Symbols, Notation, Subscripts
conventions
uppercase:
lowercase:
subscripts:
variables
X, Y, Z
constants
a, b, c
identify a specific observation in a list,
with n as the last observation
Xi X3 Xn
the tradeoff
precision vs. intelligibility
Symbols, Notation

Confound?
any problem with a study?
NO!
Confound = something that varies along with
the IV, i.e., that is not the critical difference
critical difference?
- the point of the study, the difference in
conditions that may affect the dependent variable
Typica

Normal Distribution
What is it?
same as a standardized distribution?
NO
it s a special frequency distribution (natural phenomenon)
.4
.3
p(x)
.2
.1
.0
x
Normal Distribution
frequency
of scores
The standard normal curve is
scores
a frequency distribution

Linear transformations
their effects on statistics such as the mean, deviation
scores, standard deviation, variance.
What is a linear transformation?
A linear equation
Y = b + aX,
Y = a + bX
What are effects of adding a constant, multiplying, or doing
b

Ques%ons
1. I use facebook to make invites to events
2. JB is the most talented music celeb U20
3. I believe everything in newspapers
4. Watching gangnam style makes me want to see it again and
again
5. AEer Yoga

P218 anxiety & performance
For 2 years in a row, I measured P218 math anxiety and math
performance (score on an algebra pretest)
Question: is performance linked to anxiety? Or independent?
Problems:
1. One year n = 47, second year n = 50
2. algebra test o

PSYC366
Guide to wri>ng
the discussion
Allison Brennan
Wed Feb 13, 2013
Research paper hourglass
Introduction
Method
Results due
today
Discussion
Outline
Hand in results draD assignments
Grad student discussion panel info

Regression workshop
height and shoe size
P218 Data (Arizonago wildcats)
Can you predict someone's height by looking at their
shoes?
How well?, meaning with what precision?
How many inches in height is predicted by each unit
increase in shoe size?
class da

The concept of correlation
correlation describes the relation between two
variables
note. this is still a descriptive statistic,
not an inferential one
yet!
The concept of correlation
answers the question: what happens to one variable as the
other variabl

Linear transformations
so what?
implications of linear transformations
1. create variables (scores) with desired characteristics:
mean, variance, std dev
!
!
Linear transformations
2. scores are invariant under linear transformation
instantly know effect

Pop Culture Survey
Form teams (5 or less per)
Select Team Name
Select a Pop Culture Concept for measurement
in class
Topic: Pop culture?
What would you like to know about your class
and their view of pop culture?
About yourself, relative to rest of class?

Graphing functions
a visual mapping of the relations between variables
Y Label (units)
conventions
ordinate Y - > DV
abscissa X - > IV
Y
units of y
units of x
X Label (units)
X
Graphing functions
are variables discrete or continuous ?
abscissa
IV discrete

Frequency Distributions
organizing a group of scores for visual inspection and
for making relative comparisons among scores
FREQUENCY
20
15
10
5
0
2
7
12
17
22
SCORE
27
32
Frequency Distributions
Example questions:
What is the middle score?
How many obser

Measures of Central Tendency
Three different concepts of AVERAGE, associated with three
different scale properties
What is the most frequently occurring score?
NOMINAL
What is the middlemost score?
ORDINAL
What is the "center of gravity" of all scores?
IN

Graphing - Box Plots
for ordinal data
(data are categorized based on quartiles, deciles, percentiles)
Benefits?
median, SIR (variability), range, seen at glance
skew
Cost?
loss of detailed information
Graphing - Box Plots
Median = 1.69 hours
SIR = (Q3 - Q

very useful
summary tool !
for summarizing
relations among a
group of scores
Relative FREQUENCY (%)
Cumulative frequency distributions
100
75
50
25
0
2
7
12 17 22 27
SCORE
32
Cumulative frequency distributions
point in a distribution
below which a given
p

Understanding functions using the
"black-box"
X
?
Y
condition
function?
value
Playing the "black-box game
X
X can be
any digit
from 0-5
?
Y
If you can
predict Y you
will know whats
in the black box
Principles of the "black-box" approach
1. data come in on

Popular images of the statistician
The liar
spin-doctoring
The nerd
pocket protected, but blind to reality
The whiz
all statistics is mathematically trivial
The plodder
someone has to count all this stuff
No respect!
The cure?
Huff (1975) How to lie with

regression
at the heart of statisticslinear relations
association vs. prediction
correlation vs. regression
regression
the scatterplot again
the model of correlation-regression is a straight line
Y, or DV
the regression line
X, or IV
the regression model