1. What is statistics? STATISTICS BOOT CAMP Study of the collection, organization, analysis, and interpretation of data Help us see what the unaided eye misses

2.  Descriptive Statistics:  Describe data  Help us organize bits of data into meaningful patterns and summaries  Tell us only about the sample we studied  Inferential:  Allow us to determine whether or not our findings can be applied to the larger population from which the sample was selected TWO TYPES

3. DESCRIPTIVE STATISTICS

4.  If you could have any animal in the world for a pet, what would it be?  Definition: Arrangement of data from high to low, indicating the frequency of each piece of data  Frequency polygons: illustrated frequency distribution in a line graph  Histograms: illustrated frequency distribution in a bar graph  **Frequency is always on the Y axis (vertical) FREQUENCY DISTRIBUTION

6.  Definition: a single score that represents a whole set of scores  Attempts to mark the center of a distribution  Three types: mean, median, mode  Mean: numerical average of a set of scores  Most commonly reported  Median: halfway mark in the data set, half of the scores are above and half are below  Write down numbers in ascending or descending order; find the halfway point, if there is an even number, take the average of the middle two scores  Why would we ever look at this? Extreme scores can drastically affect our mean MEASURES OF CENTRAL TENDENCY

7.  Mode: Simplest measure; The score that occurs most frequently  When is this used? Depends on research question  72% of Americans report having 0-1 drinks of alcohol per week; gov’t puts a tax on alcohol, it won’t affect most Americans  Bimodal (two modes) – better to use mode over mean/median in this case  Mean onset age for an eating disorder is 17  Two modes: peak around 14 and peak around 18  intervention program would be better suited for ages 14 and 18 than 17 MCT CONT.

8.  Mean is most commonly used measure of central tendency but can be biased by a few scores (extreme scores, outliers )  Examples:  Bill Gates walks into a coffee shop. The average income of all patrons soars. Median wealth remains unchanged.  Republicans use the average income to discuss income growth; Democrats refer to the median  19/20 of your friends have a car valued at $12,000, but another has a car valued at 120,000  Mean is 17,400  Not best measure; median is better OUTLIERS

9.  Attempt to depict the diversity of a distribution of scores  Shows us how clustered our scores are around the mean  We can be more confident in our data if there is less variability  Example: Basketball player who averages 15 pts a game  Are you more confident if their range is between 13-17 pts in first 10 games or between 5-25 pts in the first 10 games?  Range: gap between the highest and lowest score  Subtract the low score from the high score MEASURES OF VARIABILITY

10.  Standard deviation: a measure of how tightly clustered a group of scores is around their mean  Calculated by taking the square root of the variance  Both the SD and variance relate the average distance of any score in the distribution to the mean  The higher the variance and SD, the more spread out the distribution  Smaller the standard deviation, the more clustered the scores are around the mean MEASURES OF VARIABILITY: STANDARD DEVIATION

11.  How much do employees at small businesses make?  40,000  45,000  47,000  52,000  350,000  Mean = 106,800  Standard deviation = 136,021; Average difference between a score and the mean is 136,021  Discard the extreme score, SD is now 4,966.56  Distribution of first four is tightly clustered, distribution of all five is spread out STANDARD DEVIATION EXAMPLE

12.  Shows how scores are distributed in nature  Example: Height of humans  Symmetrical; Mean, median, mode are all in center  68% of all scores fall within one standard deviation of the mean; 95% within two SD NORMAL DISTRIBUTION/BELL CURVE

13.  Used to compare scores from different distributions  Can convert scores from the different distributions into z scores. Z scores measure the distance of a score from the mean in units of standard deviation  Scores below the mean have negative z scores  Scores above the mean have positive z scores  Amy scored a 72 on a test with a mean of 80 and SD of 8, her z score is -1  Clarence scored an 84 on the test, his z score is +.5 Z-SCORES

14. INFERENTIAL STATISTICS

15.  Allows us to draw inferences from our data  Sometimes sets of data can differ because of chance, not because of a real difference  When differences between data are statistically significant, the observed differences is probably not due to a chance variation between the groups  Something is considered SS, if the odds of it occurring as a result of chance are less than 5%  p =.05 INFERENTIAL STATISTICS

16.  Indicate the distance of a score from 0  90 th percentile means they scored better than 90% of the people who took the test PERCENTILES