What is statistics?

STATISTICS BOOT CAMP

Study of the collection, organization, analysis, and interpretation of data

Help us see what the unaided eye misses

Descriptive Statistics: Describe dataHelp us organize bits of data into meaningful patterns and summaries

Tell us only about the sample we studiedInferential:

Allow us to determine whether or not our findings can be applied to the larger population from which the sample was selected

TWO TYPES

DESCRIPTIVE STATISTICS

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

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

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.

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

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 variabilityExample: 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

Standard deviation: a measure of how tightly clustered a group of scores is around their meanCalculated 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 meanThe 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

How much do employees at small businesses make? 40,000 45,000 47,000 52,000 350,000

Mean = 106,800Standard deviation = 136,021; Average diff erence

between a score and the mean is 136,021Discard the extreme score, SD is now 4,966.56Distribution of fi rst four is tightly clustered,

distribution of all five is spread out

STANDARD DEVIATION EXAMPLE

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

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 scoresScores above the mean have positive z scoresAmy scored a 72 on a test with a mean of 80 and

SD of 8, her z score is -1Clarence scored an 84 on the test, his z score is

+.5

Z-SCORES

INFERENTIAL STATISTICS

Allows us to draw inferences from our data Sometimes sets of data can differ because of

chance, not because of a real differenceWhen 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

Indicate the distance of a score from 0 90th percentile means they scored

better than 90% of the people who took the test

PERCENTILES