# Quota Sampling as an Alternative to Probability Sampling? An Experimental Study

**by Keming Yang and Ahmad Banamah
University of Durham**

Sociological Research Online, 19 (1) 29

<http://www.socresonline.org.uk/19/1/29.html>

10.5153/sro.3199

Received: 10 Apr 2013 Accepted: 9 Sep 2013 Published: 28 Feb 2014

## Abstract

In spite of the establishment of probability sampling methods since the 1930s, non-probability sampling methods have remained popular among many commercial and polling agents, and they have also survived the embarrassment from a few incorrect predictions in American presidential elections. The increase of costs and the decline of response rates for administering probability samples have led some survey researchers to search for a non-probability sampling method as an alternative to probability sampling. In this study we aim to test whether results from a quota sample, believed to be the non-probability sampling method that is the closest in representativeness to probability sampling, are statistically equivalent to those from a probability sample. Further, we pay special attention to the effects of the following two factors for understanding the difference between the two sampling methods: the survey's topic and the response rate. An experimental survey on social capital was conducted in a student society in Northeast England. The results suggest that the survey topic influences who responded and that the response rate was associated with the sample means as well. For these reasons, we do not think quota sampling should be taken as an acceptable alternative to probability sampling.

**Keywords: **Probability Sampling, Quota Sampling, Representativeness, Response Rate, Social Capital

### Introduction

**1.1**In the mid-1920s, probability sampling started to replace full enumeration as an efficient way of collecting reliable information on a population (Kruskal and Mosteller 1980: 173). Nowadays, apart from national censuses, government agencies, academic institutions or commercial organizations routinely employ probability sampling to make inference about a particular population in the surveys they administer (Rao 2000:1).

**1.2** However, over the past several decades survey researchers have recognized two major difficulties in following the probability sampling procedure. The first is the rising cost of using probability samples. Some have even argued that 'cost is probably the single most important factor driving the search for new methods of sampling' (Brick 2011: 877), with the 'new methods of sampling' referring to non-probability sampling methods. The second problem is the decline of response rates, and there has been a large literature on this issue (Groves and Couper 1998; Groves, Dillman, Eltinge and Little 2002). For instance, Curtin et al. (2005) examined the response rate changes on the University of Michigan's Survey of Consumer Attitudes from 1979 to 1996. They found that the response rate faced a marked drop from 72 per cent to 62 per cent with an average decline of .75 per cent per year. Indeed, given the large amount of time, money and other resources invested in probability sample surveys, the declining response rates have led some researchers to claim that probability samples with low response rates are no better than volunteering samples (Levy and Lemeshow 1999; Brick 2011). Conversely, some have pointed out that a well-designed non-probability sampling scheme such as quota sampling could produce a quasi-representative sample (Neuman 2011: 243). To overcome these difficulties some researchers have started to look for alternative ways of drawing a sample since the mid-1900s (Stephan and McCarthy 1958; Godambe 1966; Royall 1970; Holt and Smith 1979; Thompson and Seber 1996; Heckathorn 1997; Lavallee 2007).

**1.3** The search for an alternative to probability samples points to the fundamental issue of keeping a balance between cost and quality. On the one hand, few would argue that we should sacrifice accuracy and quality while achieving speed and low cost. On the other hand, non-probability samples would become attractive to survey organizers if the quality of the results that they produce is within a 'satisfactory' range. In the end, the dilemma boils down to the following question: given that a non-probability sample is in principle inferior to probability sample in terms of representativeness, could a non-probability sampling method such as quota sampling produce a sample whose representativeness is so satisfactory that its relative low quality is acceptable considering the lower cost of running a survey, the faster speed, and maintaining the same level of response rate? If the answer is positive, then perhaps it is time for survey researchers to switch from costly probability samples struggling for a decent response rate to an equally good non-probability sample. However, there does not seem to be enough convincing evidence yet for such switch. Non-representativeness and low-response rate are two distinctive types of biases, and it seems that survey researchers have been struggling to eliminate both of them at the same time.

**1.4** Moreover, our decision should not completely reply on theoretical discussions based on probability theories with regard to the two sampling schemes as such discussions often fail to demonstrate the effects of influencing factors on the practice of sample surveys, such as the topic and reminders. Most social surveys focus on one or a few limited number of substantive topics, which will appear to be appealing to different groups of respondents. In other words, for a certain topic, the respondents of a survey could be roughly classified into two groups, those who find the topic interesting or relevant and thus are willing to participate and those who are in the opposite situation. As we shall show later in this paper, the topic of the survey will affect the willingness of participation, which in turn will affect the response rate and the potential risk of collecting biased results. We need experimental data to show whether the risk of poor or even biased representation of the population could be reduced to an acceptable level with a non-probability sample, and more importantly, we must demonstrate the source and the underlying mechanisms of such potential bias, if shown to be the case.

**1.5** It is with these objectives in mind that we conducted an experiment in which we compared the results of a probability sample with those of a non-probability sample for the same survey. As Marsh and Scarbrough (1990) have noted - they refer to the case of the UK but we think their point is applicable to social surveys in general, 'what missing in British survey research is a coherent programme reviewing the effect of different sampling procedure' (1990: 485). More recently, Brick (2011) pointed out that for the future of sampling, the relationship between probability and nonprobability sampling must be addressed in the context of the decreasing response rate and the increasing costs of data collection. We designed and conducted an experimental survey on social capital in a student society in Northeast England. We chose social capital as the theme of the survey due to its importance in university students' life and its growing importance in sociological research. We realize that the limited scope of our experiment may not allow us to reach a definite solution to the choice of sampling method. We do believe, however, that our analysis of the experiment will provide fresh evidence and insights to the comparative advantages (or disadvantages) of each sampling scheme. It is our hope that studies such as ours will eventually resolve the controversy over the choice of sampling schemes.

### The case for probability sampling

**2.1**The earliest discussion of probability sampling can be traced back to the work of Karl Pearson (Pearson and Filon 1987; Pearson 1900). After about thirty years of discussion of Pearson's ideas, Jerzy Neyman's essay 'On the Two Aspects of the Representative Method' (1934) represented a major landmark in the history of probability sampling. In his essay, Neyman compared between probability and nonprobability sampling and explained the conditions under which the estimates from non-probability samples could and could not be representative. Fifteen years after the publication of Neyman's essay, his approach of probability sampling became widely accepted by almost all leading statisticians, with a theory of probability-based design being fully developed and the first generation of statistics text books being widely adopted. In the mid-1960s, William Cochran (1964: 9) summarized the four principles of the probability sampling method as follows:

- The sampling procedure can identify how many possible samples can be drawn from the investigated population and what possible units could be included in each one of these samples;
- Each possible sample has a known probability of selection;
- The sampling method should select the samples in a process that assures that each possible sample receives its appropriate probability of being selected;
- The procedure of calculating the estimates which are going to be generalised from the sample to the population must be known and lead to a unique estimate for each sample.

**2.2** Whilst this is not a place for explaining why such sampling scheme would lead to the representativeness of sample estimates of population parameters, it is necessary to point out, albeit briefly, that it is the probability distribution of sample estimates, which are produced by such sampling procedure, that lays the foundation for representativeness. As many statistical textbooks (Lohr 2010; Thompson 2012) have explained this logic very well, there is no need for us to go into the details here. For readers without a background in survey methodology, here we offer a brief description of the key difference between stratified sampling and other types of probability sampling, particularly cluster sampling, as these two can be easily confused. Both methods categorize the target population into a certain number of groups; in stratified sampling, they are called 'strata' and in cluster sampling, 'clusters'. A key advantage of stratified sampling is that it randomly selects elements in *every* stratum. In cluster sampling, however, *only some* clusters are randomly selected in the first stage, and then a simple random sample is selected within each *selected* cluster.

**2.3** During the past decades few have criticised probability sampling. Godambe (1966) and Royall (1970) are perhaps two exceptions, who favoured the use of model-based and Bayesian approaches over the use of probability sampling (design-based). Both criticisms, however, were discussed and refuted by Holt and Smith (1979). The Bayesian approach has enjoyed an increasing popularity in recent years, but that is mostly due to the advance of data analysis and computing power rather than to the improvement of sampling methods. More relevant to our concern is the recent challenges (Brick 2011; Heckathorn 1997; Lavallee 2007; Thompson and Seber 1996) to the established status of probability sampling. Below we shall try to reveal the logic behind such challenges.

### The case for quota sampling

**3.1**While probability sampling gives the researcher the edge of inferring from the sample to the population, to fulfil its requirements strictly could bring some serious difficulties to the practice of conducting a sample survey. The most commonly encountered difficulties are the following two: the population size might be infinite or unknown, such as illegal immigrants, and the sampling frame could be too costly or inaccessible (Levy and Lemeshow 1999). It is these practical constraints, not the fundamental logic of probability sampling, that make survey researchers to seek for alternatives to probability sampling that are of low-cost as well as with a satisfactory level of representativeness.

**3.2** However, in nonprobability sampling there are no principles embraced by all non-probability sampling methods. Each method embraces different principles and fulfils different criteria, depending on the objectives and aims of the research (Bryman 2008: 183). Therefore, it is not surprising that the term 'nonprobability sampling' covers a broad range of sampling methods that considerably vary in their qualities and features (Groves et al. 2004: 249). Here we focus our attention on quota sampling because it is the non-probability sampling method that some researchers have claimed to be competent to produce results equivalent to the ones produced by probability sampling (Moser and Stuart 1953; Stephan and McCarthy 1974; Cumming 1990; Brick 2011).

**3.3** In quota sampling the entire population is divided into relevant strata, such as gender, age, class, etc. These strata are called 'quota controls' and they are chosen according to their relevancy to the topic of interest. The number of elements in each stratum in the population is estimated with external data such as census results. Then the total number of units in each stratum in the sample is the product of the corresponding proportion in the population and the predetermined sample size. Finally, in order to obtain the same (or at least very similar) proportion for each stratum in the sample, interviewers are allowed to select from the population the calculated number of units in each stratum, and they are free to choose anyone as long as the person meets the requirements of the stratum. People who are not willing to participate are simply replaced by other people who are (Brinsky 2006).

**3.4** The fundamental difference between quota sampling and probability sampling lies in the last stage. If the participants in quota sampling are assigned equal probability of being included in the sample, quota sampling will be equivalent to stratified sampling, which is a probability sampling method, and the results of both methods should be the same or very close. However, since the way of choosing the participants in quota sampling is left to the interviewers, the samples drawn with the two methods agree only in the quota-controls and may vary in other characteristics (Singleton and Straits 1999: 159). A key question then is whether the variation in these 'other characteristics' will lead to a sample biased in a certain way. Users of quota sampling including many well-established polling agencies such as Gallop in the USA and Mori in the UK would argue that these characteristics - and therefore the potential biases - are irrelevant to the topic of concern and that the efficiency and low cost of quota sampling will outweigh the potential bias. This is perhaps why quota sampling has survived disastrous predictions such as those by *The Literary Digest* in 1936 and pre-presidential elections in 1948 in the US (Jacoby and Handlin 1991). *The Literary Digest* successfully predicted the result of 1920, 1924, 1928 and 1932 U.S. presidential election without using probability sampling or defining a sampling frame for any of the previous surveys. In 1936 the magazine increased its sample from about 1 million to 10 million people assuming that this increase would improve the accuracy of its results, predicting a huge victory for Alf Landon over Franklin D. Roosevelt, which was a false prediction. The second event was the pre-election poll in 1948 between Truman and Dewey (Frankel and Frankel 1987), when most pre-election and public opinion polls were still using quota sampling (Brinsky 2006). They had broad agreement that the upcoming election would be decided for Dewey. The victory of Truman over Dewey raised serious doubts as to quota sampling and left the social research community divided about its reliability. The incorrect predictions resulted from the fact that the used quota criteria missed some important factors that affected how the Americans voted in those elections, but the question stayed as to whether the two incorrect predictions would completely invalidate quota sampling.

**3.5** Indeed, it is rare that cost is taken into account in any calculations of probability sampling; rather, it is often assumed that costing is a matter to be dealt with by survey administrators rather than statisticians, which is why some non-probability sampling methods could be claimed to have an advantage over probability ones. For example, Sudman (1966 cited by Groves 1989:249) compared six probability sampling surveys and four quota sampling surveys, showing that the average cost of quota sampling was about one-third of the average cost of probability sampling. Obviously, this claimed advantage will become more attractive when the budget under the control of survey administrators becomes tight, such as in the currently difficult financial situations in most of the European nations.

**3.6** Another factor that lends strong support to the use of non-probability sampling is the decline of response rates among probability sample surveys. The argument is that a probability sample with low response rate suffers from the same potential bias as a non-probability sample and therefore enjoys no clear advantage over a quota sample (Brick 2011). Statistically, nonresponse bias can be presented as follows (Levy and Lemeshow 1999: 394). The sample mean of a particular variable (y) for the population of size *N* is:

*y*among the potential respondents, is the mean of

*y*among the non-respondents, is the potential respondents in the population and is the potential non-respondents in the population. Then, the relative bias (RB) for due to the non-responses could be expressed as

**3.7** In other words, the relative bias is affected by both the non-response rate and the difference between the mean of the respondents and the mean of the non-respondents relative to the grand mean. In order to discover and demonstrate the effect of response rate on the results of the two types of samples, we have conducted the following experiment.

### Design of the experiment

**4.1**As far as we know, only a very limited number of studies have made a direct comparison between probability sampling and quota sampling. The first study was conducted by Moser and Stuart (1953) in the summer of 1951, which compared the results of Government Social Survey that used probability sampling with the results of a quota sample survey designed for the purpose of this experiment. The two samples were selected from the same population. They found that the results from the two samples were very close in most of the questions with only significant differences in a few questions; therefore, they concluded that quota sampling was a method that could produce good results in a cost-effective manner even though it does not possess a sound sampling theory.

**4.2** Cumming (1990) conducted an experiment in 1986 and 1987 with an aim to compare the results of two studies of the same population in Sydney's western suburbs. The first study used quota sampling and the second used probability sampling. This comparative experiment showed that the results for only three out of the fifteen questions were significantly different (*p* › 0.05). Cumming thus concluded that the agreement between the two samples in the other twelve questions suggested that 'quota sampling with age and sex quota controls may be an acceptable alternative to probability sample survey' (Cumming 1990: 137). The underlying assumption is that the percentage of questions for which the results are statistically insignificant determines whether we could use quota sampling as an acceptable substitute of probability sampling. On the other hand, it is possible that a single significant difference might be important enough to favour one methodology over the other; the importance of the difference, however, is a substantive issue that we must leave to the researcher to decide. A more general question is what would constitute an acceptable loss of accuracy when the results for some survey questions turn out to be significantly different between the two sampling methods. We do not think that this is a purely statistically matter, and we can only recommend that the researchers report all results and provide explanations for their decisions so that other researchers could make their own judgements. Finally, Cumming's experiment suffers from a serious limitation: the questionnaires used in the two surveys were not identical. The questionnaire for the quota sample consisted of 32 questions while the questionnaire for the probability sample consisted of 97 questions, and only 15 questions were common. This raises the question about the influence that answering these common questions in different contexts might have on the results.

**4.3** Our experiment has the same aim to find out whether the differences between the results from the two samples of the same population are statistically significant. In our experiment, the probability sample will be treated as a control group and the non-probability (quota) sample will be treated as an experimental group. The probability sample was drawn by following a full probability sampling procedure. In order to study the effect of reminders on the results, two reminders were sent to the respondents of the probability sample; therefore, we have three groups of respondents, each having a different response rate as a consequence of each respective reminder. They will be compared with the quota sample to examine the influence of the reminders on the relationship between quota and probability sampling. Respondents of both samples were asked to fill in exactly the same questionnaire.

**4.4** The population of this study was the members of a student society in one of the universities in the Northeast of England, and its size (*N*) was 312. It consisted of university students as well as people who were not part of the university. Members who were not university students accounted for 17% of the population, while university students accounted for the other 83%. Of the student members, 43% were master students, 39% were PhD students, while undergraduate students comprised only around 18%. The females accounted for 41% of the population and males 59%. The population had a mean age of 33.4 (*SD*=9.1). Full permission was obtained from the executive committee of the society to gain access to membership lists and records and to conduct the experiment.

**4.5** A probability sample of 40 members (*n*_{1}=40) was selected by the systematic sampling method. Since some first names tend to be more popular in certain ethnic background, the whole membership list was randomized with randomization software. In order to measure the influence of response rate, the respondents in this probability sample were divided into three groups: the participants who responded immediately without receiving any reminders (*n*=9, response rate=22.5%); the respondents who responded after receiving the first reminder (*n*=17, response rate=42.5%) and all participants in the probability sample who responded after receiving the second reminder (*n*=27, response rate=67.5%). The latter two are cumulative participant response totals in the three probability samples; that is, the sample of the 42.5% response rate includes the sample of the 22.5% response rate, and that of the 67.5% includes the other two samples of lower response rates.

**4.6** For the quota sample, two quota-controls, gender (male and female) and educational level (Master's, PhDs, and others) were used. We chose these two quota variables because they are two social characteristics that we believe are related to social capital among this particular population - it is highly reasonable to expect that students tend to make friends and join social activities that are of the same gender and/or educational level due to convenience and/or comfort. The population was therefore divided into six groups according to these quota controls. A sample of 60 members was selected by direct proportion to the population. In order to obtain the sample, two assistants were asked to fill these groups with members. Each assistant was responsible for three different groups to ensure no overlap between them. In order to restrict the assistants' freedom, they were asked to contact the members from a specific area in five locations that commonly known to be inhabited or regularly visited by the society members. Furthermore, they were asked not to approach only people they personally know or to immediately replace members who are unwilling to participate with other members without trying to persuade them or approach them again. As the reader will see soon, not all sixty selected members participated in the quota sample, but the number of non-participants is very small.

**4.7** In designing the questionnaire, we followed two principles: one, it should be simple as our purpose was not to carry out a rigorous study on this topic per se but to compare the two types of samples, and two, it should be interesting to most, if not all, members of the society. Eventually, we decided to concentrate on the members' social capital, and the table below contains the nine variables covered in the survey (Table 1; please refer to the Appendix for the questionnaire):

Table 1: Topics covered in the two sample surveys | ||

Section | Variable | Aim |

1 | Religious activities | To measure the level of the member's participation in society |

Social activities | ||

2 | Friendship | To measure personal friendships among the members |

Society contrite friendship | ||

3 | Members helpful | To measure the mutual trust and support among the members |

Members trustworthy | ||

Member trust me | ||

4 | Society support | To measure the relationship between the members and the society in terms of support and the satisfaction with the society's performance |

Society performance | ||

### Analyses of the results

**5.1**Our analysis consists of two comparisons. First, we measure the estimated mean for each variable in the probability sample with its counterpart in the quota sample and see whether their difference is statistically significant. Second and in the meantime, we present and then compare the results of the means at each level of response rate in order to examine the impact of response rate of the probability sample on the previous comparison. Below are the hypotheses that we plan to test:

**5.2** Hypothesis 1: The means of all estimates in quota sample will be equal to the means of the estimates in the probability sample at the 0.05 level of significance. (The variables that were being compared across samples were ordinal, with the exception of friendship, which was binary).

**5.3** Hypothesis 2a: When the response rate is low (before any reminder was used), there will be no significant difference between the quota sample and the probability sample as the respondents tend to be similar (people who are willing or interested in participating).

**5.4** Hypothesis 2b: When the response rate becomes higher (after using reminders), the difference between the quota sample and the probability sample will become significant due to the results submitted by the non-willing participants.

*Comparison of the means at the response rate of 22.5%*

**5.5** We start the comparison between the means of the quota sample and those of the probability sample at the lowest response rate (22.5%), that is, the results (Table 2) come from those who returned their questionnaire without receiving any reminders in the probability sample.

Table 2: Comparing the means of the two samples at the response rate of 22.5%
| ||||

Item | Sample | n | Mean | s.e. |

Religious activities | Probability | 9 | 3.78 | .324 |

Quota | 57 | 3.86 | .126 | |

Social activities | Probability | 9 | 2.44 | .503 |

Quota | 56 | 2.79 | .124 | |

Friendship | Probability | 9 | .67 | .167 |

Quota | 59 | .86 | .045 | |

Society contribution | Probability | 6 | 3.17 | .477 |

Quota | 51 | 2.90 | .146 | |

Members helpful | Probability | 9 | 3.22 | .521 |

Quota | 55 | 3.75 | .145 | |

Trust other members | Probability | 9 | 4.11 | .309 |

Quota | 58 | 3.71 | .161 | |

Other members trust me | Probability | 6 | 4.33 | .333 |

Quota | 58 | 3.48 | .158 | |

Society support | Probability | 9 | 2.33 | .553 |

Quota | 53 | 3.36 | .127 | |

Society performance | Probability | 7 | 2.43 | .528 |

Quota | 44 | 3.05 | .112 | |

**5.6** Reading the means, six out of the nine means of the quota sample are higher than their corresponding means of the probability sample; the three variables whose means of the quota sample are lower than those of the probability sample are: 'Society contribution', 'Trust other members' and 'Other members trust me'. The most interesting result is that for all variables, no statistically significant difference is found between the means of the quota sample and this first group of probability sample. Indeed, some means were almost identical such as the means of attending religious activities, although the standard errors of the probability sample are bigger due to the much smaller sample size.

**5.7** Now we test whether the differences for each variable are statistically significant by using the Mann-Whitney U test (Table 3).

Table 3: Testing the differences between the quota sample and the probability sample at the response rate of 22.5%
| ||

Item | Mann-Whitney U/chi-square | p |

Religious activities | 236 | 0.687 |

Social activities | 228 | 0.634 |

Friendship | 1,03 | 0.310 |

Society contribution | 126 | 0.484 |

Members helpful | 201 | 0.350 |

Trust other members | 220 | 0.425 |

Other members trust me | 101 | 0.096 |

Society support | 152 | 0.060 |

Society performance | 113 | 0.262 |

**5.8** The numbers in the second column are the Mann-Whitney U statistics, which represents the difference between the two rank totals, except for 'Friendship', which is a binary variable, so the chi-square statistic with continuity correction was calculated. As none of the p-values in third column is less than the conventional criterion of 0.05 - the closest is 'Society support' at 0.06, we can infer that at the response rate of 22.5%, the two sampling methods do not make a significant difference with regard to all the key variables under study.

*Comparison of the means at the response rate of 42.5% *

**5.9** The results of the comparison are presented in Table 4.

Table 4: Comparing the means of the two samples at the response rate of 42.5% | ||||

Item | Sample | n | Mean | s.e. |

Religious activities | Probability | 17 | 3.29 | .318 |

Quota | 57 | 3.86 | .126 | |

Social activities | Probability | 17 | 2.41 | .310 |

Quota | 56 | 2.79 | .124 | |

Friendship | Probability | 17 | .65 | .119 |

Quota | 59 | .86 | .045 | |

Society contribution | Probability | 11 | 2.55 | .340 |

Quota | 51 | 2.90 | .146 | |

Members helpful | Probability | 17 | 3.29 | .340 |

Quota | 55 | 3.75 | .145 | |

Trust other members | Probability | 17 | 3.76 | .278 |

Quota | 58 | 3.71 | .161 | |

Other members trust me | Probability | 12 | 4.00 | .302 |

Quota | 58 | 3.48 | .158 | |

Society support | Probability | 17 | 2.53 | .322 |

Quota | 53 | 3.36 | .127 | |

Society performance | Probability | 14 | 2.43 | .327 |

Quota | 44 | 3.05 | .112 | |

**5.9** Similarly to the first comparison, we can see that most of the means of the quota sample are higher than those of the probability sample with the exception of 'Trust other members' and 'Other members trust me'. Then we test whether the sampling method makes any statistically significant difference to the estimates of these variables (Table 5).

Table 5: Testing the differences between the quota sample and the probability sample at the response rate of 42.5%
| ||

Item | Mann-Whitney U/chi-square | p |

Religious activities | 363 | 0.102 |

Social activities | 402 | 0.313 |

Friendship | 2.828 | 0.093 |

Society contribution | 224 | 0.272 |

Members helpful | 389 | 0.280 |

Trust other members | 486 | 0.921 |

Other members trust me | 266 | 0.178 |

Society support | 283 | 0.014 |

Society performance | 219 | 0.085 |

**5.10** The p-values in the third column clearly indicates that except for 'Society support', whether the sampling method is probability or quota does not make any statistically significant difference to the results of the selected variables. This means that the 20% increase in response rate for the probability sample has made difference to the results of only one out of the nine variables.

*Comparison of the means at the response rate of 67.5%*

**5.11** As this is the last of our probability sample with the highest response rate, we make more specific explanations and observations on the results (Table 6).

**5.12** On average, participants in the quota sample are more involved in religious activities: the mean is close to four (attend religious activities more than once a week), while the mean in the probability sample is very close to three. The results of the other variable in this section ('Social activity') are almost the same. Participants in the quota sample are more involved in social activities organised by the society than the participants in the probability sample. The second section measures personal friendships among the members and the extent to which the society contributed to these friendships. The first variable 'Friendship' is a dichotomous variable which measures whether the member has any friend in society with whom they can discuss intimate and personal matters. The results show that more participants in the quota sample have friends in the society than participants in the probability sample. The second variable 'Society contribution' measures the extent to which the members believe that the society has contributed to this friendship. Similarly, participants in quota sample reported more contribution from the society than participants in probability sample.

**5.13** The third section measure the mutual trust and general support among the members of the society, including three variables measured with a five-point scale; 'Members helpful' measures the extent to which the participants think other members in the society are helpful; 'Trust other members' measures the extent to which the participants trust other members in the society, and 'Other members trust me' measures the extent to which the participants think other members trust them. As we can see, for 'Members helpful' and 'Trust other members', the means of the quota sample are higher than the means of participants in probability sample. However, the mean of the third variable 'Member trust me' is higher in probability sample than in quota sample.

**5.14** There are two variables in the fourth section: 'Society support', which measures the society's social and emotional support, and 'Society performance', which measures the performance of society in 2012 in comparison to the previous years. The mean of 'Society support' in the quota sample was higher than the mean of probability sample.

**5.15** Similar to what we did previously, we now present the statistics for testing whether the sampling method is correlated with the selected variables at the highest response rate of 67.5% (Table 7).

Table 7: Testing the differences between the quota sample and the probability sample at the response rate of 67.5%
| ||

Item | Mann-Whitney U/chi-square | p |

Religious activities | 489 | 0.005 |

Social activities | 561 | 0.047 |

Friendship | 4.83 | 0.028 |

Society contribution | 283 | 0.026 |

Members helpful | 618 | 0.202 |

Trust other members | 711 | 0.476 |

Other members trust me | 516 | 0.275 |

Society support | 454 | 0.005 |

Society performance | 342 | 0.041 |

**5.16** To sum up, apart from the third variable in third section, the means of all variables in the quota sample are always higher than their counterparts in the probability sample. Furthermore, apart from the three variables in the third section, the means of all variables in all sections in the quota sample are significantly different from their counterparts in the probability sample.

**Discussions
**

**6.1**The present study aims to find out whether a probability sample and a quota sample would produce statistically equivalent results and to examine the impact of response rate on the results. We hypothesize that quota sampling is not able to produce results that are statistically equivalent to those produced by probability sampling and that response rate has a significant effect on any difference found; more specifically, when the response rate is high we expect that the different between the two samples will be significant and when the response rate is low, the results from the two samples tend to be similar.

**6.2** The above analyses have confirmed the first hypothesis. In most of the measured variables, the estimated means produced by probability sampling are significantly different from those produced by quota sampling (*p < *0.05). These results differ from the findings by Moser and Stuart (1953) and Cumming (1990) which suggest that quota sampling produces similar results to probability sampling. Conversely, our results are generally consistent with those by Marsh and Scarbrough (1990) who have showed that there are significant differences between the estimates of probability sampling and quota sampling.

**6.3** A possible explanation of these significant differences in this study can be related to the survey topic itself. The questionnaire used in this study measures some aspects of social capital that includes levels of involvement and social support received from the society. It is possible that people who were more satisfied with the role of the society and its activities were more interested in participating in the survey, while people who were not satisfied refused to take part. This could lead to marked bias in quota sample against people who were less satisfied with the society as they were simply replaced by other participants once they had refused. Although strict instructions were given to the assistants that they do not immediately replace people who refused without making attempts to persuade them, once the assistants enters the field there is no way to insure that the given instructions were exactly followed as the assistants' judgments of selection become the dominant guiding force. This explanation agrees with what Stephan and McCarthy (1974) concluded from their review of many empirical studies about quota sampling; that is, interviewers must be well trained and closely monitored to be able to persuade people who refuse to participate and not replace them immediately once they refuse. Otherwise, assistants' decision in selecting the respondents will be the main source of bias.

**6.4** The direction of the difference between the probability and quota sample supports the previous explanation for the significant difference between the two samples. With the exception of 'Other members trust me' variable, the means of all other variables in quota sample were significantly higher than their counterparts in the probability samples. This demonstrates that the participants in the quota sample had much higher positive perceptions about the society and were much involved in its activities than the participants in the probability sample.

**6.5** It is important to note that the results do not completely confirm the first hypothesis. The hypothesis predicts that the difference between the two samples will be significant in all variables. However, the results show that there are three variables whose means are not significantly different. It is worth pointing out that all of the three variables are from the third section which measures the level of mutual trust and support among the members generally and they are the only variables measured using Likert scale. It is difficult to ignore the similarity between the three variables while we are seeking for an explanation for this exception. A possible explanation for this exception might be that the investigated population was remarkably homogeneous regarding these three variables. High level of homogeneity means there is a good chance that any selected sample will produce similar results and there is no need to select large and probability sample to ensure representativeness. This assumption is supported by the fact that through the three comparisons made in this study no mean of these three variables is significantly different from its counterpart in the other sample.

**6.6** The results also support our hypotheses that response rate is an influential factor in the relationship between quota and probability sampling. In both sampling processes, people who were interested in the survey topic or had a personal motivation for participating in the survey would be the first people to respond, while people who were not interested in the survey topic were more likely to refuse. The main difference between the two ways of sampling is that in probability sampling three attempts were made to persuade those who refused or failed to respond to participate in the survey. If they did not respond, they would be counted in the rate of nonresponse which determines whether the obtained data should be weighted to achieve representativeness. However, in quota sampling these people were simply replaced with people who were willing to participate and were more likely to have different opinions of the society from those who were unwilling to participate. Therefore, if the probability sampling failed to achieve high rate of response, or if the interviewer immediately replaced people who are unwilling to participate, the respondents in both samples would be biased toward people who were interested and had personal interest in participating. The comparison between the quota sample and the first group in probability sample indicates that there was no significant difference between the two samples in most variables. After we included the people who responded after receiving the first reminder (the second group) the difference between the two samples in some variables became larger but remained statistically insignificant. However, when the all participants in the probability sample were included in the comparison (the third group in the probability sample with the highest response rate), all variables, with the exception of the three variables in the third section, became significantly different from their counterparts in the quota sample.

**6.7** This can be explained with logic that the first group of respondents in the two samples tended to be people who are interested in the survey topic. It can be assumed that those people had positive perceptions about the society tended to respond positively. However, when the reminders were sent, people who were less interested or those who had negative perceptions started to respond, which changed the means of the probability sample to became significantly different from the means of the quota samples. This assumption can be supported by the fact that most of the means in the first group of probability sample were much higher than their counterparts in the second group of probability sample, and the same relation existed between the second and the third groups in the probability sample. This means that people who responded later had less positive perceptions about the society which changed the means of the probability sample to become significantly different from the quota sample.

**6.8** Furthermore, we can examine the connection of response rate with the differences of sample means by using the effect size measure *r *(Rosenthal 1994: 232-3):

*t*= -3.021,

*p*< 0.05,

*r*= 0.6), which indicates large significant difference between the two means. However, when the response rate decreases to 22.5%, the difference is not significant anymore (

*t =*-.239,

*p*> 0.05,

*r*= 0.03), which indicates that the two means were almost identical. At the level of 42.5% response rate, the difference increased but under the level of significant (

*t =*-1.961,

*p*> 0.05,

*r*= 0.24), indicating that the difference between the two means is medium but still not significant. Similarly, for the 'Social activity' variable, the two means were also significantly different at level 67.5% of response rate (

*t*= -2.198,

*p*< 0.05,

*r*= 0.24). However, at level 22.5% of response, the difference was not significant and the size effect was smaller than the one at level 67.5% of response (

*t =*-.659,

*p*> 0.05,

*r*= 0.21). At the level of 42.5% of response the difference was increased but under the level of significant (

*t =*-1.120,

*p*> 0.05,

*r*= 0.23). In another word,

*the higher the response rate is, the more different the two means are*. We think this is an interesting and important finding.

**Conclusion
**

**7.1**Overall, these findings demonstrate that quota sampling cannot be regarded as an acceptable alternative to probability sampling. The findings have confirmed that quota sampling tends to be biased toward people who are willing, easily accessible and interested in the research topic. Thus, quota sampling is not able to produce representative samples similar to the one produced by probability sampling. However, in the light of the decreasing rate of response and the increasing costs of probability sampling, the findings empirically demonstrate that more significant differences emerged between quota and random sampling when greater efforts were made to increase the response rate of the random sample; that is, probability sampling has no advantage over quota sampling when the response rate is slow (such as between 20% to 30%) . In some previous studies this was given as an assumption but was not proven empirically. In short , quota sampling might be an acceptable alternative or 'second best' when it is impossible to achieve high response rate in probability sampling, but survey researchers must note that the lack of significant differences between the results obtained from the two types of sample do not necessarily mean that these results were identical.

**Appendix. Questionnaire used in the experiment
**

**Note: In order to keep confidentiality, the name of the society and other possibly revealing information has been concealed.**

How often do you attend religious services conducted by this Society? (Religious services include all type of prayers.)

- Every day.
- More than once a week.
- Once a week.
- At least once a month.
- Less often.
- Never

- Always.
- Usually.
- Sometimes.
- Rarely.
- Never

I should be very careful 0 1 2 3 4 5 Most members of the society can be completely trusted

In general, would you say that most members of this Society completely trust you or they try to be very careful when they deal with you? Answer on a score of 0 to 5

They try to be very careful 0 1 2 3 4 5
They completely trust me when they deal with me

In general, would you say that most of the members of this Society try to be helpful or that they are mostly looking out for themselves. Answer on a score of 0 to 5

Mostly looking out for themselves 0 1 2 3 4 5
Most of them try to be helpful

Do you have a friend who is a member of this society with whom you can discuss intimate and personal matters?

- Yes (If yes, please answer the next question)
- No (If no, please choose 'I do not have one' in the next question)

- 100%
- 75%
- 50%
- 25%
- 00%
- I do not have one

- 100%
- 75%
- 50%
- 25%
- 00%

- Very good
- Good
- Normal
- Poor
- Very poor

- Male
- Female

- School Student
- Undergraduate
- Master
- PhD
- Higher
- Not a student

- 17 or younger
- 18-22
- 23-29
- 30-39
- 40-49
- 50-59
- 60 or older

- Yes
- No

## References

BRICK, M. (2011) 'The Future of Survey Sampling',*Public Opinion Quarterly*(Special Issue) 75(5), p.872-888. [doi://dx.doi.org/10.1093/poq/nfr045]

BRINSKY, A. (2006) 'American Public Opinion in the 1930s and 1940s: The Analysis of Quota-Controlled Sample Survey Data', *The Public Opinion Quarterly* 70(4), p.499-529. [doi://dx.doi.org/10.1093/poq/nfl021]

BRYMAN, A. (2008) *Social Research Method*. London and New York: Oxford University Press.

COCHRAN, W. (1964) *Sampling Techniques*. New York: Wiley.

CUMMING, R. (1990) 'Is probability Sampling Always Better? A Comparison of Results from a Quota and Probability Sample Survey', *Community Health Studies* 14(2), p.132-137. [doi://dx.doi.org/10.1111/j.1753-6405.1990.tb00033.x]

CURTIN, R., PRESSER, S. and SINGER, S. (2005) 'Changes in Telephone Survey Nonresponse over the Past Quarter Century', *Public Opinion Quarterly* 69 (1), p.87-98. [doi://dx.doi.org/10.1093/poq/nfi002]

GODAMBE, V. (1966) 'A New Approach to Sampling from Finite Populations. II. Distribution-Free Sufficiency', *Journal of the Royal Statistical Society Series B (Methodological)* 28, p.320-28.

GROVES, R. (1989) *Survey Errors and Survey Cost.* Hoboken, New Jersey: John Wiley & Sons. [doi://dx.doi.org/10.1002/0471725277]

GROVES, R. (2006) 'Nonresponse Rates and Nonresponse Bias in Household Surveys', *Public Opinion Quarterly* 70(5), p.646-675. [doi://dx.doi.org/10.1093/poq/nfl033]

GROVES, R. M., & COUPER, M. P. (1998) *Nonresponse in Household Interview Surveys*. New York: John Wiley & Sons. [doi://dx.doi.org/10.1002/9781118490082]

GROVES, R. M., DILLMAN, D. A., ELTINGE, J. L., & LITTLE, R. J. A. (Eds.) (2002) *Survey Nonresponse*. New York: John Wiley & Sons.

GROVES, R., PRESSER, S., and DIKE, S. (2004) 'The Role of Topic Interest in Survey Participation Decisions', *Public Opinion Quarterly* 68(1) p.2-31. [doi://dx.doi.org/10.1093/poq/nfh002]

HECKATHORN, D. (1997) 'Respondent-Driven Sampling: A New Approach to the Study of Hidden Populations', *Social Problems* 44, p.174-99. [doi://dx.doi.org/10.2307/3096941]

HOLT, D. and SMITH, T. (1979) 'Post-Stratification', *Journal of the Royal Statistical Society Series A *142, p.33-46. [doi://dx.doi.org/10.2307/2344652]

JACOBY, J. and HANDLIN, A.H. (1991) 'Non-probability designs for litigation surveys', *The Trademark Reporter* 81, p.169-179.

KRUSKAL, W. and MOSTELLER, F. (1980) 'Representative Sampling IV: The History of the Concept in Statistics, 1895-1939', *International Statistical Review* 48, p.169-95. [doi://dx.doi.org/10.2307/1403151]

LAVALLEE, P. (2007) *Indirect Sampling.* New York: Springer. [doi://dx.doi.org/10.1007/978-0-387-70782-2]

LEVY, P. and LEMESHOW, S. (1999) *Sampling of Populations: Methods and Applications.* New York: John Wiley & Sons.

LOHR, S. L. (2010) *Sampling: Design and Analysis.* CA: Duxbury Press.

MARSH, C. and SCARBROUGH, E. (1990) 'Testing nine hypotheses about quota sampling', *Journal of Market Research Society (JMRS) 32(4), p.485-506.*

*
MOSER, C.A. and STUART, A. (1953) 'An experimental study of Quota Sampling' Journal of the Royal Statistical Society Series A 116(4), p.349-405. [doi://dx.doi.org/10.2307/2343021]*

*
NEUMAN, W. (2011) Social Research Method. Pearson, 7th Edition.*

*
NEYMAN, J. (1934) 'On the Two Different Aspects of the Representative Method: The Method of Stratified Sampling and the Method of Purposive Selection', Journal of the Royal Statistical Society 97, p.558-625. [doi://dx.doi.org/10.2307/2342192]*

*
PEARSON, K., & FILON, L. N. G. (1897) 'On the probable errors of frequency constants and on the influence of random selection on variation and correlation', Proceedings of the Royal Society of London, 62, p.173-176. [doi://dx.doi.org/10.1098/rspl.1897.0091]*

*
PEARSON, K. (1990) 'On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling'. Philosophical Magazine 50, p.157-175. [doi://dx.doi.org/10.1080/14786440009463897]*

*
RAO, P. (2000) Sampling Methodologies with Applications, USA: Chapman & Hall. [doi://dx.doi.org/10.1201/9781420057614]*

*
ROSENTHAL, R. (1994) 'Parametric Measures of Effect Size', p.231-243 in Harris M. Cooper, Larry V. Hedges (eds.), The Handbook of Research Synthesis, Russell Sage Foundation.*

*
ROYALL, R. (1970) 'On Finite Population Sampling Theory under Certain Linear Regression Models', Biometrika 57, p.377-87. [doi://dx.doi.org/10.1093/biomet/57.2.377]*

*
SINGLETON, R. and STRAITS, B. (1999) Approaches to Social Research, 3rd edition. New York: Oxford University Press.*

*
STEPHAN, F. and MCCARTHY, P. (1974) Sampling Opinions: An Analysis of Survey Procedure,2nd edition. New York: Wiley.*

*
SUDMAN, S. (1966) 'Probability Sampling with Quotas', American Statistical Association Journal 20, p.749-71. [doi://dx.doi.org/10.1080/01621459.1966.10480903]*

*
THOMPSON, S. (2012) Sampling, 3rd Edition. New York: Willey-Blackwell. [doi://dx.doi.org/10.1002/9781118162934]*

*
THOMPSON, S. and SEBER, G. (1996) Adaptive Sampling. New York: Wiley.*

*
*