Normality of data

The normality of data is required to be verified as the researcher is going to have hypothesis testing of theoretical model of trust using Structural Equation Modelling analysis with the use of AMOS (Arbuckle, 2007). This requirement is rooted in large sample theory from which SEM methodology was spawned. Thus, before any analysis of data are undertaken, it is important to check that this criterion has been met.

Normality refers to the distribution of the data for a particular variable. The normality can be assessed by the following numerical and visual outputs:

i. Skewness and Kurtosis ii. The Shapiro- Walk test

iii. Histograms, Normal Q-Q plots and Box plots

i. Skewness and Kurtosis: Lack of symmetry (skewness) and pointiness (kurtosis) are two main ways in which a distribution can deviate from normal. The values for these parameters should be zero in a normal distribution.

Skewness is a measure of symmetry or the lack of symmetry. A distribution or data set is symmetric if it looks the same to the left and right of the centre point. Skewness is not needed on 5-point Likert scale. Therefore, it will be found for descriptive variables like age, gender, position in the virtual team, etc. Table 6.12 shows the results of skewness.

Chapter 6: Data Collection, Analysis and Research Results

142

Table 6.12: Skewness results

Statistics

Age Gender Edu_Qual Total_Exp Avg_size Avg_Tenure Pos

N Valid _{323 323 323 323 323 323 323} Missing _{0 0 0 0 0 0 0} Mean _{39.23 1.33 3.23 6.97 9.98 3.05 1.26} Std. Deviation _{5.766 .471 .589 3.238 3.118 1.347 .441} Skewness score .934 .720 -.104 .880 .140 1.185 1.081

An absolute value of the score greater than 1.96 or lesser than -1.96 is significant at P < 0.05, while greater than 2.58 or lesser than -2.58 is significant at P < 0.01, and greater than 3.29 or lesser than -3.29 is significant at P < 0.001. In small samples, values greater or lesser than 1.96 are sufficient to establish normality of the data. However, in large samples (200 or more) with small standard errors, this criterion should be changed to ± 2.58 and in very large samples no criterion should be applied (that is, significance tests of skewness and kurtosis should not be used) (Field A, 2009).

Kurtosis is a measure of whether the data are peaked or flat relative to a normal distribution. That’s data sets with high kurtosis tend to have a distinct peak near the mean, decline rather rapidly and have heavy tails. Data sets with low kurtosis tend to have a flat top near the mean rather than a sharp peak. A uniform distribution would be the extreme case. Table 6.13 shows the kurtosis data.

Chapter 6: Data Collection, Analysis and Research Results

143

Table 6.13 Kurtosis data

Statistics N Kurtosis scores Valid Missing V1 323 0 1.859 V2 323 0 1.302 V3 323 0 .664 V4 323 0 1.415 V5 323 0 1.438 V6 323 0 -.750 V7 323 0 .986 V8 323 0 -1.006 V9 323 0 1.306 V10 323 0 -1.166 V11 323 0 .858 V12 323 0 1.745 V13 323 0 1.241 V14 323 0 -.413 V15 323 0 -.784 V16 323 0 .479 V17 323 0 1.552 V18 323 0 -.494 V19 323 0 1.546 V20 323 0 .186 V21 323 0 -.172 V22 323 0 -.811 V23 323 0 -1.084 V24 323 0 -.743 V25 323 0 1.234 V26 323 0 -.714 V27 323 0 .587 V28 323 0 .101 V29 323 0 1.206 V30 323 0 .272 V31 323 0 -.646 V32 323 0 .074

As the sample for this research is large (>300), the absolute value of the score greater than 2.58 or lesser than -2.58 is significant at p<0.01. So from table 6.12 and table 6.13, it can be deduced that data is not skewed and does not show kurtosis also.

ii. The Shapiro- Walk test

SPSS provides the K-S (with Lilliefors correction) and the Shapiro-Wilk normality tests and recommends these tests are to be used only for a sample size of less than 50 (Elliott AC, 2007). The Shapiro–Wilk test utilizes the null hypothesis principle to check whether a sample came from a normally distributed population or not (Shapiro, 1965). The null- hypothesis of this test is that the population is normally distributed. Thus, if the p-value is

Chapter 6: Data Collection, Analysis and Research Results

144

less than the chosen alpha level, then the null hypothesis is rejected and there is evidence that the data tested are not from a normally distributed population; in other words, the data are not normal. On the contrary, if the p-value is greater than the chosen alpha level, then the null hypothesis that the data came from a normally distributed population cannot be rejected (e.g., for an alpha level of 0.05, a data set with a p-value of 0.02 rejects the null hypothesis that the data are from a normally distributed population) (Field A, 2009) However, since the test is biased by sample size, the test may be statistically significant from a normal distribution in any large samples.

In this research, p-value for this test comes out to be less than 0.05 and it rejects null hypothesis. It is understood from (Oztuna D, 2006) that for small sample sizes, normality tests have little power to reject the null hypothesis and therefore small samples most often pass normality tests. For large sample sizes, significant results would be derived even in the case of a small deviation from normality. Therefore this test cannot be relied upon.

iii. Histograms, Normal Q-Q plots and Box plots: To discover the shape of the distribution in SPSS, a histogram is made and a normal curve is plotted. If the histogram does not match the curve, then the data may have normality issues. And same goes with Normal Q-Q and Box plots (Ghasemi, A, 2012). Other than two variables, all the Q-Q plots came to be fine.

So in summary, it is assumed through the results of normality tests that the given data is normalized and is ready to be used for Structural equation modelling.