15.301/310, Managerial Psychology Prof. Dan Ariely Recitation 6: Descriptive Statistics What wrong with giving survey in class? -select by people who come to class. Is something wrong with that? -more people come to exam some people come earlier, some people come later, maybe we want to think about that when giving the survey Today we talk about a most exciting topic - Measurement In general, we think there are 4 types of scales: nominal, ordinal, interval, and ratio. And those have diff properties and diff ways to think about them nominal scale just a label, doesn’t tell us bigger or smaller, no order, can’t infer any relationship such as gender – no order or bus number – some people take bus 1, some bus 15. we know anything about bus 1? No, just labels can think of others? -student ID# Assume random -U/G No, because we know one is more than the other. Grad degree, means also got u degree, it is more. Doesn’t mean learned more, but more yrs of school How about days of the week – nominal? No, we know about relationship. Tues comes 2 days after Sunday What else? -ethnicity -what city you are from Is this actually nominal? This is a very good point though You can think about things as being nominal, and we can think of them as having some relationship. Think about cities – we know east or west coast. From LA, SF, we know something about the cities, so is a relationship -any nominal label – alphabetical That’s right. Big issue is what is nominal Depends on our goal Ex. Say I think women nicer than men, I could say gender is not a nominal scale if we think about niceness All about the question – what is the thing you want to use it for?Bus numbers Could be Cambridge has some system for bus #s Buildings at MIT – nominal? Look random, but some logic somewhere. At least some of the numbers For those things, it would be not nominal Nominal – no particular use Think about it – put on x axis, switch around and it would not make any difference. Switch in any way want – no difference Ordinal Scale Is continuity in number, but only continuity in the # In fact, ordinal, interval, and ratio scales all have continuity in the data, but depend on different description of this data Ordinal – knowing one, know is bigger than something else Know house #17 is further away than #15, but don’t know by how much. Don’t know how big distance Interval scale – intervals the same between Ratio Scale – intervals between same plus there is a meaningful zero. Why we care about meaningful zero? -neutral pt Ok, but why do we care about it? Multiply things and is meaningful Think about deg F, think about today, 50 degrees. And then – oh, today is 100. is it twice as hot as yesterday? No. 0 not a meaningful 0 What if heart rate 40, exercise, goes up to 80. would we say heart rate has doubled? Absolutely. 0 is meaningful pt, so can double numbers, divide them, keep their meaning. Ratio scale Allows to measure in percentages What are some ratio scales? -population Meaningful zero and 75 people is 5 more than 70, etc (interval) -Kelvin temp scale -price 0, know what is. If $1, half as much as $2 15.301/310, Managerial Psychology Recitation 6 3/1/2005 Prof. Dan Ariely Page 2 of 15-typing WPM Time spend in morning getting ready Number pencils in your hair Lets talk about interval scale Graduation scale but without a meaningful zero. Mostly physical measurements Distance, time, weight -voltage. Comparing, not consistent zero I lack knowledge in that domain. Likely Am I hot or not is a great website 2 undergrads Started program, sitting in coffee shop watching people walking by. Made a program that is like people walking by. See pictures of people, rate them I have my picture posted on that site I don’t look very often. First looked, very disappointed, then rating went up We have lots of data from them Anybody seen the adds in SF? The two founders, naked with the laptops in front of their… where their underwear would be and it shows their real rating. Not real attractive Was slight deviation Interval scale or ordinal scale? We know 5 is more than 4. but do we know if 7 from 6 is same as 4 from 3? Diff in 2 scales is if intervals are of equal size on scale Clearly not ratio scale The reason this is so important is in a lot of these scales we do research – how happy are you feeling, how attractive do you find this person, how likely are you to buy this thing? -ordinal equal size, interval… or other way around? Ordinal means one is more than the other, but we don’t know the size of the differences Interval also gets bigger, but the amount of the step is always the same. Then ratio has all properties of previous 2 plus a meaningful zero Thing about scales is we can use them statistically. Can you take an average of a nominal scale? Anyone say no? 15.301/310, Managerial Psychology Recitation 6 3/1/2005 Prof. Dan Ariely Page 3 of 15Anyone say yes? Looks odd to take average of nominal scale. If I code every female in this class as 1 and every male as 0 and take the average, what would I get? Proportional number of people in the class Usually people say nominal scale can’t take average of Which is often true Bus 1, bus 15, can’t say something about bus 8, meaningless Apt numbs, harder to imagine, but some cases might make sense All depends on what scale you have and what you need to know Year when something founded – what scale? -interval Why not ratio? 0 defined by part religion. If think of nothing existing before, but existing after, but otherwise not meaningful 0 Altitude. What is alt? -ratio yeah Population? -ratio Sad point about these scales And the reason I emphasize them so much – is that in most cases when you ask for peoples opinions on these scales, we behave as if ratio scale. Double, say people at MIT twice as happy as people at Harvard. Nevertheless, these scales not always ratio scales. Every time we double, we make the assumption is ratio, but is not always ratio. Many cases, behave as if ratio scale, wishing have interval scale, but in most cases we only have ordinal scale. 1-10 scales, hard to assume each step is same size. Means all we have is ordinal. The happy thing is we have stats. More people we get, even though only have ordinal scale, treat as ratio scale, a lot of stats are indifferent to this assumption Good to try to think about making ratio or