20¢ = 25¢

Hailing from Australia, I've often been puzzled by American currency mores. Why "nickel" and "dime"? (I still can't remember which is which after a decade in the U.S.) Why is a dime (10¢ if you're wondering) smaller than a nickel (5¢)? What do Americans have against their 50¢ and $1 coins? Why do all banknotes look the same? (A practice that has been ruled to be in violation of the Disabilities Act.) Why don't Americans use $50 and $100 bills?

Besides all of these questions, I've wondered whether quarters (25¢) or 20¢ coins (as we have in Australia) are more efficient. I define efficiency for a system of coinage as requiring the fewest coins for an arbitrary amount of change between 1¢ and 99¢. Although Australia withdrew 1¢ and 2¢ coins from circulation in 1992, I made the comparison as close as possible by looking at a system with 1¢, 5¢, 10¢, 20¢/25¢, and 50¢ coins. The result, as the title of this piece suggests, is that 20¢ and 25¢ coins are equally efficient--the average number of coins required for amounts of change between 1¢ and 99¢ is 4.24 in both cases (SD is 1.71 in both cases).

As I mentioned earlier, though, Americans have a strange aversion to 50¢ coins, while pre-1992 Australia had 2¢ coins. If we take this into account, the average number of coins required for change in the U.S. rises to 4.75 while the Australian average falls to 3.43, meaning that you get on average more than a coin extra in change in the U.S.

The next step, of course, is to ask whether it is possible to do better than 5¢, 10¢, 20¢/25¢, and 50¢ coins altogether. Might we in fact better be served by 4¢, 12¢, 37¢, and 74¢ coins with respect to minimizing change? (Actually, yes. This would require 4.02 coins on average.) I've cleared most hurdles to specifying this problem in AMPL (a mathematical programming language for optimization problems) and will return with my "rational" scheme for change in the near future.

Of course, not all amounts of change are created equal. In currency regimes with 1¢ coins, prices tend to end in nines (Basu 1992, 2006; Demery and Duck 2007), while in Australia prices end in fives. Ideally, we would weight the number of coins by the probability of receiving change of that amount in a transaction. However, a cursory search has not revealed a useful dataset for these calculations.

References

Basu, Kaushik. 1997. "Why are so many goods priced to end in nine? And why this practice hurts the producers." Economics Letters 54:41-44.

-----. 2006 "Consumer cognition and pricing in the nines in oligopolistic markets." Journal of Economics & Management Strategy 15:125-141.

Demery, David and Nigel W. Duck. 2007. "Two plus two equals six: an alternative explanation of why so many goods prices end in nine." Discussion Paper No. 07/598, Dept. of Economics, University of Bristol, Bristol, UK.)

A Checklist for Critically Reading Quantitative Research

The following is an attempt to create a heuristic for evaluating the quality of quantitative social scientific research with zero assumed background in social scientific methods.

1. Is the information contained solely in a press release and/or interview or is a report or article in a scholarly journal available? If a report or scholarly journal, was the research reviewed by knowledgeable peers?

2. Is the basic methodological information required by the American Association for Public Opinion Research's Standards for Minimal Disclosure available, either in the report or a methodological appendix?

a. Who sponsored the survey, and who conducted it. Commentary: Search for information on the researcher and the company that actually carried out the data collection, if different. Have either been cited by AAPOR for violating its Code of Professional Ethics and Practices (e.g., )? Alternately, have company principals held posts in professional associations like AAPOR (c.f. Tom Smith, Mark Shulman) and/or publish methodological articles and give presentations at meetings like the American Statistical Association? Does the research firm used primarily conduct political polls, market research, or academic research? Naturally, look for commentaries on the specific piece of research. Where research is sponsored by an organization with an agenda that might influence research (i.e., just about all Jewish communal research), does the researcher explain the nature of their relationship with the sponsor?

b. The exact wording of questions asked, including the text of any preceding instruction or explanation to the interviewer or respondents that might reasonably be expected to affect the response. Commentary: Are the questions worded in a way that might bias the answer? If the results are very different to previous research, has the author used standard questions? If not, do they justify their items? Are there any skip patterns that fail to collect information from important populations? If the researcher combines items to form a scale or index, does s/he explain exactly how it was done? Does s/he report measures of scale reliability (e.g., Cronbach’s/coefficient alpha > .75)? Does the index/scale actually seem to reflect what the researcher says it does? Quite often, it doesn’t.

c. A definition of the population under study, and a description of the sampling frame used to identify this population. Commentary: Is there any reason to think that the sample might differ systematically from the population it is intended to represent? Was it a convenience sample (a.k.a. open sample)? Was it from an opt-in Internet panel? Does the sample just constitute Jews by religion? If there is a reasonable probability of bias, is it likely to have increased or decreased the reported results of the study? Does the author address any possible limitations of the sample?

d. Sample sizes and, where appropriate, eligibility criteria, screening procedures, and response rates computed according to AAPOR Standard Definitions. At a minimum, a summary of disposition of sample cases should be provided so that response rates could be computed. Commentary: The lack of a response rate is a major red flag. The response rate should be accompanied by a specification of the exact response rate formula used (e.g., AAPOR RR3). Better research will not only list the response rate but will address possible biases.

e. A discussion of the precision of the findings, including estimates of sampling error, and a description of any weighting or estimating procedures used. Commentary: If the survey uses an opt-in Internet panel or a convenience sample, estimates of sampling error are inappropriate and should never be reported. Discussion of weights may distinguish between design weights and poststratification weights (which correct for biases). If poststratification weights are used, the discussion should specify what variables were used and where how targets for adjustment were derived.

f. Which results are based on parts of the sample, rather than on the total sample, and the size of such parts. Commentary: If analyses exclude parts of the sample, is there a reasonable justification for their exclusion?

g. Method, location, and dates of data collection. Commentary: How long was the field period? How many contact attempts were made? Did the researcher try to convert refusals? Overall, does it appear that sufficient effort was put into collecting the data?

3. If the researcher describes something as a well-established fact, is it in fact widely supported? Often, it is not. Do a quick fact-check.

4. Does the researcher actually present evidence that directly supports their conclusions? Is there any evidence in the research that contradicts the researcher’s assertions? (This is surprisingly common.) Look carefully for situations where some related data is shown, “hand-waving” takes place (i.e., unsupported assertions are made), and a conclusion is stated definitively.

a. For processes involving changes over time, is there actually evidence of change over time or does the researcher base her/his analyses on differences between age groups? If so, can one reasonably expect there to be lifecycle effects?

b. For processes involving individuals, does the researcher base their conclusions on aggregated data?

5. Does the researcher omit any relevant outcomes? First, were there questions asked that aren’t reported? Second, were any topics simply not asked about? Is there a reason to expect that the omitted topics might diverge from the reported results?

6. If the researcher asserts that X caused Y, does s/he control for other factors that might be expected to influence the outcome?

a. Simple bivariate analyses are far more prone to biases than are regression analyses with suitable controls, which tend to be quite robust, even for biased samples.

b. How important are exact estimates to the researcher’s findings? The more research depends on a specific figure (e.g., the number of Jews in the United States), the more vulnerable it is to shortcomings in data collection.

c. Did the researcher omit any relevant explanatory variables? First, were there any topics asked about that weren’t included in the analysis? (Typically, where a variable is not significant, a researcher will say something like “X, Y, and Z did not have a significant effect and are omitted; model not shown.”) Second, were there any potentially relevant explanatory variables omitted? If so, what explanatory variables included in the analysis might be picking up the omitted variables’ effects?

d. Does the researcher report whether effects were statistically significant? This is especially important where sample sizes are small. (Note that statistical significance isn’t appropriate in cases where all relevant units were surveyed, like many Birthright reports, or for convenience and other nonprobability samples.)

e. If the sample size is very large, are the effects reported large enough to be meaningful?

7. For evaluation research on the effectiveness of a program or policy:

a. How does the researcher estimate the program effect? In declining order of rigor, these are:

i. True experiments that randomly allocate individuals or other units like communities into treatment or control groups.

ii. Quasi-experimental designs that have nonrandom treatment and control groups and measure outcomes before and after the treatment intervention begins. Does the researcher document whether systematic differences exist between treatment and control groups? If there are differences, what steps does the researcher take to take account of these?

iii. Quasi-experimental designs that either measure participants before and after the treatment but do not have a control group or measure treatment and control groups only after intervention. For participant-only pre/post designs, are there other factors such as aging or a major event like a terrorist attack that could also explain the results? For treatment and control post-only designs, does the researcher model the characteristics of the groups and control for them when analyzing outcomes.

iv. Treatment-only post-only designs that ask retrospective questions about attitudes and behavior. Are the events being recalled memorable? Is there a reason to believe that respondents may have recall errors, like telescoping events?

v. Treatment-only post-only designs that ask about program satisfaction and self-perceptions of program effect. These are very weak.

b. Does the researcher generalize about the program’s effect beyond the type of people who actually participated? For instance, does a study of a program of outreach to intermarried Reform synagogue members claim that the program will work for all intermarried families? Is this a reasonable assumption?

Lessons Learned--Part 1--RAID 0+1

I'm something of an experiential learner. Herewith the first things from the school of "dear God that was a stupid thing to do"--and a few that I actually got right the first time.

Never, ever use RAID 0+1 with an Intel ICHxR chip I like to build computers. Like many a PC do-it-yourselfer, I sometimes get too ambitious. Yes, I could build simple computers, but where's the fun in that? My first project was putting my Dell Dimension 8200 (or something like that) into a new (flashy, naturally) case. Of course, Dell used a proprietary motherboard format that didn't fit the new case. I got out my trusty drill and drilled new holes in the case backboard to accommodate standoffs. Of course, I decided to keep the motherboard on the computer to line up the holes. Not a smart idea, that. The case kept going, the motherboard didn't. I eventually combined bling (the case of course had a clear window) in the form of blacklight CCFLs, glow-in-the-dark sleeves on the power cables and light-up round IDE cables with overengineering (I managed to squeeze a Thermalright SI-120 on my new and undrilled ASrock 939Dual-SATA2 (AMD 3800X2), along with a fan for my RAM (with flashing lights!), a fan clamped on top of the Northbridge heatsink, some massive Panasonic fans throwing about 100 CFM, a Radeon 9700 All-in-Wonder with aftermarket heatsink fan (later joined by an Nvidia 7600 which I somehow managed to keep myself from sticking extra fans on--the Dual-SATA2 supported both AGP and PCI-E, so who was I to pike out?), and two (count 'em, two!) WD Raptor 72GB drives in RAID 0, plus two more data hard drives. So, my first computer (still going all these years later despite the odds) boasted 10 fans (2 case, 1 CPU, 2 RAM, 1 Northbridge, 1 PSU, 2 video) and four hard drives, all wrapped in an aluminium case that practically acted as an amplifier, was a tad noisy. A couple of years later, the kind people I work for let me build a new computer for myself. I did my homework this time. I got a normal motherboard (Gigabyte GA-965-DS3R), a sensible case (a big steel Antec case with a modular 500W PSU), a nice Core 2 Duo E6850 (plus a huge whomping Thermalright Ultra-120 with lovingly lapped copper base plus and my fastest Panasonic air pusher), four WD K-series 250GB drives with an RAID 0+1 partition for data and an 8GB RAID 0 partition for the swap file, 4GB of DDR2-800 RAM (later upped to 8GB), and Win XP 64-bit. (I ran XP 64-bit on my previous workstation, a Dell Precision 380 in the days before 64-bit printer drivers.) RAID 0+1, I thought, was the piece de resistance,. It would be safe, unlike my RAID 0 at home, and speedy, unlike the RAID 5 in the Precision 380. It merrily dispatched Stata analyses with blistering speed until I got back from winter vacation to discover that it wasn't running and reported that one of the disks had failed. Fine, I thought. It used crash on occasion, recovering with RAID errors, and this would finally let my identify the failing drive. I jotted down the failed drive's serial, pulled it, got a new one from Microcenter, installed it, and...and...it wouldn't recover. I'd get to the RAID BIOS, tell it to rebuild (all the information was there, thanks to the +1 part of the RAID) and it wouldn't boot, going straight to asking to boot from CD. I consulted the Intel Matrix RAID web pages (the board used an ICH-9R northbridge) to discover that, yes, it would recover once it booted into Windows. What one would do if one couldn't boot into Windows in the first place wasn't mentioned. Which brings me to the lesson learned. As I found out subsequently, the boot sectors of the first two disks of a RAID 0+1 array are necessary for it to boot properly. Naturally, I experienced failure in disk 1. Intel's Matrix RAID, while in just about every other way a truly admirable system, as a partially software RAID controller, needs an OS to recover, and that doesn't work with a corrupt boot section. Next time, RAID 1 or a proper RAID card! The news wasn't completely awful, though. I did have data redundancy and Vincent from PC-Maker in Waltham, after several days of pain, managed to pull out all my (and my employer's) data for far less than the $2,000 plus of data recovery companies. As it happened, my automated backup at work, other than being almost impossibly large and bringing down the repeated wrath of the network admins at work on me as I tried to recover from it, had stopped backing up my hard drive. I have a sensible new computer (a Dell OptiPlex) on the way and the sad carcass of my second DIY computer awaiting cannibalization.

My Bar Mitzvah Sermon

[A sermon I gave for my bar mitzvah, celebrated on December 26, 2009 / Tevet 9, 5770. Why a bar mitzvah at my age? The sermon answers this question. Posted at the instigation of my cousin-in-law, Matthew Pliskin.]

As I stand here today at the age of 34, celebrating my bar mitzvah, many of you will no doubt be asking, “Why so late?” I do so because it has been 13 years since I converted to Judaism. While an adult convert remains an adult, it nevertheless seemed appropriate to mark the anniversary. I would like to reflect for a few minutes on why I became a Jew, and then draw some tentative inferences. My path to Judaism was not the one of the religious seeker, drawn by its beauty and insight, nor that of the person drawn to Judaism through their beloved. Rather, I was born in the ambiguous position of the child of a Jewish father and non-Jewish mother, raised in no religion. My religious education, such as it was, consisted of going to Easter services at a Catholic cathedral, midday services at a high church Anglican congregation, and Saturday morning services at a synagogue at about age seven. I knew I belonged in the synagogue, and that feeling never left me. I have no idea why I felt Jewish, not Catholic. My family was culturally Christian, with a Christmas tree and an Easter egg hunt, not a hanukkiah and a seder. This is not, perhaps, a surprise as my mother, bitterly resent it though she may, went to a Catholic boarding school and then college, while my father was sent to the rabbi once a week in the year before his bar mitzvah. I felt closer to my Hungarian lapsed Catholic grandmother than my Viennese secular Jewish grandmother. Even today, daraszfesek moves me in ways babka never will. Nevertheless, there is a yawning chasm, for the child of a Jewish father and a non-Jewish mother, between feeling Jewish and being a Jew. Two things made possible this transition: the Australasian Union of Jewish Students and a first year class in Jewish Civilisation, Thought, and Culture at the University of Sydney. The class was intellectually exciting and started filling in what I had never learned. The Union of Jewish Students gave me the social ties to other Jews that I had never had. I set the process of conversion in motion at the beginning of my second year of college, having spent the summer in Israel with my great uncle Paul Avrahami, zichrono livracha, and my great aunt, Miriam Avrahami. Israel was again to play a role in my Jewish life a year later, when I met Jodi.

I had threatened to draw some lessons from my story, so let me inflict them on you.

First, intermarriage is too often seen in the Jewish community as the end of all Jewish life. It is not. The differences in outcomes we observe between the children of intermarriages who were raised as Jews and children of inmarriages are, for the most part, the product of the children of intermarriages having received less in the way of Jewish education and socialization and are not set in stone [see here and here for details]. Short of being brought up as a Christian, which happens in less than half of all intermarriages, I am the worst case scenario—I never even saw a lit menorah or sat at a seder as a child—yet I’m standing here today, have a Ph.D. in Jewish studies and sociology, and work at the Cohen Center for Modern Jewish Studies at Brandeis University. Most children of intermarriages actually have a better chance than I do. So, when a family is interested in raising Jewish children, for goodness’ sake, help them out! Don’t question whether the children will “really” be Jewish or whether all Christian symbols are purged from their house.

Second, educate your children. My grandmother gave my father to a rabbi for one day a week for a year, yet had the temerity to tell the rabbi that he had failed when her son married a non-Jew. He never had a chance! Even if he had married a Jewish woman with as much education, I doubt my childhood would have been much more Jewish—what could they have taught me, if they themselves knew so little? Harping on the need to marry a Jew is of little utility, I suspect, and downright harmful when your actions, both in the education your child receives and the home they grow up, doesn’t speak of love of Judaism. In this vein, let me note that probably about half of all Jews by choice convert after marriage. I can’t prove it, but I doubt that many of these had in-laws who opposed the marriage in the first place or frowned on the couple.

Third, support Jewish life on the college campus. It is no surprise that I first reached out to the Jewish community while at college, because that’s when I acquired autonomy. For me, both Jewish studies and Jewish student organizations were critical. Had I been born a few years later, I would probably have said the same thing about Birthright Israel. This does not hold only for people like me, but for those raised as Jews, too. Decades ago, college life was not all that important—we could be sure that marriage and childbearing, following soon after graduation, would draw young adults back into the Jewish community. With extended delays before marriage and longer still before having children, college age programs like Birthright Israel are especially important. In the case of Birthright, my colleagues and I were able to demonstrate that, five to nine years after the trip, people who went on the trip were considerably more likely to marry Jews than those who did not [see here for details].

As I conclude, let me say that I doubt my story is all that unusual these days. Being at a college in a department focused on Jewish life, I have the privilege of being acquainted with many young adults, whether as a colleagues or students, and many of them came from mixed backgrounds not unlike my own. Like me, they are driven by a strong love of Judaism and the Jewish people that has been forged, not extinguished, by the winding road that led them hither, and I rejoice at the thought of what they will bring to Jewish life in the coming decades.

Thank you and Shabbat Shalom.