Chapter 3 Research Methodology and Data Collection
3.7.6 Non-Response Rate and Sample Size
The questionnaire survey is used mostly to collect data, because it allows a large sample quantity of the research population to be collected in a highly cost-effective way (Saunders et al., 2009). The research used an e-questionnaire to collect data from e- consumers who purchase online luxury products. The questionnaire contained a series of 5 Likert-type (1-5 disagree/agree) statements developed from the literature review.
This research project sent questionnaires randomly to 1000 consumers in the USA and UK who purchase online luxury products. In addition, the researcher chose only those who had purchased luxury online items from websites within the last six months. In order to test the accuracy of the data, the researcher checked for missing data.
Indications of missing data are “…information not available for a case (or subject) for which other information is available” (Hair et al., 2006, p.38). Generally, missing data is caused by the respondents refusing to respond to one or more questions of the questionnaire, from the UK sample, the researcher excluded 352, from the USA sample;
the researcher excluded 335 returned questionnaires with missing data. Consequently, 313 forms remained, valid and free of missing data. The resulting of responses rates are 52.72% and 47.28% for both UK and USA, respectively. The questionnaire was administrated between 15th June and 15th October 2014. A month earlier the survey had
been checked from the supervisory team who gave me a final agreement to launch the survey. Starting from 15th June 2014, the online questionnaire was distributed to the target participants in the UK and the USA at the same time. Questionnaires then received back from the participants were immediately given an identification number and checked for completeness. At the end of the month, the returned surveys were checked once again for completeness and reconciled against those delivered. A high response rate of 100% was achieved (Saunders, 2009). Non-response bias was assessed by comparing early respondents with later respondents on key belief variables (Armstrong & Overton, 1977). No significant differences in any of the variables were found, providing no evidence of non-response bias (Ha & Stoel 2009) (see Table 4.2 in Chapter 4). Table 3.7 demonstrates the results of the data collection phase and shows the response rate for the survey questionnaire. The table also compares the response rate to that of the pilot study.
Table 3.7 Online Survey
Sent Emails Failed/Bounced Emails
Delivered Emails
Returns Response Rate
COLS 1000 50 950 650
(313Usable)
48.15%
The response ratio for the consumers buying online luxury shopping was 313 (165 usable from UK and 148 USA) out of 1000 delivered, which records a response rate of 48.15% from the usable valid data (313). In addition, unlike other structural equation model tools, it is widely acknowledged that the PLS-SEM can produce robust results with relatively limited sample sizes (Henseler et al., 2009; Reinartz et al., 2009; Hair et al., 2014). In their recent Monte Carlo Simulation, Reinartz et al. (2009) found that the PLS-SEM can provide acceptable levels of statistical power with 100 observations. The authors suggested that the researchers in PLS can easily compensate the low sample size effect by increasing the number of indicators and using indicators with high loadings. Similarly, Chin (2010) states that “…to play it safe, one might recommend 100 or 200 [respondents] to improve accuracy”
(p.662). A widely cited and applied rule of thumb for the minimum sample size required to run a robust PLS-SEM algorithm is that “the sample size be: (1) ten times the number of indicators of the scale with the largest number of formative indicators, or (2) ten times the largest number of structural paths directed at a particular construct in the inner path model”
(Henseler et al., 2009, p.292); a similar rule was argued by Hair et al. (2011; 2014a) and Peng and Lai (2012). Hair et al. (2014a) also stress the fact that researchers should take into
account the statistical power that the study can achieve when determining the appropriateness of the sample size. In general, Hair et al. (2014b) acknowledge that the PLS-SEM achieves higher levels of statistical power than other statistical techniques. Despite the fact that Pallant (2007) acknowledges that when the sample size is greater than 100, the statistical power should not be an issue, Hair et al. (2014a) suggest using the following table adapted from Cohen (1992) as guidance to determine the appropriate sample size to produce significant results (see Table 3.8). However, the determination of the sample size is important in building the number of sample which has to be neither low, to avoid the risk of inadequate information, nor high to avoid the risk of being inefficient (Scheaffer et al., 1986, Zain, 1995).
The choice of sample size relies on several factors such as the size of the entire population;
the level of margin of error required, the level of certainty; and the types of statistical techniques used to analyse the data (Saunders et al., 2009).
Table 3.8 Sample Size Recommendation in PLS-SEM
Statistical Power of 80%
Maximum Number of Arrows pointing at a construct
5% Significance level Minimum R square
0.10 0.25 0.50 0.75
2 110 52 33 26
3 124 59 38 30
4 137 65 42 33
5 147 70 45 36
6 157 75 48 39
7 166 80 51 41
8 174 84 54 44
9 181 88 57 46
10 189 91 59 48
Source: Adapted from Hair et al. (2014a)
There is no definitive standard with regard to sample size. It can be considered as small (less than 100 samples), medium (between 100 and 200 samples), and large (more than 200 samples). From these classifications, 313 samples can be regarded as the critical size (Hair et al., 2010). Furthermore, statistical power is higher in a sample size of 100 or more, according to SEM. The sample size of this study was 165 and 148 (UK and US respectively), totalling 313. The number of observations is above the minimum required when applying the above cited rule of thumb. In fact, when taking into account Cohen’s statistical power rule, the maximum number of arrows pointing toward one construct is three (the present case), thus the minimum sample size required to achieve a statistical power of 80% with a significance level at 5% and detect an R square with at least 0.25, would be 59 observations. As for the
abovementioned rule proposed by Henseler et al., (2009), Hair et al. (2011; 2014a) and Peng and Lai (2012), the larger of the above cited two options is ten times the number of indicators of the construct with the largest number of largest number of reflective indicators, which is the variable consumer attitude (Att) with eight items, and hence the minimum sample size would be 80. Additionally, when considering the statistical power based on Table 3.8, for the minimum sample size required to achieve a statistical power of 80% with a significance level of 0.25% and detect an R square with at least 0.10, the researcher would need 189 observations. Therefore, it can be concluded that the sample sizes for both countries 313 are sufficient to run a robust PLS-SEM analysis.