5.4 SAMPLING STRATEGY
5.5.4 Determination of sample size
Sample size refers to the limited number of elements that represent the whole population (Saunders et al., 2016) that will ultimately participate in the actual study (Macmillan & Schumacher, 2010; Bryman
& Bell, 2015). Sekeran and Bougie (2013) warn that the decision about the size of a sample can be very difficult. They further point out that the correct sample size is dependent on the nature of the population under the study and the purpose of the research. Other factors governing the size of a sample include the population variability (Neuman, 2015), confidence level, and confidence interval (Saunders et al., 2016; Sekeran & Bougie, 2016). Admittedly, Cooper and Schindler (2012) observe that much folklore
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surrounds this issue. The following sections discuss the determination of the sample size for the quantitative study and the qualitative study.
5.5.4.1 Quantitative study
The researcher used Yamane's formula (1967) to determine the sample size for the quantitative study.
Past researchers in entrepreneurship and management research (Nyangara et al., 2015; Mhizha, 2014;
Anyanga & Nyamita, 2016; Kowo, et al., 2018) using the cross-sectional research surveys have adopted Yamane’s formula in determining sample size for their studies. While it can be argued that Yamane’s formula is old, its consistent use over the years by many academic researchers is evidence that it is still valid, dependable, and widely acceptable (Anyanga & Nyamita, 2016; Kowo, et al., 2018). The formula is highly recommended for stratified random sampling (Israel, 2002). The following formula was used to calculate the sample size for the study.
𝑁 (1 + 𝑁(𝑒)²)
Given the 9 242 manufacturing SMEs in Harare, the required sample size was 368, calculated as illustrated below. Where:
N- Population size (9 242) e- Margin of error (0.05)
n ̥= 𝑁 1+𝑁(𝑒)²
n ̥ = 𝑁
1+
𝑁²−1𝑁n ̥= 9242 1+9242(0,05²)
Therefore n =
383.405 1+ (
383.4059242
)
=
383.405 1.041
=368
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Therefore, the sample size for the study is 368 using Yamane's formula. The sample size in each sector is proportional to the size of the population.
TABLE 5.2: SAMPLE SIZE PER STRATA
Sector Percentage Population in sector Proportional Sample size
Food products 22 2 033 81
Clothing & footwear 15 1 386 55
Wood & furniture 30 2 773 110
Chemical & petroleum 10 924 37
Metals 23 2 125 85
Totals 100 9 242 368
Source: Author compilation
The sample size drawn for this study fits very well with Roscoe's (1975)'s rules of thumb. Roscoe (1975) cited in Sekeran and Bougie (2013) proposes that a sample size larger than 30 but less than 500 are suitable for most studies. The sample size in this study is 368, more than 30 but less than 500. Roscoe further proposes that where the sample can be classified into subgroups the sample size should be at least 30 for each category. In this study, there are five mutually exclusive groups, with more than 30 respondents in each group.
5.5.4.2 Qualitative study
The determination of sample size in qualitative research is different from quantitative studies (Boddy, 2016; Malterud, Siersma & Guassora, 2016; Bryman & Bell, 2015). The sample size in qualitative research should be large enough to ensure that all-important perceptions are uncovered (Mason, 2010;
Saunders et al., 2016), generate sufficient data to fulfill the study questions (Bryman & Bell, 2015), and describe the phenomenon of interest understudy (Malterud et al., 2016; Boddy, 2016). The question which needs to be answered now is how large should be the sample size for qualitative studies?
Adopting an ethnographic approach in non-quantitative research calls for data being rich in qualitative detail, a parametric distribution is not necessary; nor is statistical manipulation (Dana & Dumez, 2015).
Different scholars have recommended various guidelines for determining the appropriate sample size for qualitative studies (Malterud et al., 2016). Saturation is one of the principles in sample size determination for qualitative studies (Saunders et al., 2016; Boddy, 2016; Malterud et al., 2016). Table 5.3 below provides a summary of sample size determination guidelines in qualitative studies.
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TABLE 5.3: SAMPLE SIZE DETERMINATION GUIDELINES FOR QUALITATIVE RESEARCH
Sample Size Research Type Research Authority
5-25 Phenomenology Creswell (2013)
Less than 20 Phenomenology Crouche and McKenzie (2006)
20-30 Grounded theory Creswell (2014)
20-40 Grounded theory Marshall et al. (2013)
12-60 Case study Adler and Adler (2012)
15-30 Interviews Creswell (2013)
20 plus All qualitative studies Green and Thorogood (2009)
25 plus All qualitative studies Charmaz (2012)
Less than 10 Grounded theory Boddy (2016)
Source: Author (developed from literature)
Qualitative sample sizes of 20-30 are appropriate for researchers using grounded theory to inquiry (Creswell, 2014; Warren, 2002), sample size between 12 and 60 with a mean of 30 are advisable (Adler
& Adler, 2012 cited in Bryman, 2016), sample sizes of less than 20 ensures maximum participation and involvement of participants (Crouche & McKenzie, 2006), sample sizes of 10 are considered sufficient for sampling among a homogenous population (Boddy, 2016), 5-25 for phenomenology and 15-30 interviews for case studies (Creswell, 2013), 20 plus all qualitative studies (Green & Thorogood, 2009) and 15 plus (Guest et al., 2006). Bryman (2008) on the other hand laments the absence of ideal sample size in qualitative studies.
According to Bryman (2016), the sample size for qualitative studies should be able to support reasonable and convincing conclusions but will vary from situation to situation, hence researchers in qualitative studies must balance forces. Onwuegbuzie, Leech and Collins (2012:289) note that "In general, sample sizes in qualitative researches should not be so small as to make it difficult to achieve data saturation, theoretical saturation or informational redundancy. At the same time, the sample should not be so large that is difficult to undertake a deep, case-oriented analysis".
With all these recommendations, the sample size for the in-depth interviews was 15 as determined by data saturation. The sample size is consistent with most of the sample size guidelines for qualitative studies described above.
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TABLE 5.4: SAMPLE SIZE FOR IN-DEPTH INTERVIEWS
Sector Sample size
Clothing & footwear 3
Wood & furniture 3
Chemical & petroleum 3
Food products 3
Metals 3
Total sample size 15
Source: Own compilation
The researcher observed that the theoretical saturation was reached at 15 interviews with the owner/managers. The main aim of qualitative studies is to collect rich data and not to infer (Saunders et al., 2016). Hence, a small sample size of 15, studied in great depth is suitable (Gliga, 2016).