Intro to Psychology Statistics Supplement

Descriptive Statistics: used to describe different aspects of numerical data; used only to describe the sample. Includes measures of central tendency, variability, and correlation Inferential Statistics: uses probability theory to allow researchers to generalize and predict results of the population outside of the sample; used to determine whether or not a hypothesis is supported or rejected Can make inferences about a population from a sample Can compare multiple groups to each other (i.e. experimental and control)

Statistics Supplement Measures of central tendency Mean Median Mode Variability Range Standard Deviation

Statistics Supplement Normal Distribution – the “bell curve”

Statistics Supplement

Many things are normally distributed: Intelligence Scores [(Mental Age) / (Chronological Age)] x 100 = IQ  Mean IQ = 100  Std. dev = 15 IQ over 130 is exceptionally smart IQ under 70 is one criteria for Intellectual Disability

Statistics Supplement We use assumptions about the normal distribution in order to determine if data collected comply with a known distribution or are significantly different You can also compare a single score to a population distribution to see how rare it is Percentiles and standardized tests

Statistics Supplement SAT v. ACT SAT Mean = 1026 SD = 209 ACT Mean = 20.8 SD = 4.8 Which is better, getting a 1277 on the SAT or a 28 on the ACT?

Statistics Supplement Correlation & Regression Correlation coefficient R describes the strength and direction of the relationship between two observed variables -1≤ r ≤ 1 -1 being a perfect negative correlation +1 being a perfect positive correlation 0 represents no relationship Linear Regression equations draw an imaginary line through the data cluster; the slope and intercept of the line is used to predict future values based on previous data Expressed as y = mx + b

Statistics Supplement

Just because something has a strong correlation doesn’t mean there is a cause/effect relationship Many statistics can be misleading if you don’t pay close attention

Statistics Supplement Inferential statistics Determine whether a sample of data is due to chance responding or due to a meaningful trend Can compare two or more groups Can compare a group to a known norm Can compare longitudinal data from the same group

Statistics Supplement Statistical Significance Statistical Significance is achieved when the probability of getting a specific set of data by chance is extremely slim  Typically, this probability is less than.05 or 5%  IF the groups were the same, THEN the probability of getting that sample by chance would be very unlikely. Therefore, the researcher concludes that the groups are (probably) not the same.  Because of the way statistics tests work, a researcher can never “prove” anything. They can only demonstrate how probable or improbable a certain event is.  If someone claims they have “proven” anything, don’t trust them.

Statistics Supplement Power Statistical power is the ability to correctly detect an effect if one exists Power is effected by: Sample size Reliability and validity of measures Within vs. between participants designs Effect size of the treatment

Statistics Supplement Type I Error: False Positive The researcher incorrectly determines that there is an effect when in reality none exists The probability of a Type I error is α α is determined by the researcher based on how bad implications for a false positive would be Type II Error: False Negative The researcher incorrectly determines that there is not effect when in reality there is an effect The probability of a Type II error is β β can be reduced by increasing Power

Statistics Supplement While researchers want to find statistically significant differences between their groups, just because something is “statistically significant” doesn’t mean that it is practically significant. Studies with very large sample sizes can detect tiny differences that may not be meaningful

Statistics Supplement Be a thoughtful consumer of science Ask: How big was the sample? What was the effect size? Was the sample representative of the population? Did they use random assignment? Did they have an appropriate control group? Were the measures reliable and valid? Was the study blind/double-blind?