Levels of Measurement PDF

imagine that you are a psychologist and 0:03 you want to do a study to see whether 0:05 eating breakfast will help kids focus 0:07 you think that the students who eat a 0:10 healthy breakfast will do best on a math 0:12 quiz students who eat an unhealthy 0:14 breakfast will perform in th...

imagine that you are a psychologist and 0:03 you want to do a study to see whether 0:05 eating breakfast will help kids focus 0:07 you think that the students who eat a 0:10 healthy breakfast will do best on a math 0:12 quiz students who eat an unhealthy 0:14 breakfast will perform in the middle and 0:16 students who do not eat anything for 0:18 breakfast will do the worst on a math 0:20 quiz so how do you do your study where 0:24 do you even begin in research one of the 0:28 first things that you have to do is 0:29 identify your variables or factors that 0:32 can change for example whether a person 0:35 eats breakfast or not is a variable it 0:37 varies from person to person and perhaps 0:40 from day to day a person can eat a 0:42 healthy breakfast eat an unhealthy 0:44 breakfast or not eat breakfast at all if 0:47 eating breakfast did not vary every 0:50 single person would eat the exact same 0:52 thing for breakfast every single morning 0:54 likewise performance on a map test is a 0:57 variable because it varies from person 0:59 to person 1:00 Suzy might do great on a math quiz while 1:03 Jonas fails it or Suzy might do well 1:06 today but not as well tomorrow 1:08 whatever the reason scores on a math 1:11 quiz change and therefore they are 1:13 variables so we know that our variables 1:16 are eating breakfast in math performance 1:18 but how do we measure them there are 1:21 four major scales or types of 1:23 measurement variables nominal ordinal 1:26 interval and ratio the scale of 1:30 measurement depends on the variable 1:32 itself let's look closer at each of the 1:35 four scales and what types of variables 1:37 fall into each category you might have 1:40 noticed a difference in our two 1:41 variables while scores on a math test 1:43 are reported as numbers eating breakfast 1:46 isn't numeric a person eats a healthy 1:49 breakfast an unhealthy breakfast or no 1:51 breakfast at all these are not numbers 1:54 but categories a nominal scale of 1:57 measurement deals with variables that 1:59 are non numeric or where the numbers 2:02 have no value in other words we can put 2:05 them in any order and it wouldn't matter 2:06 think about the numbers on the jerseys 2:08 of football players is the player 2:10 wearing number one a better player than 2:12 the player 2:13 wearing number 82 maybe but that doesn't 2:16 have anything to do with the numbers 2:18 they wear jersey numbers have no value 2:21 as far as telling us anything about the 2:23 ability of the players it's just a way 2:25 to identify them 2:26 other examples of variables measured on 2:29 a nominal scale include gender race and 2:32 the number on pool balls 2:35 sometimes for statistical analysis a 2:38 researcher will give non numeric 2:40 variables numeric values for example we 2:43 might say that students who eat a 2:44 healthy breakfast are negative 1 the 2:47 students who eat an unhealthy breakfast 2:48 are 0 and the students who do not eat 2:51 breakfast are positive 1 these numbers 2:53 are just a way to mark who is in which 2:55 group but don't really have value let's 2:58 say that instead of looking at grades on 3:00 a specific math quiz we want to look at 3:03 the letter grades overall for the course 3:05 for each student so Suzie has an A and 3:08 Jonas has a D and there are other 3:10 students with B's and C's and FS in this 3:13 case the letters are not completely 3:15 meaningless unlike football player 3:17 jerseys for example we know that Suzy is 3:20 doing better than Jonas but how much 3:22 better an ordinal scale of measurement 3:25 looks at variables where the order 3:28 matters but the differences do not 3:29 matter when you think of ordinal think 3:33 of the word order in the case of letter 3:37 grades we don't really know how much 3:39 better an A is than a D we know that a 3:42 is better than B which is better than C 3:44 and so on but is a 4 times better than D 3:47 is it 2 times better in this case the 3:50 order is important but not the 3:52 differences have you ever filled out one 3:54 of those customer service surveys that 3:56 company send out they might ask a 3:58 question like how was your experience 4:00 today and asked you to rate it on a 4:02 scale of one to ten those two are 4:05 ordinal other examples of variables 4:07 measured on an ordinal scale include 4:10 difficulty hard medium easy and the 4:13 order of finishing a race first place 4:16 second place and so on okay but what if 4:19 we want to measure something where the 4:20 difference is between the numbers do 4:22 matter for example what if we decide 4:25 that the temperature of a person's 4:26 breakfast matters 4:27 we believe that the kid who eats the 4:29 hottest breakfast will do best on the 4:31 math test and the kid who eats the 4:33 coldest breakfast will do the worst when 4:35 the order and differences between the 4:37 levels of a variable matter but they are 4:39 not in a ratio it is measured on an 4:42 interval scale intervals are the 4:44 distance between two things so you can 4:47 remember this because we are looking at 4:48 the distance between levels of a 4:50 variable temperature is a good example 4:52 of a variable measured on an interval 4:54 scale if one kid eats a breakfast that 4:57 is a hundred degrees and another eats 4:59 one that is 50 degrees the difference 5:02 between those two breakfasts is 50 5:04 degrees that tells us something about 5:06 how far apart they are likewise if it 5:09 was 70 degrees last month and it is 35 5:11 degrees today we know how many degrees 5:14 warmer it is but note that we wouldn't 5:17 say it's half as warm today as it was 5:20 last month that doesn't make sense that 5:22 is why while the differences are 5:24 meaningful the ratios are not but what 5:28 if the ratios are meaningful as well as 5:29 the differences let's go back to our 5:32 original idea we want to look at the 5:34 nominal variable of eating breakfast and 5:36 we also want to look at the scores of 5:38 the students on a math quiz if Suzy gets 5:41 a 90 on the test and Jonas gets a 45 we 5:44 know that Suzy did twice as well as 5:46 Jonas the scores which our percentages 5:49 are ratios that is the numbers tell us 5:53 how much of one thing we have in 5:54 comparison to another thing variables 5:57 measured on a ratio scale are numbers 5:59 where the order differences and ratios 6:02 are all meaningful think about it like 6:05 this if you can say that's twice as much 6:08 about one number in relation to another 6:10 then it can be measured on a ratio scale 6:13 things like number of minutes in a 6:15 commute weight or height are all ratios 6:18 Suzy can spend twice as long commuting 6:21 be half the weight or twice the height 6:24 of Jonas in psychological measurement 6:29 and research design there are four major 6:32 scales of measurement used to talk about 6:34 variables a nominal scale includes 6:37 variables where the order of the units 6:38 does not matter or 6:41 scales consist of variables where the 6:43 order matters but the difference between 6:45 the units does not matter an interval 6:48 scale looks at variables where both the 6:50 order and difference is meaningful but 6:52 the ratio of the units is not meaningful 6:55 finally a ratio scale is made up of 6:58 variables where the order difference and 7:00 ratio all matter