AP PSYCHOLOGY: UNIT I Introductory Psychology: Statistical Analysis The use of mathematics to organize, summarize and interpret numerical data

PART ONE Statistical Analysis: The Basics on Distributions

Analysis: The Basics on Distributions Frequency Distribution  A table or graph that shows how often different numbers or scores appear in a particular set of scores Histogram  A bar graph that shows a frequency distribution Polygon  A line graph that shows a frequency distribution

Analysis: The Basics on Distributions Glasses of H2O # of People Frequency Distribution Histogram Polygon

Analysis: The Basics on Distributions The Normal (Bell) Curve  A special frequency polygon in which the scores are symmetrically distributed around the mean Mean, median and mode Used as a guideline for intelligence, height, weight, etc.

Analysis: The Basics on Distributions Positively Skewed Distribution  Scores are concentrated at the low end of the distribution Negatively Skewed Distribution  Scores are concentrated at the high end of the distribution Bimodal Distribution  Frequency distribution in which there are two high points rather than one

The height of hobbits The height of NBA players

PART TWO Statistical Analysis: Descriptive Statistics Descriptive statistics are used to organize and summarize data Key Descriptive Statistics 1.Central Tendency 2.Variability 3.(Correlation Coefficient)

Analysis: Descriptive Statistics WHY is the description of data important?

Analysis: Descriptive Statistics Measures of Central Tendency  Mean  The arithmetic average of ALL scores in a distribution  (Impacted by outliers)  Median  The middle score in an ordered distribution of scores; the 50 th percentile  (Not impacted by outliers)  Mode  The most frequent score in a distribution of scores  (Not impacted by outliers) Numbers that best represent the most typical score of a frequency distribution

AliBenCarolSaraEvanGregHalIngaJayMary Outliers IMPACT the mean! Mean IQ Score (114.6) Median IQ Score (101 ) Outliers IMPACT the mean!

Analysis: Descriptive Statistics Measures of Variability  Range  The difference between the highest & lowest scores in a distribution  Standard Deviation  The measure of the average difference between each of the values in a data set (If the scores are clustered around a central point, the measures of variability will be SMALLER…) Refers to how much the scores in a data set vary from each other and from the mean

Scores are clustered around a central point; smaller range and standard deviation Scores are more spread out and NOT clustered around a central point; larger range and standard deviation

Standard Deviation in Action

1SD 68.3% of population Standard Deviation in Action

2 SD 95.4% of population

PART THREE Statistical Analysis: Inferential Statistics “Is there a difference between the means of the two samples?” “Are these results statistically significant?” If we have results from two (or more) samples, we can ask…

Analysis: Inferential Statistics Inferential Statistics  Statistical analysis of two (or more) sets of data to: 1. Reduce the possibility of error in measurement 2. Determine if the differences between the data sets are greater than chance variation would predict  Inferential statistics look for statistical significance  A statistical statement of how likely it is that an obtained result occurred by chance A t-test is used to determine whether two means are significantly different; yields a p-value

Analysis: Inferential Statistics p-value  A measure of confidence in the observed difference  Allows researchers to determine the probability that the difference was due to chance  A p-value of LESS than 0.05 (<o.05) is the common criterion for statistical significance  Translation The probability that the results are due to chance alone is less than 5 times out of 100 One can be 95% certain that the results are real and not due to chance alone