OT 781 - Hypothesis Testing

Hypothesis

A way for quantitative researchers to demonstrate the probability that what happened in their sample will likely happen in the population

Probability

A foundational concept in statistics and can be used to understand how well our sample aligns with the population. Target or Favorable Outcome divided by total number of outcomes.

Hypothesis Testing Steps

• Make an educated assumption/guess about the population

• State the hypothesis; use the hypothesis to predict the characteristics of the population

• Draw a random sample from the population

• Test the sample (make observations) to see if assumptions are true

• Draw a conclusion based on observations

• Make inferences about population based on sample observations

Null (Statistical) Hypothesis

• There is NO difference or relationship/association between x and y

• H0 : x = y

• Researchers goal typically is to reject null hypothesis

• Null hypothesis is not stated in writing

Alternate Hypothesis

• There is a difference or relationship/association between x and y

• HA : x ≠ y, which means x < y or x > y

• Researchers goal typically is to accept the alternate hypothesis

Directional (Alternate) Hypothesis 

• Researcher hypothesizes there is a difference, but does not say / predict which way the difference is:
  • HA : x ≠ y
  • Uses two-tailed test in statistics

Type I (Alpha α) Error [False Positive-Exaggerates the findings]

• Researcher rejects a null hypothesis that is actually true

• Concludes that a there is a difference (or association) between the groups (based on the sample) when in fact there is no difference (or association) between the two population groups.

• Usually happens through sampling error

Type II (Beta β) Error [False Negative- Underestimates the findings]

• Researcher fails to reject a null hypothesis that is really false.

• Concludes that there is NO difference (or association) between the groups (based on the sample) when in fact there is a difference (or association) between the two population groups

• Usually happens due to small sample in the study