S TATISTICAL R EASONING IN E VERYDAY L IFE

In descriptive, correlational, and experimental research, statistics are tools that help us see and interpret what the unaided eye might miss. Apply simple statistical principles to everyday reasoning.

3 D ESCRIBING D ATA A meaningful description of data is important in research. Misrepresentation may lead to incorrect conclusions.

M EASURES OF C ENTRAL T ENDENCY : A single score that represents a whole set of scores Mean: the average of a distribution Median: the middle score in a distribution; half the scores are above it and half are below it Mode: the most frequently occurring score(s) in a distribution

Measures of Variation The need to know how similar or diverse scores are. Range: the difference between the highest and lowest scores in a distribution More useful standard for measuring how much scores deviate from one another is the standard deviation Standard Deviation: a computed measure of how much scores vary around the mean score It better gauges whether scores are packed together or dispersed and shows how much individual scores differ from the mean

SD= √[( SUM OF DEVIATIONS )²/ NUMBER OF SCORES ]

Think about how scores tend to be distributed in nature: Large numbers of data often form a symmetrical, bell-shaped distribution known as a bell curve or normal curve Most scores fall near the mean (68% fall within one standard deviation of it) and fewer and fewer near the extremes Percentiles express the standing of one score relative to all other scores in a set of data. SAT score in 85 th percentile. You scored higher than 85% of other test takers.

8 M AKING I NFERENCES 1. Representative samples are better than biased samples. 2. Observations with less variation are more reliable than ones with more variation ones. I. ( an average is more reliable when it comes from scores with low variation) 3. More cases are better than fewer cases. When is an Observed Difference Reliable?

9 W HEN IS A D IFFERENCE S IGNIFICANT ? When sample averages are reliable and the difference between them is relatively large, we say the difference has statistical significance.  Alpha is the accepted probability that the result of an experiment can be attributed to chance rather than the manipulation of the independent variable.  Given that there is always the possibility that an experiment’s outcome can happen by chance, psychologists have set alpha at.05, which means than an experiment’s results will be considered statistically significant if the probability of the results happening by chance is less than 5%.