AP Psychology September 2014

What is “Statistics”?  A common language for describing, organizing, and interpreting data  Aspects:  Distribution  Central Tendencies  Variation

DISTRIBUTION  Frequency of the occurrence of scores in a data set

CENTRAL TENDENCIES  A typical or representative value for a data set  Measured using …  Mean  Mathematical average  Sum of all scores divided by total number of scores  Median  Midpoint, or 50 th percentile of scores  Half of scores are above it, and half are below  Mode  Most frequently occurring scores

Caveats for Using Central Tendencies  A few atypical scores can distort the mean.  A skewed (lopsided) distribution can lead to misleading use of data

Normal Distribution  Symmetrical and bell-shaped when graphed  Mean, median, and mode are all the same

Skewed Distributions  POSITIVELY SKEWED  One or just a few HIGH scores  Data set contains more LOW scores  NEGATIVELY SKEWED  One or just a few LOW scores  Data set contains more HIGH scores

Skewed Distributions

VARIANCE  How similar or diverse the scores are in a data set  Aspects  Range  Gap between lowest and highest scores  Standard Deviation  COMPUTED measure of how much scores vary around the mean

Standard Deviation

Inferential Statistics  How do we …  make generalizations from samples?  decide if differences are significant  infer that an observed difference accurately estimates the true difference?

Inferential Statistics A difference is significant when … * the sample averages are reliable * the difference between sample averages is large An observed difference is reliable when … * the sample is representative * observations are less variable

Which of the data sets is more statistically significant? Case ACase B  The four-year science course grades of 300 graduating LPHS seniors are recorded in a study of science performance among CPS high school students.  The four-year science course grades of 3,000 graduating seniors from various CPS schools in different neighborhoods are recorded in a study of science performance among CPS high school students.

Which of the data sets is more statistically significant? Case ACase B  The average science course grades of LPHS graduating seniors is higher for females than for males. Specifically, the average course grade for females was 83%, and for males it was 70%.  The average science course grades of LPHS graduating seniors is higher for females than for males. Specifically, the average course grade for females was 83%, and for males it was 81%.

Which of the data sets is more statistically significant? Case ACase B  The average science course grades of LPHS graduating seniors is higher for females than for males. The data also show that the majority of grades for females declined from year to year throughout their four years of high school.  The average science course grades of LPHS graduating seniors is higher for females than for males. The data also show that the majority of students individually earned the same grade for all science courses they had taken.

Which of the data sets is more statistically significant? Case ACase B  A high school senior goes on a one-day college visit and has the opportunity to attend two different classes while he is there. He finds both of the instructors to be engaging and dynamic. He tells his friends that the school has “awesome teachers.”  A high school senior goes on a two-week college visit and has the opportunity to attend three different classes every day, for a total of 15 different classes. He finds 10 of the instructors to be engaging and dynamic. He tells his friends that the school has “awesome teachers.”