Transcript Stats

Essential Questions
• EQ 1-5: How do psychologists draw
appropriate conclusions about behavior
from research?
Do Now:
• Take the 3 handouts, and go over your
homework with your table. Make sure you
all agree on the answers!
Growth
of
Psych
Approaches
to Psych
Careers
The Science of
Psychology
Ethics
Research
Statistics
Methods
Sampling
Descriptive
Correlation
Naturalistic
Observation
Case
Study
Survey
Experiment
Descriptive
Central
Tendency
Inferential
Variance
We
are
here
Why do we need statistics in
psych?!
• Descriptive Statistics:
– Central Tendency
• Mean, median, and mode
• skewed distributions
– Variance
• Range
• standard deviation
• normal distributions
• Inferential Statistics:
– Statistical significance
• t-test and the p-value
Statistical procedures analyze and interpret data
and let us see what the unaided eye misses.
Central Tendency
• Tendency of scores to congregate around
some middle variable
• A measure of central tendency identifies
what is average or typical in a data set
Measures of Central Tendency
Mode: The most frequently occurring score
in a distribution.
Mean: The arithmetic average of scores in a
distribution obtained by adding the
scores and then dividing by their
number.
Median: The middle score in a rank-ordered
distribution.
Practice:
What is the mean, median, & mode of the
following distribution:
1, 6, 3, 12, 8, 11, 9, 10, 4, 6
Normal Distributions
•The distribution of data also gives us key info.
•We know that many human attributes…
•e.g height, weight, task skill, reaction time,
anxiousness, personality characteristics, test
data, attitudes, birthdays, etc.
•…follow a normal distribution.
Practice:
• Imagine that you are a golfer of aboveaverage ability and that you have the
opportunity to play the greatest golfer in the
world (say Tiger Woods). If you want to
maximize your slim chance of winning,
how much golf would you elect to play,
given the choices of 1, 18, 36, or 72 holes?
• A certain town is served by two hospitals. In the larger
hospital about 45 babies are born each day, and in the
smaller hospital about 15 babies are born each day.
Although the overall proportion of boys is about 50
percent, the actual proportion at either hospital may be
greater or less than 50 percent on any day. At the end
of a year, which hospital will have the greater number
of days on which more than 60 percent of the babies
born were boys?
• (a) the larger hospital
• (b) the smaller hospital
• (c) neither--the number of days will be about the same
(within 5 percent of each other)
Negatively Skewed
Positively Skewed
Let’s look at the salaries
of the employees at
Dunder Mifflen Paper in
Scranton:
$25,000-Pam
$25,000- Kevin
$25,000- Angela
$80,000- Jim
$100,000- Andy
$100,000- Dwight
$300,000-Michael
The median salary looks good at
$80,000.
The mean salary also looks good at
about $93,500.
But the mode salary is only $25,000.
Maybe not the best place to work.
Then again living in Scranton is kind of
cheap.
Central Tendency
The mean doesn’t work in a
skewed distribution
The Median is much better
• Descriptive Statistics:
– Central Tendency
• Mean, median, and mode
• skewed distributions
– Variance
• Range
• standard deviation
• normal distributions
• Inferential Statistics:
– Statistical significance
• t-test and the p-value
Two Measures of Variation
Range: The difference between the highest and
lowest scores in a distribution.
7, 98, 46, 38, 54, 78, 9, 5, 45, 23
18
• Standard Deviation:
the variance of scores
around the mean.
• The higher the
variance or SD, the
more spread out the
distribution is.
• Do scientists want a
big or small SD?
Shaq and Kobe may
both score 30 ppg
(same mean).
But their SDs are
very different.
Normal Distribution
21
Standard Deviation in Action
• A couple needs to be within one standard
deviation of each other in intelligence (10 points
in either direction). —Neil Clark Warren, founder
of eHarmony.com
Normal Distribution
Practice Prob:
• What is the standard deviation for the
numbers: 75, 83, 96, 100, 121, and 125?
• Descriptive Statistics:
– Central Tendency
• Mean, median, and mode
• skewed distributions
– Variance
• Range
• standard deviation
• normal distributions
• Inferential Statistics:
– Statistical significance
• t-test and the p-value
Inferential Statistics
• You are trying to reach conclusions that
extend beyond just describing the data.
• Inferential stats allow us to apply the
research data to the entire population, not
just the sample. I can apply RHS data to all
high school students in the US. ONLY
USED WITH EXPERIMENTS (CAUSE &
EFFECT)
•Does caffeine improve our reaction time?
•We recruit 40 people and give (random assignment)
»20 a caffeine pill (experimental group)
»20 a sugar pill (control group)
•We give them a brief reaction time test and record
the results.
•Yes, group results are different. . .
Why can’t I be done?!
• You don’t know if that difference was due
to your IV (caffeine) or just dumb luck.
• You have to be sure that the results are
statistically significant
Statistical Significance
*You can never 100% fully prove anything in science,
because you can never know if it was 100% not due to
chance
*You can only reject the null hypothesis, which is the
opposite of your hypothesis
*Statistical Significance: Means that the results of the
experiment were most likely NOT due to random
CHANCE/dumb luck. p-value < .05%
*(never a 0% p-value) BUT if the p-value is less that
.05%, you can be confident enough to disprove null
hypothesis (statistically significant)
T-test results
•Does caffeine improve our reaction
time?
•Caffeine condition has a lower mean
RT.
•We run a t-test on our samples and get:
»p = 0.039
•Can we be confident that the
difference in the data is not due to
chance?