Download Chapter 2 - AP Psychology

STATISTICS
STATISTICS
• Statistics: The use of math to describe,
summarize, and interpret numerical data from
research.
• 2 Types of Statistics:
1. Descriptive: used to describe and summarize
research data
2. Inferential: used to interpret data and infer
conclusions from research data
DESCRIPTIVE STATISTICS
(DESCRIBE & SUMMARIZE)
Measures of Central Tendency
• Median: the middle score of a distribution
• Mean: the average score of a distribution
• Mode: the score that appears most frequent in a
distribution
• Bimodal- more than 1 mode
DESCRIPTIVE STATISTICS
(DESCRIBE & SUMMARIZE)
Measures of Variation/Dispersion
• Range: the difference between the
highest and lowest scores in a
distribution
• Standard Deviation: how much a
score varies from the mean
• Variance: how far a set of scores are
spread out
• SD²
DESCRIPTIVE STATISTICS
(DESCRIBE & SUMMARIZE)
Graphing Data
• Frequency Distribution: An orderly arrangement
of scores indicating the frequency of each score
or group of scores.
• Used to summarize research data
• Used to make a graph
• Y-axis: frequency
• X-axis: data measure
DESCRIPTIVE STATISTICS
(DESCRIBE & SUMMARIZE)
• Histogram: a bar graph
that presents data
from a frequency
distribution
DESCRIPTIVE STATISTICS
(DESCRIBE & SUMMARIZE)
• Frequency Polygon: a
line graph that presents
data from a frequency
distribution
• Conversion of
histogram into
frequency polygon
DESCRIPTIVE STATISTICS
(DESCRIBE & SUMMARIZE)
Types of Distributions
1. Normal: a symmetrical,
bell-shaped distribution
2. Positive: an asymmetrical,
skewed distribution
3. Negative: an asymmetrical,
skewed distribution
DESCRIPTIVE STATISTICS
(DESCRIBE & SUMMARIZE)
Normal Distribution
Remember
this:
68-95-99
Mean, median, and mode are the same or VERY similar
DESCRIPTIVE STATISTICS
(DESCRIBE & SUMMARIZE)
Standard Score
• Z-Score: the number of standard deviations away
from the mean for a particular score
• -z = scores below the mean
• +z = scores above the mean
• Z=X-M/SD
DESCRIPTIVE STATISTICS
(DESCRIBE & SUMMARIZE)
Percentile Score
• Percentile: the distance of a score from zero
• Measure of relative position for comparable scores
• Indicates what percent of people scored below and
above a given score
• Each 25% is known as a quartile
DESCRIPTIVE STATISTICS
(DESCRIBE & SUMMARIZE)
Skewed Distributions
• Caused by outliers
• Outliers: extreme scores
• Affect measures of central tendency
• Since the median splits your data exactly in half,
it will always fall between the mean and the
mode, regardless of whether your distribution is
positively or negatively skewed
• The mean will always be closest to the outlier
DESCRIPTIVE STATISTICS
(DESCRIBE & SUMMARIZE)
Negative Skewed Distribution
• The order of the measures of central tendency
are mean, median, mode
• Caused by an outlier with a LOW score
• Most scores are high
• Scores pile up at the high end of the scale
DESCRIPTIVE STATISTICS
(DESCRIBE & SUMMARIZE)
Positive Skewed Distribution
• The order of the measures of central tendency
are mode, median, mean
• Caused by an outlier with a HIGH score
• Most scores are low
• Scores pile up at the low end of the scale
LET’S PLAY WITH CANDY!
INFERENTIAL STATISTICS
(INTERPRET & INFER)
• Null Hypothesis (Ho): predicts no relationship
between variables
• Alternative Hypothesis (Ha): predicts a cause and
effect relationship between variables
• Chance: random
• Statistically Significant: experiment results are
NOT likely due to chance
• P-value: calculated probability used for
hypothesis testing
INFERENTIAL STATISTICS
(INTERPRET & INFER)
P-Value
• Probability that the results are due to chance
• <5/100 = <.05 = <5%
• When running inferential tests, if the results reveal a
p-value less than .05 (p<.05), we say the results are
“statistically significant”
• Another way to say it is “less than 5/100 (or 5%)
chances that the observed results are random”
• Results are NOT due to chance
INFERENTIAL STATISTICS
(INTERPRET & INFER)
Hypothesis Testing
• When the p-value is <.05 you reject the null
hypothesis because you have statistically
significant results
• When you reject the null hypothesis you accept
the alternative hypothesis
• There is a cause and effect relationship between the
IV and DV shown by the differences between the
experimental and the control groups
INFERENTIAL STATISTICS
(INTERPRET & INFER)
Making Inferences
• When the difference between the results of the
control group and experimental groups are relatively
large, we say the difference has “statistical
significance”
• This means that the difference between the two
groups did NOT happen by chance
• So there is a causal relationship between the IV and
the DV that account for the differences in the groups