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Silicon Valley is known for its many technology companies and scientific breakthroughs. And, whether you like it or not, technology still happens to be a male-dominated field. So, it should come as no surprise that the male to female ratio in the bay area is rather high. In fact, some sources put it as high as 5:1 in some parts of the Valley. That's why the women in Silicon Valley have a little saying:
Since it's not uncommon to hear women lament the difficulty of finding a "normal", heterosexual male in Silicon Valley, I started getting curious as to what the exact male-to-female ratio was in and around Stanford University in Palo Alto, CA.
The chance to find out arose when, as a final project for a statistics class on sampling techniques at Stanford, I decided to do a study of the male to female ratios in local bars. I used cluster sampling to survey from the bars in three cities. The results were somewhat surprising. If you're interested in the full report, it's available in Adobe Acrobat PDF format via the links below. Otherwise, I've included a brief summary for your reading pleasure.
|The Report (72 kb)||- the meat and potatoes.|
|Data (12 kb)||- just one page of male/female counts by individual bar.|
Although ratios varied widely from one bar to the other, I found that on average, in the cities of Palo Alto, Menlo Park and Mountain View, the male to female ratio was about 5 to 3. More precisely, I found that the ratio was about 62% men to 38% women (95% confidence interval for men = [59.46%, 64.54%]). These ratios differed widely depending on the type of bar that was surveyed, and were sometimes as high as 3-to-1.
This study was conducted using a two-stage cluster sample. The primary sampling units (psu) were cities near Stanford University, and the secondary sampling units (ssu) were individual bars within those cities. In the interest of time and simplicity, the "population" from which the clusters were selected consisted of the area spanned by four cities, Mountain View, Palo Alto, Menlo Park and Redwood City. Two of these (Menlo Park and Palo Alto) were selected at random to serve as primary sampling units. Then a list of all the bars in Menlo Park and Palo Alto were compiled and from these another simple random sample was taken (the ssu's).
A disadvantage to using two-stage cluster sampling is the loss of precision when compared techniques like random or stratified sampling, but for reasons that I explain more in the actual report, it was not possible to use stratified sampling without considerable difficulty. Once the primary sampling units were determined, the challenge was to create a comprehensive list of bars for both selected cities. This was done with the aid of the telephone book, dining and entertainment guides, and, perhaps most helpful, Yahoo!'s online directory. Most important in compiling a list, however was defining the term "bar". There are many different establishments, all with different closing times, menus, policies, clientele, and atmospheres. For the purposes of this study, a "bar" is defined as an establishment which has the following characteristics:
- serves alcoholic beverages (beer, wine, and/or hard liquor)
- is open past 10pm at night on Thursdays, Fridays and Saturdays.
- there must be at least 1.5 hours between the time when the establishment stops serving food and the time when it stops serving alcoholic drinks (this does not include hors d'oeuvres or small snacks served at the bar).
Due to time constraints, the actual study was conducted over three days Thursday, Friday and Saturday June 7, 8, and 9, 2001. These days seemed the most reasonable, since bars traditionally conduct the most business on these evenings. A friend and I collected data over a period of two to three hours each night. The order in which bars were visited was determined largely by their respective closing times and not by geography. That way, we reduced bias that would have occurred if we had counted all the bars in one city early in the evening, and all the other bars late at night.
My friend and I would enter the bar at the same time and slowly move from one end to the other, counting people as we went. Handheld mechanical click-counters (like they use at amusement parks) were used to allow for full concentration on counting. Once the back of the bar was reached, we turned around and counted a second time, moving from the back towards the front of the bar. One of us was assigned men on the way into the bar, while the other counted women. During the second count we switched, and one took women while the second counted men. We got quite good at counting, and it's worth mentioning that the number of men and women was almost always the same on both passes through each bar. In the few instances where that was not true, the average of the two numbers were used. The difference was never more than 5 percent.
At one bar (the British Banker's club), there was a cover charge to get in. My friend and I didn't want to pay $10 each just to go inside for five minutes and count some people, so I talked to the door man and told him about my project. He looked very skeptical and was about to deny us entry when I showed him my mechanical click-counter and said "If I wasn't really doing a project, do you think I'd bring a friggin' counter with me to a bar?" He looked at our counters, laughed, and waved us in. So, kids, if you're looking to get into a bar for free, bring a hand-counter with you and sweet talk the door man.
Despite all the planning that was done, there were a few challenges that arose during the course of the experiment. One challenge was how to deal with individuals who entered or exited the bar after we started counting. Many bars are in a continual state of flux, and getting all patrons to stand still during counting is impossible. Luckily, this was only a problem at a couple crowded bars. Additionally, it was often the case that as people entered the bar, others exited, keeping the total inside the bar approximately constant. Also, the fact that this problem was only encountered in very large bars meant that small changes in total bar numbers had a very small effect on the overall proportion of males to females.
The survey data describe a two-stage cluster sample with unequal cluster sizes. Also, it is important to keep in mind that the value of interest is a proportion, not a total. Therefore, I decided that using ratio estimation to find the mean proportion of males for the population would be the best model.
The data from all three nights for the first city (Palo Alto) were strung together to form a single vector with 21 data points. By sampling the same seven bars in Palo Alto each night it was possible to treat the eighteen (18) original bars as a population of (3 x 18 = 54) fifty-four, from which a sample of size 3 x 7 = 21 was taken. Similarly, in Menlo Park three of six bars were sampled each night, for a total of nine out of eighteen. This made more sense than calculating variances for each night, because it lowered the overall variance and summarized all the information for each city.
The actual calculations can be found in the report, above, but the results are as follows. For the four cities included in the study, the estimated average percentage of men across all bars was 62%, with a standard deviation of 1.27%. Thus, a 95% confidence interval becomes [59.46%, 64.54%], a margin of error +/- 2.54%.
Based on this study's findings, it's safe to say that the ratio of men to women in bars near Stanford University and Palo Alto is rather high. At 5 men for every 3 women, the ratios seem to be in a woman's favor. Of course, this says nothing about the ratio of single men to single women. The bars with the highest male/female ratios were the Oasis in Menlo Park and Antonio's Nut House in Palo Alto. They both had ratios of 3 to 1.
In any case, the data do suggest that the ratio of men to women in local bars is consistently rather high, though not as high as some people claim. Perhaps this knowledge will encourage bachelors to improve their skills at making themselves interesting and attractive to women. It is unclear, however, if women will continue to find Silicon Valley's male goods "odd", even if the numbers are in their favor.
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