Week 9: QUANTITATIVE RESEARCH (3) MA CORPORATE SOCIAL RESPONSIBILITY ACP011C – RESEARCH METHODS FOR CSR Week 9: QUANTITATIVE RESEARCH (3) Using SPSS to analyse survey data Richard Charlesworth Week 8 - Introduction to Quantitative Research (2)

Learning outcomes Types of data – review Types of Analysis Statistical hypothesis tests – how to conduct tests Classical vs Non-parametric methods Overview of methods & data types

Types of data – a review Nominal data Ordinal data arbitrary codes representing categories of description e.g. – gender, ethnicity Ordinal data ordered codes representing categories which have an underlying sequence or order (so they are not arbitrary) e.g - data from questions measured on a Likert scale, rankings Cardinal data (called ‘Scale data’ in SPSS) not codes; have units of measurement on an interval/ratio scale e.g. – age (years), salary (£, €, $ etc..) Why is this important? the type of data determines the methods of analysis available to the researcher

Two main types of analysis Association between variables: Examples: Is there evidence of an association between gender and attendance pattern, or gender and reason for joining? Is there an association between the two ratings of service quality? Differences between groups of respondents Is there a difference in average ages between male & female members? Do members attending at different times share the same opinions on range of sports/activities on offer? Does membership lead to improved levels of fitness?

Statistical hypothesis tests Some examples of statistical hypotheses: There is no association between gender and attendance pattern There is no difference in average ages between male & female members There is no difference in opinion between members attending at different times, on the range of sports/activities on offer Membership does not lead to changes in fitness levels Your hypothesis What do you notice about these hypotheses? Not necessarily what we ‘want’ to be true ‘Difficult’ to prove (verification), ‘easy’ to disprove (falsification) “Theories should be formulated in a way that will make them most easily exposed to possible refutation” (Easterby-Smith et al)

Statistical hypothesis tests Findings from data analysis Your hypothesis How close do these have to be for us to conclude that our findings from the data analysis support the hypothesis? yes yes? yes/ no? How far apart do these have to be for us to conclude that our findings from the data analysis reject the hypothesis? no? no

Statistical hypothesis tests Findings from data analysis Your hypothesis H0 Decision rule How far apart do these have to be for us to conclude that our findings from the data analysis reject the hypothesis? If the probability of these findings occurring when H0 is true, is LESS THAN 5%, we REJECT H0 How close do these have to be for us to conclude that our findings from the data analysis support the hypothesis? If the probability of these findings occurring when H0 is true, is MORE THAN 5%, we ‘fail to REJECT’ H0

Statistical hypothesis tests Findings from data analysis Your hypothesis H0 Decision rule We have chosen to conduct this test at a 5% level of significance – this is the probability of wrongly rejecting H0 5% is a common choice – a balance between a low level of error and a level of sensitivity that will pick up genuine differences between the test data and H0 Sometimes test are conducted at 1% or even 0.1% levels of significance – but it is harder to reject H0, and hence there is less chance of making the error of wrongly rejecting If the probability of these findings occurring when H0 is true, is LESS THAN 5%, we REJECT H0 If the probability of these findings occurring when H0 is true, is MORE THAN 5%, we ‘fail to REJECT’ H0

Statistical hypothesis tests What is true if H0 is rejected? Some examples of null hypotheses H0: There is no association between gender and attendance pattern There is no difference in average ages between male & female members There is no difference in opinion between members attending at different times, on the range of sports/activities on offer Membership does not lead to changes in fitness levels Rejection of H0  acceptance of the alternative hypothesis H1: There is an association between gender and attendance pattern There is a difference in average ages between male & female members There are differences in opinion between members attending at different times, on the range of sports/activities on offer Membership does lead to improved fitness levels

Statistical hypothesis tests Tests are focussed around two hypotheses, which link to the research questions/hypotheses: Null hypothesis (H0) – the assertion being tested Alternative hypothesis (H1) The test is conducted under the assumption that H0 is true We test whether evidence from the survey data supports H0, or causes us to reject it in favour of H1 H0 is framed so that a rejection of it usually reveals something positive or interesting in the research. So H0 could be (for example).. No association between gender & opinion, or.. No difference between groups of respondent

Statistical hypothesis testing cont’d SPSS calculates a test statistic (which differs from test to test), and the probability of it occurring if H0 is true. If this probability is very small (usually taken as < 5%), we take this as evidence that H0 is not supported by the data, and we reject it in favour of H1 The 5% test criterion is known as the ‘level of significance’. It is the probability of wrongly rejecting the null hypothesis H0 Levels of significance of 1% or 0.1% can be used, and when rejecting, lead to highly significant outcomes – but it is also harder to reject H0

Example 1: Chi-square test The chi-square (or cross-tabulation) test is among the most common in survey analysis From the SPSS output below we can see that there is a large variation between male and female priorities. But is this evidence of male and female members having their own separate agendas for joining, or simply due to chance fluctuations? The chi-square test is used to test whether ‘reason for joining’ is independent of ‘gender’

‘Is the main reason for joining the centre associated with the respondent’s gender?’ The chi-square test is based on the following hypotheses: H0: No association between reason for joining & gender (i.e. they are independent) H1: Reason for joining & gender are associated (they are dependent) SPSS calculates the test statistic (known here as the Pearson Chi-square), and its probability (its level of significance, abbreviated here as ‘Sig’) assuming H0 is true: Pearson Chi-Square = 10.300 Probability (Sig) = 0.036 Assuming a 5% level of significance we reject H0 because Sig = 3.6% < 5%, and conclude that reason for joining and gender ARE NOT independent

Probability (Sig) value The test statistic is based on the differences across all 10 cells, between what happened (‘Count’), and what would be expected to happen (‘Expected Count’) if gender and reason for joining were independent Test statistic Probability (Sig) value Since 0.036 (or 3.6%) < 0.05 (or 5%), we reject H0 at a 5% level of significance, and conclude that reason and gender ARE NOT independent

Example 2: Kruskal-Wallis test The Kruskal-Wallis test is used to test for differences between groups. Do members who attend at different times of the day share the same opinions on the range of sports/activities offered by the Centre? The test is based on the following hypotheses: H0: No difference between groups – i.e. groups share a common opinion H1: The groups do not share a common opinion SPSS calculates the test statistic (coincidentally also based on the Chi-square distribution), and its probability (its level of significance, abbreviated here as ‘Sig’) assuming H0 is true: Chi-Square = 1.319 Probability (Sig) = 0.517 Assuming a 5% level of significance we have no evidence to reject H0 because Sig = 51.7% > 5%, and we conclude that members attending at different times of the day share much the same opinions

Probability (Sig) value Test statistic Since 0.517 (or 51.7%) > 0.05 (or 5%), we have no evidence to reject H0 at a 5% level of significance, and conclude that members who attend at different times of the day do not differ significantly in their opinion on the range of sports/activities Probability (Sig) value Note this does not mean that all members have exactly the same opinions. Rather that any differences between groups of members are not significant. Moreover, the size of the probability value indicates that we are nowhere near rejecting the null hypothesis.

Classical vs Non-parametric methods Classical methods are based on statistics such as the mean, standard deviation or variance, and analyses such as regression & correlation. These approaches are appropriate for cardinal data. Moreover the associated tests usually have quite stringent requirements that the data follow specific theoretical distributions (usually the normal distribution). Management questionnaires typically generate largely ordinal and nominal data, so Classical methods are rarely of much use. Even if the data is cardinal, the distribution requirements may not be met. More often than not, this leads us to apply Non-parametric (or distribution-free) methods. The 2 tests demonstrated (Chi-square test & Kruskal-Wallis test) fall into the broad category of Non-parametric methods.

An overview of methods & data types (selective) Nominal data Ordinal data Cardinal data Descriptive statistics Mode Median; Inter-quartile range Mean; Standard deviation Tests of association & strength of relationship Chi-square contingency test; Cramer’s V, Phi coefficient Spearman’s rank correlation coefficient; Kendall’s coefficient of concordance; Kendall’s partial rank correlation coefficient Pearson’s correlation coefficient; Multiple correlation coefficient & partial correlation Tests of difference Mann-Whitney U-test (2 groups); Wilcoxon’s signed rank test (paired obsns); Kruskal-Wallis test (2+ groups) t-test (2 groups); paired t-test (paired obsns); Analysis of Variance Estimating the relationship between 2+ variables Linear (or non-linear) regression; Multiple regression