Analysis of Variance
one-way ANOVA
Comparing more than two samples
ANOVA allows us to compare more than two
samples at a time.
Even though we could always run t tests for
every two samples we want t
Central Tendency
Shapes of different distributions
What is the distribution
of the rolls of a single
die?
Shapes of different distributions
What is the distribution
of the rolls of a single
die?
1
6
S
Quantitative Methods
PSYC 120
Luis F. Schettino
Statistics
Why do we need statistics?
The natural world is full of patterns, but many of
those patterns are not easy to detect.
Science uses mathemat
Central Tendency and Variability
The Normal Curve
Mean
Mode
Median
In a perfect bell-curve, the mean, mode and
median are all at the same central location.
The Mean
The mean is the best descriptor of
Power
Significance
When we set out to test a hypothesis using hypothesis
testing methods, we essentially carry out a bet.
Because we are comparing two and only two
hypotheses, the results can only f
Variables, scales, distributions
Scales of Measurement
Scales of measurement describe the
properties of numbers.
They tells us how informative a number is.
Scales of Measurement
Scales of measureme
Directional Tests, Effect Size
Directional Tests
We can test hypotheses that claim a direction
to our data.
Instead of using the = sign, we use > or <.
Directional tests allow us to move the region
Confidence Intervals
A t test
The chancellor oat City
University is worried that
the grades have fallen in
the past year. The grade
point average for
graduating students in the
previous 5 years was 2
Cumulative Distributions and
Percentiles
Cumulative Frequency Distribution
Sometimes we want to know a bit more about
our data by looking at how they are
distributed.
One way to learn more is to see
z scores 2
Obtaining scores from areas
This is the reverse problem from finding a
percentage limited by a score under the normal
curve.
Here we want to know which score (or scores)
is the limit for
Graphing Frequency
Distributions
Graphing Distributions
Y-axis or ordinate
The Graph
3
2
1
Origin
0
0
1
2
X-axis or abscissa
3
Tick marks
The Histogram
Start at zero or make sure your reader knows you
The Standard Error of the Mean
The random sampling
distribution of the mean
is a probability
distribution. That is, a
distribution that shows
us the values that
sample means can take
and the probabil
Two-way ANOVA
Interactions and Nested Designs
Assumptions for a Two-Way ANOVA
Normality: data come from a population that is
normally distributed.
Random sampling: data were sampled randomly.
Indep
Repeated Measures ANOVA
Assumptions
The populations are normally distributed: as
sample size increases, ANOVA can deal with
slight skewing of the data. Large sample sizes
are best.
Assumptions
The p
Hypothesis Testing
Statistical Inference
In statistical inference we are interested in
drawing conclusions about a population based
on a sample.
This is because it is either impractical or
impossibl
z scores
Fear of dogs
Dogs are our preferred pets
because of their sociality.
But, of course, they are also
carnivores and can defend
themselves.
Fear of dogs
Dogs are our preferred pets
because of th
More on Correlation
Correlation IS NOT causation
The fact that two variables are related does
not mean that one of them necessarily causes
the other.
That is, a relationship only means that the
vari
Independent Samples t-Test
Part 2
Look at your data
The first thing you want to do when
conducting an analysis is to look at your data.
Ballistic Movement Data
30
25
20
Inaccuracy Scores (count)
15
s
Chi Square
Chi Square
While the other tests we looked at during the
course involved the use of interval and ratio
scales, 2 (ki square) only requires the frequency
of occurrence of a set of events.
Correlation
Correlation and Prediction
Correlation refers to the level in which two
variables are related.
If two variables are strongly correlated, when
we know a value for one of them we have a
be
Two-way ANOVA
Factorial Designs
Factorial Designs
While a one-way ANOVA can tell us
something about the differences between
different levels of a single variable, factorial
designs can do that for mo
Chi Square 2
Independence between variables
Chi square can be used to
determine whether two
variables are somehow related
(having one affects the other,
similar to a correlation).
The null hypothesi
Prediction
Questions
According to the regression
equation for a particular
problem in prediction, when X
= 81, Y= 317; and when X=92,
Y = 317.
What is the value of r? How
can you tell?
What is the
The Standard Deviation
The Standard Deviation
The standard deviation is the square root of the
variance. This simplifies both the calculations
and the conceptualization of variability.
Smaller stand
Probability and the Normal
Distribution
Probability
The probability of an event taking place can be
expressed as percentages (e. g. candidate x has
a 60% probability to win the election) or as
odds (