Title EPS_MODULE 1 - STATISTICS.pdf ✅

7/16/25 2 Types of Data ACTIVITY : COMPLETE THE TABLE BELOW 3 and George. What many people feel uncomfortable about in psychological measurement is the crudity of the measures and the coldness of the attempt. Nevertheless, it is hard to see how someone could claim that Rick is more energetic or more impulsive, or even that George falls into a ‘contemplative’ category, without some description that would come close to measurement, or at least to categorising. Categorical and measured variables Let’s follow up that last point and introduce two major types of variable that can produce two different forms of data – categorical and measured. Suppose your friend Karen says: ‘Lucy is a Pisces, extremely extroverted and six foot tall.’ Karen has introduced three variables on which she has assessed Lucy. The first is a category system – people fall into one category or another and they can’t be placed in between (forgetting, for now, all that stuff about ‘cusps’!). You can’t be half a Pisces or 2.7 Aries, in the same way as you can’t have voted 0.7 Labour. You may not fully agree with a government’s policies but the voting system forces you to choose either them or another party. In these cases, the set of star signs or political parties would be called a CATEGORICAL VARIABLE. It is useful to call any other sort of variable that operates above the level of mere categorising a MEASURED VARIABLE. This is the sort of scale Karen used for her second two measures. She has not measured extroversion on a quantified scale but she has placed Lucy as ‘more extreme’ than many other people. She must therefore have some crude concept of degree of extroversion by which people can be separated. On the last measure, of course, there is no argument (apart from the issue of going metric!). Feet and inches are divisions on a measured scale which is publicly agreed, standardised and therefore checkable. In very many experimental studies the independent variable is categorical and the dependent variable is a measured variable. Have a look at Table 13.1 which shows this distinction for several of the experiments we have discussed so far in this book. Cover up columns 2 and 4 if you wish to test yourself. Notice that the only categorical dependent variable in the table is the dropping or not of the leaflet in the Cialdini et al. study and that, in this study, the independent variable was measured. However, for data analysis purposes, as will be explained, we can treat it as categorical, as did Cialdini et al. Statistics – organising the data 333 Independent variable Categorical/measured Dependent variable Categorical/measured Good or bad news categorical Worry score measured bulletin Complex or simple categorical Number of seconds measured visual pattern gazed at Perform in front of categorical Number of errors made measured audience or alone Number of pieces of measured treated Dropped leaflet categorical litter already on ground as categorical – see text or not Table 13.1 Level of measurement of several independent variables and dependent variables. CONCLUSION ? IVs will always be “categorical” variables, but DVs can be both continuous/measured as well as categorical variables Coolican 3 SCALES OF MEASUREMENT 4 4
7/16/25 3 Scales of Measurement Measurement is the application of rules for assigning numbers to objects/events/behaviors. The rules are the specific procedures used to transform qualities of attributes into numbers Properties of Scales ○ Identity : Each value has a unique meaning ○ Magnitude: The property of “moreness” ○ Equal intervals: Difference between two points at any place on the scale has the same meaning as the difference between two other points that differ by the same number of scale units. ○ Absolute Zero: When nothing of the property being measured exists. 5 Goodwin 5 Scales of Measurement : Nominal Scale Used for classification/as identifiers Data differs in quality not quantity Has the property of identity – all members of a category must be assigned the same number and that no two categories may share the same number. Count data/ frequency Examples: ○ Sex, eye color, clinical status etc. ○ Qualitatively different behaviors of nursery school kids – play alone, play together ○ Research Question: Is a woman more likely to give her phone number to a man if he is accompanied by a dog? Statistical Analysis: Test of proportions, Chi Square 6 Goodwin Scales of Measurement 107 For our purposes, the nominal scale of measurement was whether or phone number was given or refused (two categories of response). For this research study, the response depended upon whether the dog was present or absent. The data can then be organized by the number of women falling into one of four conditions, which are illustrated in the table below: Phone number given Phone number refused Dog present 28 52 Dog absent 9 71 It is important to note that the measure used is whether the phone number was given or refused, not whether the dog was present or absent. The researchers in this case were wondering if the presence (or absence) of the dog affected women’s behavior (giving or refusing a phone number). Ordinal Scales Ordinal scales of measurement are sets of rankings, showing the relative standing of objects or individuals. College transcripts, for example, often list a student’s general class rank: 1st, 2nd, 3rd, 50th, and so on. From these rankings, you can infer that one student had higher grades than another. Relative standing is the only thing you know, however. Dan, Fran, and Jan would be ranked 1, 2, and 3 in each of the following cases, even though Dan is clearly superior to Fran and Jan as a student only in the second case: Case 1 Case 2 Dan’s GPA 4.0 Dan’s GPA 4.0 Fran’s GPA 3.9 Fran’s GPA 3.2 Jan’s GPA 3.8 Jan’s GPA 3.0 Studies using ordinal scales ask empirical questions like these: • If a child ranks five toys and is given the one ranked third, will the ranking for that toy go up or down after the child has played with it for a week? • Do students rank order textbook authors in the sciences and in the humanities differently when they are told the gender of the writers? • How do young versus old people rank 10 movies that vary the amount of sex and aggression they contain? A good example of an ordinal scale is from a study by Korn, Davis, and Davis (1991). Historians of psychology and department chairpersons were asked to list, in rank order from 1 to 10, the psychologists they considered to have made the most important contributions to the field. Two sets of rankings were solicited—one for the top 10 of “all time” and the second for a “contemporary” top 10. The returns were then summarized to yield a picture of eminence in psychology. Who topped the chart? B. F. Skinner was considered the most eminent contemporary psychologist by both historians and chairpersons. Department chairs also ranked Skinner first for all time; historians, who tended to select psychologists from earlier periods for their all‐time list, dropped Skinner to eighth place and put Wundt on top. One important point about ordinal scales of measurement is that often rank order data are derived from other data. For example, Haggbloom 6
7/16/25 4 Scales of Measurement : Ordinal Scale Sets of rankings, showing the relative standing of objects or individuals Does not reflect the differences between or the ratios among them. Examples: ○ Birth order, ranking of sociability in adults, rankings of leadership ability. Studies using ordinal scales ask empirical questions like : ○ If a child ranks five toys and is given the one ranked third, will the ranking for that toy go up or down after the child has played with it for a week? ○ Do students rank order textbook authors in the sciences and in the humanities differently when they are told the gender of the writers? ○ How do young versus old people rank 10 movies that vary the amount of sex and aggression they contain? Statistical Analysis: Spearman’s rho 8 Goodwin 8 Can you rank order the following scores ... 9 positions. It may be annoying to be beaten by one-tenth of a second in a cycle race when you and the leader were ten kilometres ahead of the rest of the bunch, but what goes on your record is just ‘second’. To the horserace punter it doesn’t matter by what margin Golden Girl won – it won! In Figure 13.1 we can see that Simon is a lot taller than YOU but the ordinal scale hides this fact. How to rank data Giving ranks to scores or values obtained in research is very easy but must be done in a precise, conventional manner, otherwise the various significance tests based on ranks will give misleading results should you calculate them by hand. Suppose we have to rank the scores of eight people on a general knowledge test, as shown in Table 13.4. The score of 14 is lowest and gets the rank 1. In competitions we usually give the winner rank ‘1’ but in statistics it is less confusing to give low ranks to low values. Persons five, six and seven, with 15 each, ‘share’ the next three ranks (of second, third and fourth). In sport we might say ‘equal second’, but in statistical ranking we take the median value (see p. 349) of the ranks they share. If the number of positions is odd, this is just the middle value. From 2, 3 and 4 the middle value is 3. If the number is even we take the number midway between the two middle ranks shared. Persons one and four share the ranks 5 and 6. The point midway between these is 5.5. If four people shared 6, 7, 8, 9, the rank given to each would be 7.5. Statistics – organising the data 337 Variable Categories Type of children’s play Non-play/Solitary/Associative/Parallel/Co-operative Type of pet owned Dog/Cat/Guinea pig/Rabbit/Horse/Bird/Other Ethnicity Black/White/Asian/Other Marital status Single/Married/Cohabiting/Separated/Divorced Table 13.3 Typical categorical variables. Person Score Rank of score 1 18 5.5 2 25 7 3 14 1 4 18 5.5 5 15 3 6 15 3 7 15 3 8 29 8 Table 13.4 An example of ranking – interval- level data changed to ordinal-level data. 9