I meet many clients who worry about sample size trying to ensure they get an enough large sample so that statistically significant differences can be found and inferences to a larger population can be made, but they often don’t know that these statistical tests were meant to work within the probability sampling theory framework.
Since the advent of online panels and the increase of online surveys using panel-provided samples, the issue of testing for significant differences using standard parametric tests has become a moot point in many research studies.
Nowadays many of the surveys conducted online use samples provided by online panels, but these are mostly convenience samples (non-probability). The populations of online panels include respondents who are willing to participate in studies, excluding those unwilling to be part of the panel who may be members of the target population we are after.
In probability sampling, each possible respondent from the target population has a known probability to be chosen. Probability sampling helps us to avoid some of the selection biases that can make a sample not representative of the target population. For more on this read Does A Large Sample Size Guarantee A Representative Sample?
A single probability sample doesn’t guarantee to be representative of a target population, but we can quantify how often samples will meet some criterion of representativeness. This is the notion behind confidence intervals. The probability sampling procedure guarantees that each unit in the population of interest could appear in the sample.
By taking into account all possible random samples that can be taken from a population, we can estimate how often the true value of an estimate can be expected to be within a specific range of values. So, when we talk about a 95% confidence interval, this really means that the true value of a particular variable is expected to fall within an interval of values 95 out of 100 times we repeat the procedure. When an opinion poll indicates that 50% of people are in favor of a political decision with a +/-3% margin of error at a 95% confidence interval, it is really saying that we can expect that between 47% and 53% of people will be in favor of the decision 95 out 100 times, if we were to repeat the poll. When we test for significant differences, we are looking to see if the value falls outside that range.
Unfortunately, taking a probability sample is hard and costly. For most consumer research studies and social behavior studies, we really don’t know the size of the actual population of consumers behaving in certain ways or consuming certain products, and trying to find out would make the research prohibitively expensive. This is why we often have to settle for convenience samples like the ones offered by online panels. They still can offer valuable insights if designed with care, but again doing statistical testing in a convenience sample is pointless since the assumptions about probability sampling are violated.
Online panels are here to stay, and they will continue to be a source for affordable sample for market research. Research using convenience sample is often better than not research at all if the survey is well designed and screening criteria are used to define the target population.
A more appropriate case for testing statistically significant differences are random samples taken from a customer database, since this is essentially the population frame where we can count all members and estimate their probability to be chosen.
However, if you don’t have a customer database or are interested in surveying non-customers, then use a convenience sample, if that is what your research budget can afford or there is no other way to get to the actual population frame (list to pull the sample from), but don’t fret about testing for significant differences. You may feel more confidence if you are able to replicate the results in repeated surveys, but be always cautious about inferences made from convenience samples since there could be a hidden systematic bias in the data.
It is always important that whenever you use convenience samples you consider the following when analyzing the results:
1. Who is systematically excluded from the sample?
2. What groups are over- or underrepresented in the sample?
3. Have the results been replicated with different samples and data collection methods?
If testing for significant difference gives you peace of mind, even when using convenience samples, do it to confirm the “direction” of the data, but restrain yourself from doing inferences to a larger population.