It's not just laymen. Many experts express doubts in the manner in which certain statistics are developed or presented.
The most likely cause for biased statistics is the person or organization has a self interest in obtaining certain results. The manner in which subjective statistics are developed may include:
a) Excluding some information. For example, a survey of 1,000 people shows a slight preference to brand A over brand B, but if we just take the first two days of the survey, Brand B is better, so if our company produces brand B, we take the first two days.
b) Unfair comparisons. For example, I want to show that my new fertilizer is better than all others. I fertilize my corn plant with brand A which is specially prepared for vegetables, and in the comparison plot, I use brand B, which is for lawns. I can claim that my product beat out the most commonly used fertilizer.
c) Unrealistic Assumptions. See attached link. Scientists conducted a study of Florida panthers and concluded that the restricted area was not a problem. However, they only considered day time activity, while it is a well known fact, that panthers are more active at night.
d) Surveys with loaded questions: For example, the question, Given that 40% of all accidents are alcohol related and laws are not being enforced for lack of manpower, do you think we need more policemen? Question is put in a fashion to steer respondent in one direction.
e) Biased presentations= Many examples are available. In fact there's a book on how to lie with graphs.
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Laypeople may have a distrust of statistics due to various reasons. One possibility is the complexity and technicality involved in statistical analysis and interpretation that may be difficult for them to understand. Additionally, the misuse or misrepresentation of statistics by media or certain individuals can contribute to skepticism. Finally, people may have personal biases or preconceived notions that make them skeptical of statistical data.
Two syllables in distrust (dis-trust)
Paranoia
There are two types of statistics. One is called descriptive statistics and the other is inferential statistics. Descriptive statistics is when you use numbers. Inferential statistics is when you draw conclusions or make predictions.
Psychological statistics is the application of statistics to psychology.
The statistics (pl.) indicate that statistics (sing.) is a pseudo-science.