Question

To find out if wealthier people are happier we collect data from 50 people about their income and their overall happiness on a scale from 1 to 10. The correlation coefficient comes out to be -0.25. Given that r=0.025 which means this is a weak negative correlation. In terms of strength, we can conclude that the correlation between income and happiness is moderate. In terms of direction, there is a negative correlation between happiness and income.  If we increase the number of subjects in the study to 1000 the errors will increase therefore we may not obtain the desired correlation. It is important to select data randomly because randomly selected data are biased free and give us an unbiased estimator for the population. Consider an example of students interested in a youth festival in a school. If we collect considered statistics class as a sample and get data from all the students this will not be a representative of the population here which is the school.

This is the response I received from my instructor:

Your description of the correlation coefficient was correct overall. Remember that it ranges from -1 to +1 and the closer it is to 0 the weaker it is, and the closer it is to 1 the stronger it is. As a result, if you have a correlation coefficient of -0.25, it would be closer to 0 than 1, which would imply it's relatively weak, although moderate is the word you used. It's not always clear how strong or weak, however, as there aren't definitive cut-offs to determine that. There's another consideration regarding sample size in that as you have a smaller size, there's the chance that the subjects who volunteer for studies have their own inherent reasons for volunteering. In most studies, subjects are volunteers and are therefore a very select group that usually has an interest in the subject or have a reason to participate. In other words, it seems that having a biased sample is almost inevitable as most studies require that subjects volunteer on their own. What does that say about the validity of the research experiments in which subjects volunteer for them - should researchers attempt to eliminate this option? How??

Please help with what he is asking.

What does that say about the validity of the research experiments in which subjects volunteer for them - should researchers attempt to eliminate this option? How??

What does that say about the validity of the research experiments in which subjects volunteer for them - should researchers attempt to eliminate this option? How??

this is the question and I don't know how to answer it

Answer 1

Volunteer Bias, sometimes referred to as Consent Bias is very much a reality in research experiments of almost every nature, and becomes more critical when it pertains to critical decision parameters including socio-economic measures, medical research etc. It is generally used to mean that the participants do not represent the population, and therefore could lead to under or overestimation of the research parameters, whether qualitative or quantitative.

It is generally difficult to estimate the impact of volunteer bias and the direction of its effect. Volunteers tend to be more educated, come from high social class and more approval motivated. It might be the case that non-response is due to apathy or misconception than to principled objection or confidentiality issues, thus leading to a systematic loss of people with differing opinions or infographics towards the study. Hence, making it even more difficult to identify which subsets of the population are not proportionally represented in the study.

Measures to counter this effect would generally imply increasing the effort and cost behind the research. Hence there is always a tradeoff between these two, though in general no amount of statistical manipulation can remedy poor data. That is to say, there are no direct, fool-proof methods to counter this bias, though systematic and cost increasing measures can be suggested based on type of study. Perhaps the most feasible, yet counter intuitive method would be directed sampling; reaching out to certain communities or subsets who seem left out through proper channels, bypassing the volunteering paradigm itself. In studies where confidentiality seems to be a deciding factor towards volunteering, ensuring anonymity might increase participation and decrease volunteer bias. Towards the opposite spectrum, in cases where direct data is available, permission to access the same without consent might be the best recourse, when it is evident that a low response rate would compromise the validity of research.