Hi, I of course have to argue with Robin J But not on all points In the one sample, quantitative variable case, instead of bootstrapping, I have students sample from a made-up population. So this is still a bit ad hoc, but I think helps them better see the sampling from population connection we are emphasizing at this point in the course. With proportions, I agree that you have to decide whether you want to use a hypothesized value or the sample proportion to estimate the SD. In my class I want students to think about both methods, partly to see it often doesn’t make a difference, especially with a large sample size, which I assume is what the CCSSM will focus on. And of course, “traditional” methods make the same “arbitrary” decision – use hypothesized if you have one, use sample if you don’t. We do have students try lots of different null values the first time we are creating a confidence interval of plausible values (and that’s when we introduce the idea of level of significance), but we have added a feature to the technology to make this a little more efficient once they get the idea (think slider). My hope, though I don’t have a lot of data and what I do have isn’t “great,” is that students will be better able to focus on the interval being for the *parameter* rather than the common misconception that it’s an interval for sample proportions that I worry bootstrapping might reinforce. Basically I want students to think about a confidence interval as estimate +- 2SD, which they seem to get pretty easily, and then we can worry about the details of how to estimate the (right) SD in different cases/use technology. This is what we carry over to other statistics later in the course. I think CCSSM is focused on having students understand sampling variability and the idea of margin-of-error, of the proportion being close to the parameter and that the “plus or minus part” depends on sample size. Lots of good ways to get those ideas across. Like them, I’ve been starting with proportion, I guess they thought mean would be too tough as they didn’t want to have them get into bootstrapping. There is more discussion on exactly this issue on the SBI blog: https://www.causeweb.org/sbi/?cat=14 Beth *From:* sbi-bounces(a)causeweb.org [mailto:sbi-bounces@causeweb.org] *On Behalf Of *Robin Lock *Sent:* Tuesday, May 05, 2015 1:17 PM *To:* Simulation-Based Inference *Subject:* Re: [SBI] How to estimate parameters: To bootstrap or not? Daren - I'm a firm believer in using the bootstrap as the way to get a margin of error via simulation. The ideal way would be to form a sampling distribution but, in the real world, taking 1000's of new samples from the actual population is not a feasible way to assess the accuracy of the one estimate you have from an original sample! I think that the logic of hypothesis testing is already tricky for students to get a handle on, to have intervals depend on inverting that logic seems even trickier. The example you provided in the CCSS Progressions document is even more confusing. Here's what I gather is its "logic" Start with a sample of size 50 with a sample proportion of 0.40. You want to estimate its "margin of error". 1. Suppose the population proportion is really p=0.50. Simulate a sampling distribution using that p. 2. Observe that the sample phat=0.40 is not far in the tail of that distribution, so 0.50 is a "plausible" value for the population proportion. - Not bad so far. 3. Estimate the standard error by finding the std. dev. of the sample proportions in the distribution generated around p=0.50 (SE=0.07). 4. Use 0.4 +/- 2*(0.07) = 0.4 +/-0.14 = 0.26 to 0.54 to get a CI of similar "plausible values. Of course the SE for p=0.5 and p=0.4 are not a lot different, but I don't see the logic of picking some random "other" proportion, when you can do the simulation just as well aound p=0.40 (which is what the bootstrap would do in the first place!). I wonder what advice the document would give for finding a CI when phat=0.12? I think it is possible to do an interval more coherently by doing lots of tests for lots of null parameters and seeing which would be rejected for the sample data, but (a) That sort of guess/check process is not very efficient. (b) I'd like to downplay the hard 5% reject Ho decision, and would rather have a test p-value be interpreted as "strength of evidence" (c) Creating the simulations to test lots of nulls is more problematic (especially via simulation) for other parameter situations like a difference in proportions, difference in means, or correlation. The bootstrap procedure is pretty straightforward: take lots of samples (with replacement) from the original sample, calculate the statistics of interest, estimate SE as the std. dev. of all those bootstrap statistics. A rough margin of error as 2*SE is easy to find and the same process works for lots of different parameters. Robin On 5/3/2015 4:03 PM, Daren Starnes wrote: Happy May, everyone. There is an interesting thread on the AP Statistics Teacher Community about two distinct views on estimating parameters via simulation. This came up because the Common Core State Standards includes this Statistics and Probability standard S-IC.4 Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. View #1: Use bootstrapping. View #2: Determine whether "nearby" values of the parameter are plausible by simulating a "null distribution" with that parameter value and seeing if the observed statistic is a believable outcome from such a null distribution. Keep doing this for other nearby values until you have an interval of plausible values for the parameter. The attached CCSS Progression document seems to suggest View #2, at least as far as estimating a proportion is concerned. There is no discussion of how to estimate the margin of error for a mean in this way (I wonder why!). This seems like an issue that this experienced group of SBI folks would already have grappled with--both philosophically and pedagogically. So I thought I would ask what the prevailing wisdom is. Daren Starnes _______________________________________________ SBI mailing list SBI(a)causeweb.org https://www.causeweb.org/mailman/listinfo/sbi -- Robin Lock Burry Professor of Statistics St. Lawrence University _______________________________________________ SBI mailing list SBI(a)causeweb.org https://www.causeweb.org/mailman/listinfo/sbi