Choosing Appropriate Statistical Techniques for Hypothesis Testing

This section of the chapter will discuss the essence of data and its features in order to understand the nature of contents collected. There are three sub-sections which will explain normality, homogeneity, and independence of measure and interval data.

3.7.1 Assumptions of Normality

Both the Kolmogorov-Smirnov and Shapiro-Wilk tests can be used to analyse date when the sample demonstrates a normal distribution (Field, 2013; Hair et al., 2010). To test normality of distributions for all of the constructs within the study, Kolmogorov-Smirnov and Shapiro-Wilk tests were carried out. Results from these tests were highly significant, meaning that the sample distribution is significantly different from the data distribution of a normal population (Field, 2013), thus the assumption of normality is violated in all scales. It is, however, to have an incorrect result if researchers have a large sample, of more than 200 responding participants (Field, 2013; Pallant, 2011), in this instance it is more important to look at the shape of the bell curve, which demonstrates the distribution of data; the visual inspection of histograms shows that the shape of distributions does not deviate much from the bell curve of a normal distribution (see Appendix C for examples).

It is therefore advisable to use critical values exposed (Mardia, 1970). The procedure quantifies the departure from normality in the sample and provides an outline of whether the difference in the sample is statistically significant (Arbuckle, 2008;

Doornik and Hansen, 2008; Mardia, 1970). It is also important to understand how robust the selected estimation method is against the departure from normality, in order to make use of this information. If the departure from normality is large enough to be significant then the alternative may be that it is small enough to be undisruptive. If the p1 column shows small numbers, they are likely to be seen, however small numbers in the p2 column will point to observations which are unlikely to be far from the centroid under the assumption of normality. The test is based on observations which are furthest from the centroid in AMOS software. In this study, none of the probabilities in column p2 are very small. Thus, there is no evidence that the most unusual observations should be treated as outliers (under the assumption of normality). It is suggested that cases should be removed if both p1 and p2 for Mahalanobis d² are .000 (Arbuckle, 2008;

Doornik and Hansen, 2008; Mardia, 1970). In the study there was no sample which has a p1=p2=.000. The outcomes of the above tests demonstrate that the data is metric, thus parametric tests were used for subsequent analyses.

3.7.2 Homogeneity

Another assumption made regarding variances when data is fitted to a model relates to the parameters and null hypothesis. Using least squares method, parametric analysis offers the optimal estimate of variance if it is equal across different values of a predictor variable. Null hypothesis significance testing, however, assumes that the variance of an outcome variable is equal across different values of the predictor and, if this is not so, the test is likely to be inaccurate (Field, 2013). To ensure estimates of parameters and significance tests are correct, the researcher must assume homoscedasticity, or homogeneity of variance (Cook and Wall, 1980; Louzada et al., 2014).

Homogeneity means that different groups within the dataset will share variances of other groups within the sample population, with no strange outliers of extreme value. In the case of this thesis, therefore, people from different groups would demonstrate the same variance in response to one question, as the next group would do. For instance, a group may be staff, supervisors, or managers, within the whole sample population. As one may expect results to vary dependent on the question being answered, homogeneity would show that the variance between minimum and maximum response would be the same in one group as it is for the other two. When estimating parameters within linear models, if equality of variance is assumed, then estimates should be optimal when using least squares method.

In order to assess homogeneity of variances, this study has used scales to enable the ranking of levels of agreement or disagreement on a numerical scale. There are a number of different tests available to use, also in SPSS, for the analysis of homogeneity of variances (Pallant, 2011).

In addition, it is possible to use the Levene Test which was offered in 1960 as an alternative to the previous Bartlett Test (Bartlett, 1937; Katz et al., 2009). The Levene Test analyses the data and tests whether the variances within the data set offer scores which are the same for each of any set of groups being used in the sample (Pallant, 2011). If the test is used and the significance (sig.) value is over .05 (for example, 0.06, 0.27, etc.), then the assumption of homogeneity is not validated, and grouped members offer very similar scores amongst each other within the data for a specific question (Katz et al., 2009; Pallant, 2011). Whilst the Bartlett Test is suitable enough to test

homogeneity within data which is normally (or almost normally) distributed, it offers little use for data which is skewed, with the Levene Test being less sensitive to skewed or biased data, and offers less Type 1 errors in the analysis (Conover et al., 1981; Katz et al., 2009). This will be tested in the next chapter in comparing group analysis.

The Levene Test also analyses the equality of variances a part of the t-test. The purpose of the t-test is to identify is to test hypotheses which have been posed by the researcher.

It is not failsafe, and can show errors which point toward the wrong conclusion when considering the response to hypotheses in research (Pallant, 2011). If one were to incorrectly reject the null hypothesis, with it in fact being true, it would be considered a Type 1 Error, which happens when considering there to be a difference between groups which does not actually exist. To minimize this occurring, the researcher should select a suitable alpha level, normally of .05 or .01 (Field, 2013; Pallant, 2011). The second error which can be made (a Type 2 Error) occurs when the null hypothesis is not rejected when it is really false. This would suggest that there is no difference between groups, but there actually is! However, the inverse relationship between the two error types means that if trying to limit Type One Errors, essentially there will be an increase in the possibility of Type 2 Errors occurring (Field, 2013; Katz et al., 2009; Pallant, 2011). This will be tested in the next chapter in “comparing group analysis”.

Post-hoc (posteriori) comparisons offer the ability to show a number of comparisons and to explore the differences offered by each of the groups within the study. To do this though is a two stage process, starting with the calculation of the F-value, or ratio. This calculation identifies any significant differences between groups in the study, and a significant finding permits the researcher to continue to the next stages of analysis (Field, 2013; Pallant, 2011). Use of any post-hoc analyses helps to safeguard against Type 1 Error, due to the vast number of comparisons being made of the data set, and is completed by setting tighter criterion for significance, which can ultimately make significance harder to achieve. A smaller sample poses further hindrance in achieving significance given that the difference in scores of a smaller group can, in itself, appear to be very large (Gauvain and Lee, 1994; Pallant, 2011). This will be tested in the next chapter in comparing group analysis.

3.7.3 Independence of Measure and Interval Data

The assumption of independence poses that errors in the model aren’t related to each other. This means that respondents in the study do not confer with one and other when answering questions in the survey. It is understood that the model will be used to predict results based on the responses of those within the sample population, and that there will be some responses which differ from expectation (errors). When respondents do not confer, and give answers independently, then independence is experienced, and the error in one person’s set of responses is not influenced by the error in predicting another person’s response. Whilst standard error can be calculated by using the associated calculation (figure 3.3) whereby standard error is equal to the standard deviation being divided by the square root of the sample population size, fortunately SPSS offers the ability to run this during analysis tests. The standard error was calculated for each item using the Descriptive Statistics function ((Field, 2013):

𝑆𝐸𝑥̅ = 𝑠

√𝑛 Figure 3.2: Standard Error Calculation

However, the above formula is only appropriate if the observations, or responses from participants, are independent. If there is no independence, then there is a risk of violating tests for confidence intervals, and confidence tests in the analysis (Pallant, 2011). The web-based package used (Survey Monkey) in this study relies on internet browser history being cleared prior to the next user entering their responses. To some extent, therefore, two or more people would have to allow sufficient time to complete their responses, and clear the cache and history on their pc, laptop, tablet or smartphone, before another user completed the survey on the same device. However, this does not allow for people to be independent in a situation where they are perhaps using devices next to each other in a workplace. Given that the respondents targeted work in restaurant settings, it is unlikely that they completed the survey together, in the workplace, where it is likely to find that mobile communication devices are forbidden for use due to being in a customer-facing environment, requiring professionalism.

Consider now the introduction of Erving Goffman in this thesis to (and how) people entering an institution type setting can be debased, and removed of personal items.