Fundamental Statistics for Social Research

Step-by-Step Calculations and Computer Techniques Using SPSS for Windows

Duncan Cramer

• Publisher: Routledge
• Year: 2003
• Topic: Social Sciences
• eBook ISBN:
  9781134693245
• Subtopic: History & Theory in Psychology
• Index: Social Sciences

This accessible introduction to statistics using the program SPSS for Windows explains when to apply and how to calculate and interpret a wide range of statistical procedures commonly used in the social sciences. Keeping statistical symbols and formulae to a minimum and using simple examples, this book:
* assumes no prior knowledge of statistics or computing
* includes a concise introduction to the program SPSS for Windows
* describes a wider range of tests than other introductory texts
* contains a comprehensive range of exercises with answers

Fundamental Statistics for Social Research covers SPSS Release 6 for Windows 3.1 and Release 7 for Windows 95. It will prove an invaluable introductory statistics text for students, and a useful resource for graduates and professionals engaged in research in the social sciences.

1 Role of statistics in social research

A major aim of the social and behavioural sciences is to develop principles which explain and provide new insights into human behaviour. One way of evaluating what appear to be sound and promising principles is to examine the extent to which they are consistent with carefully controlled observations of human behaviour. In other words, the validity of principles needs to be tested by conducting empirical research wherever possible. If the data do not agree with the principle under scrutiny, the principle may have to be modified and then re-examined. Alternatively, the way in which the controlled observations were made may have been mistaken and a new set of data may have to be collected. Suppose, for example, we tested the idea that people are likely to repeat the aggression they see in others but we found no evidence to support such a relationship. In this case, it might be necessary to make the principle more specific by proposing that individuals are likely to imitate aggression which is rewarded rather than punished, and then to test this revised proposition. On the other hand, the measure of aggression we used may have been unsuitable for the purpose and may have to be replaced with a more appropriate test.

Statistics play a vital role in collecting, summarising and interpreting data designed to empirically evaluate a principle. Consequently, an understanding of this important subject is necessary both to carry out research and to be able to critically evaluate research that has been, or is going to be, conducted. The function that statistics serves in social research can best be briefly illustrated by looking at the ways in which it is involved in testing a principle. Take, for example, the simple idea we have already introduced that people tend to imitate what they have observed. If this is the case, then individuals who, say, have watched a violent incident shown on television should be more likely to behave in this way than those who have not seen this incident. One approach to testing this idea would be to select two groups of people and to show one group (known as the experimental group, condition or treatment) a film or video containing a violent incident and the other group (the control group) a similar film not containing the violent sequence. After viewing the film, the aggression displayed by both groups of people would be observed to see if the groups differed as expected.

Suppose that the people who had watched the violent incident showed more aggression subsequently than those who had not been exposed to this violence. Before it could be concluded that these results confirm the principle that individuals tend to imitate what they have observed, at least three essential and related statistical considerations need to have been met. The first is that participants should have been randomly sampled from the population (e.g. Bowley 1913). A random sample is one in which each member of the population has an equal chance of being selected for the sample. The second is that the sampled participants should have been randomly assigned to the two groups (Fisher 1925b, 1935). Random assignment means that individuals have an equal probability of being assigned to each group. The third is that the difference in observed aggression between the two groups should be statistically significant (Fisher 1926, 1935), which means that the difference has a one in twenty probability or less of occurring simply by chance.

RANDOM SAMPLING

When testing a principle, we usually want to know how valid it is of people in general. Since it is not possible to test everyone when examining a particular generalisation, we carry out our study on a sample or subset of people. The idea of a sample implies that there is a larger population from which it is drawn. This population is often not specified because we assume the principle to be generally true. For example, when we postulate that watching violence on television causes aggression, we presumably believe that this holds true for all people where watching television is part of their cultural experience and that this principle does not simply apply to the people we have tested. In other words, we want to be able to generalise the findings from our sample to the population as a whole.

There are two main ways in which we can select a sample of objects or cases, which need not be people, of course. The first method is to draw a simple random sample where every object in a given population has an equal probability of being chosen. To do this, the population of objects needs to be specified and known and some random procedure employed for selecting objects. To give a simple example, suppose we wanted to draw a small sample of five people from a class of twenty which was the population of interest. We could assign a number from 1 to 20 to each of the individuals in the class. We could then go to a table of random numbers and select the first five numbers which fell between 1 and 20, which may be 13, 9, 17, 18 and 5. The five people who had those numbers would constitute our sample. In this method, everybody would have a one in four probability of being selected.

The second method of sampling is to generate a non-random sample where the probability of choosing an object from a specified population is not known. An example of this approach would be if we selected the first five people according to whether their surname started with letters closest to the beginning of the alphabet. This method would be non-random because people whose surname began with these letters would have the highest probability of being chosen.

Because of the difficulty of obtaining a random sample, many studies in the social sciences use non-random samples and assume that the sample can be thought of as random. If, however, we believed that the principle we were investigating only applied to people with certain characteristics, then we could see if this assumption was true by testing this principle on people with and without those characteristics. For example, if we thought that watching violence only made males more aggressive and did not affect females, then we could test this idea on a sample of males and females. If, on the other hand, we wanted to know how common a particular behaviour was in a specified population, we would require a random sample to answer this question. For example, we would need a random sample to find out how many adults living in Britain viewed violent programmes on television. How accurate our estimate was would partly depend on the size of that sample. If we had used a non-random sample, we would not be able to estimate this figure because we would not know how representative that non-random sample was of the population.

RANDOM ASSIGNMENT

Having obtained our sample, we then need to randomly assign them to the two conditions. One way of trying to do this is to flip an unbiased coin. The two faces of the coin are used to represent the two groups. For example, it can be agreed before hand that if the coin lands with the side showing the head (‘heads up’), then the first of two people will be assigned to the group that will see the violent episode. The second person will be allocated to the group that will not be shown the violent incident. If, on the other hand, the coin lands with the side which does not display the head (‘tails up’), then the first person will be assigned to the group which will not see the violent sequence, while the second participant will be allocated to the group which will be shown the violent episode. This procedure of assigning two people at a time with one coin throw will ensure that the number of people in both groups will be similar, although a similar number of people in each group is not itself a statistical requirement.

The reason for random assignment of participants to conditions is to try and ensure that there is no bias in the way that people are allocated to the two groups and that every person has an equal chance of being in either group. If random assignment is not used, then there is the possibility that one group will contain individuals who may be more prone to show aggression. If this happened, the results obtained could not be explained in terms of which films the participants had seen. Because this is a very important point to grasp, it will be further elaborated.

There are potentially a very large number of factors which may predispose individuals to be aggressive, some of which we may not readily recall or even be aware of. For example, participants who had had a poor night’s sleep or gone without breakfast may be more irritable than those who had slept well or had had a hearty breakfast. Men may be more inclined to show their aggression than women, and so on. Now, it is possible to control for some of these factors by holding them constant, such as restricting participation to men or to women. Alternatively, the role of these factors may themselves be investigated by including both women and men in the study. However, because we are not necessarily aware of all the factors that might influence aggressiveness and because it would be difficult to study or to hold constant all those variables that we were conscious of, it is better to try to control for these extraneous factors through random assignment. By randomly assigning participants to treatments, it is more likely that the people in both groups will be similar in terms of a whole host of other characteristics. For example, random assignment will make it more probable that the two groups will contain the same number of people who had a disturbed night’s sleep, missed breakfast or were male.

However, when only a small number of participants are involved in a study and are randomly assigned to conditions, there is a greater probability that the number or proportion of people who have the same characteristic will differ in the two conditions. This point can be illustrated by looking at the possible results of tossing a varying number of coins. The two sides of the coin can be thought of as denoting any variable which can take on two equiprobable values such as being a woman or man. If we tossed the coin once, then the probability of it turning up heads would be one of two possibilities (a head or a tail), which can be represented as the proportion 0.5 (i.e. 1/2 = 0.5).

If we tossed two coins once, there are four possible or theoretical outcomes as shown in Table 1.1: (1) a head on the first coin and a tail on the second; (2) a tail on the first coin and a head on the second; (3) two heads on both coins; and (4) two tails on both coins. The probability of obtaining both a head and a tail (regardless of the coin) would be two out of four possibilities or 0.5 (2/4 = 0.5). The probability (or p value) of obtaining two heads would be one out of four possibilities or 0.25 (1/4 = 0.25). Similarly, the probability of having two tails would also be one out of four possibilities or 0.25.

Table 1.1 Four possible outcomes of tossing two coins once and their probability

If we assume that we are randomly assigning only two participants to one of the two conditions, then we can see that the probability of having all women or all men in this condition is 0.5. We can calculate the probability of any particular outcome from any number of coins by simply multiplying the probability of the two outcomes of each of the coins being used. So this probability would be 0.25 for two coins as we have already noted (0.5 × 0.5 = 0.25), 0.125 for three coins (0.5 × 0.5 × 0.5 = 0.125) and 0.0625 for four coins (0.5 × 0.5 × 0.5 × 0.5 = 0.0625). For any number of coins, there can only be one outcome which contains all heads and only one which consists of all tails. To work out the probability of obtaining both these outcomes, we simply add up their separate probabilities, which is 0.5 for two coins (0.25 + 0.25 = 0.5) as we have already calculated, 0.25 for three coins (0.125 + 0.125 = 0.25) and 0.125 for four coins (0.0625 + 0.0625 = 0.125). It should be clear then that as the number of participants increases, the probability that random assignment will lead to participants in any one group having all of one characteristic should decrease.

Of course, it is possible to check whether random assignment has resulted in the participants in the two conditions being similar in various ways before being shown the two films. However, in order not to overtax the participants’ good will, it is preferable to limit this pre-testing to those variables of most direct interest, which in this case would be their aggressiveness before seeing the film. A pre-test is a measure taken before the experimental manipulation is carried out as opposed to a post-test which is taken after the manipulation has been carried out. This pre-test information can be used in three ways. First, participants with similar pre-test aggressiveness can be matched, blocked or paired in terms of their scores and then randomly assigned to one of the two conditions. This matching procedure will ensure that the participants in the two conditions will be similar in terms of their initial aggressiveness.

Second, without resorting to matching, the pre-test aggressiveness scores of the participants in the two conditions can be compared after all the data have been collected. If the scores in the two conditions differ, then random assignment has not been effective so far as the key variable of aggressiveness is concerned. The way of determining whether two groups of scores differ is itself a statistical issue which will be introduced below. If the pretest scores differ, then there are statistical procedures, such as analysis of covariance, which take these differences into consideration. This particular procedure will be described in Chapter 10.

Third, if the pre-test scores do not differ, then they may be compared with the post-test aggressiveness scores of the participants after they have seen the film to determine the nature and sta...

Table of contents

• Front Cover
• Half Title
• Title Page
• Copyright
• Contents
• List of Boxes
• List of Figures
• List of Tables
• Preface
• 1 Role of statistics in social research
• 2 Measurement and univariate analysis
• 3 Introducing SPSS for Windows
• 4 Statistical significance and choice of test
• 5 Tests of difference for interval/ratio data on unrelated samples for one factor
• 6 Tests of association for interval/ratio data
• 7 Bivariate and multiple regression
• 8 Tests of difference for interval/ratio data on related samples for one factor
• 9 Tests of difference for interval/ratio data on unrelated samples for two factors
• 10 Tests of difference for interval/ratio data on mixed samples for two factors
• 11 Tests of difference for categorical data
• 12 Tests of difference for ordinal data
• 13 Tests of association for categorical and ordinal data
• 14 Measurement reliability and agreement
• Appendices
• Answers to exercises
• Bibliography
• Index