Examples of Statistical Inference

Influence of Teacher Reputation on Rating

From onlinestatbook

Questions:
  • Does an instructor’s prior reputation affect student rating?
  • Does the size of this effect depend on student characteristics?
Experimental Design:
  • subjects viewed video of a lecture of a teacher after reading an evaluation of the instructor, then they rated the instructor.
  • subjects where randomly assigned two conditions: Charismatic (reading a good evaluation), Punitive (reading a bad review of the instructor)
Descriptive Statistics:
  • Boxplot showing the student rating vs the two conditions. Ratings seem higher for the charismatic teacher.
  • N, Mean, Median, Skewness, Kurtosis etc are calculated for both conditions
Inferential Statistics:

  • Independent samples t-test used to test the differences. The result is significant, supporting the conclusion that instructor reputation affects ratings.

  • Assumptions:
    • Each score is sampled independently and randomly: Ok, as the students are randomly assigned to a condition.
    • Normal distribution of the scores within each condition: Violated to a moderate degree because of the skewness.

    They assessed that this was not important using the data analysis lab. - Equality of variance between the two populations: Ok

Mediterranean Diet and Health

From onlinestatbook

Question:
  • Is a mediterranean diet healthier than a diet with high-saturated fat?
Experimental Design:
  • 605 survivors of a heart attack assigned to either the AHA diet or the Mediterranean diet
  • Over a 4 year period, patients following the Mediterranean diet were seen initially, then after two months, then once a year to check observance.
  • The other group was assumed to follow the diet.
  • Information was collected on number of deaths from cardiovascular causes, non fatal heart-related episodes and tumors.
Descriptive Statistics:
  • Histogram, frequencies tables. 20% of the AHA diet patients had at least one illness, compared to 10% on the Mediterranean.
Inferential Statistics:
  • A Chi-Square test can be used to check if there is a relationship between diet and outcome..
  • Conclusion that outcome is related to diet and that Mediterranean diet is superior to the AHA diet.

Who is buying iMacs

From onlinestatbook

Question:
  • Are the buyers of the latest Mac new buyers, or did they previously have a Mac product
Experimental design:
  • They asked 500 of the new Mac purchasers if they owned or had owned a Mac
Results:
  • 83 new computer owners, 60 who had a Windows computer, 357 who had owned a Mac
  • Proportion of first time computer owners = 0.167.
  • The 95% confidence interval on the proportion is calculated ( 0.13<CI<.20 ) therefore, it is likely that between 13% and 20% of new Mac buyers are first time computer owners.
Assumptions:
  • No reason seen that would violate the assumptions of normality or independence.
Epilog:
  • After one year, Apple reports that 1/3 of new buyers are first time computer buyers. This is outside the CI range. Is this a sampling error ? Other factors?