intervention, while potentially understating the value of aggressive containment measures.  The epidemiology models I have seen look really pessimistic, and they seem like they can only justify any intervention by arguing that the health sector will be overwhelmed, which now appears unlikely in a lot of places.  The Austin report did a trick of cutting off the time axis to hide that total infections do not seem to change that much under the different social distancing policies; everything just gets dragged out.

But, if the selection concern is right, the pessimism might be misplaced if the late epidemic R_0 is lower, potentially leading to a much lower effective spread rate and the possibility of killing the thing off at some point before it infects the number of people required to create the level of immunity the models are predicted require.  This seems feasible based on South Korea and maybe China, at least for areas in the US that are not already out of control.

I do not know the answers to the questions raised here, but I do see the debate on Twitter becoming more partisan, more emotional, and less substantive.  You cannot say that about this communication.  From the MR comments this one — from Kronrad — struck me as significant:

One thing both economists and epidemiologists seem to be lacking is an awareness for the problems of aggregation. Most models in both fields see the population as one homogenous mass of individual

Hi, I am confused about whether Styrofoam is a compound, heterogeneous mixture, or homogeneous mixture? And why? Different places on the internet are saying different things.