The Misuse of Statistics Solutions

• A non-representative sampling occurs when the sampling methods: 

  • Do not match    population parameters   
  • Do not allow everyone in a population    an equal chance of being selected   
• Misuse of statistics can occur when a researcher provides a non-representative sampling that:

  •    Ignores representative sampling methods   
  •    Possibly introduces bias and errors   

Types of Non-Representative Sampling

• Some non-probability sampling methods include:

  •    Convenience   : Researchers only sample people closest/most convenient to them.

  •    Self-Selected   : Members of the population choose to participate in the study.

  •    Small Sample   : The sample is too small to draw any valid conclusions about the population.

• Some types of non-statistical reporting include:

  •    Selective   : Only the “good” information is presented to represent what the researcher wants to show.

  •    Detached   : The statistic lacks a point of reference or basis for comparison, i.e., the “compared to what” part of the sentence is missing.

  •    Misleading Visuals   : A number or graph is shown in a way to “prove” a point, but is not representative of the population.

  •    Biased or leading    questions.

Example 5

1. Name the intended purpose of study.
2. Identify and explain the misuse of statistics.

The principal at East Middle School wanted to prove that the school’s After-the-Bell tutoring program causes an increase in student test scores. Signing up for After-the-Bell is voluntary. At the end of the school year, the principal reported: “The average test scores of After-the-Bell students increased 15%. This proves the tutoring program effectively boosts student achievement.”


1. Purpose of Study: Determine if After-the-Bell’s tutoring program   improves student test scores   .

2. Misuse:
   

   Identify	Explain
   Self-selected	Students can join the program voluntarily.
   Detached	The statement, test scores increased 15%, does not provide any basis for comparison.

Example 6

Identify and explain the misuse of statistics and suggest how to improve it.


The Start-Up Tech firm was hiring and wanted to attract more applicants. The company’s founder earns a $2 million annual salary. The three managers earn $150,000 annually. The other 30 employees earn $60,000 annually each. Start-Up Tech posted: “Come join our team! The average salary at our firm is $125,000!”


Sample: Selective. The firm used the average instead of the median, making the potential annual salary for most employees seem higher than it actually is.


Sample: The founder earns more than the combined annual salaries of 30 employees, which skews the average annual salary upward. The median annual salary should be used instead.