Psychology 2010, Introduction to Statistics
Lecture 5:
Instructor
Teaching Assistant
Liqiang Huang
Kelvin, Lui Fai Hong
Review
Core logic of hypothesis testing
How will the scores be distributed if an idea
is not right (Comparison Distribution).
Something
Two-Sample t-test
In the previous lecture we discussed how to test
whether the mean of a population is larger than a
known value (the mean of population 2)
For example, in one sample t-test, we can test
whether exercise will increase the hours of sleep,
w
One-Sample, Paired t-test
The main problem of Z test:
Z test is often practically impossible because the
variance of population is unknown
How to solve this problem?
We estimate the variance ourselves!
Naturally, we estimate the population variance by
cal
Correlation
Lucy wants to know whether more exercise will make
one happier, so she measured 5 students hours of
exercise as well as their levels of happiness
Participants
Hours of exercise
Happiness
A
9
7
B
8
7
C
0
2
D
7
6
E
6
3
This type of data cannot b
One-way ANOVA
Comparing Multiple Groups
Previously, we discussed how to test whether 2
groups have the same means
What if we want to know whether 3 or more
groups have the same means or not?
For example, we want to test whether living costs
are different
Chi-square Test
Hypothesis Testing on
Nominal Variable
A question we would often face
Hiking Club in CUHK has 100 students, distributed
in 4 majors. You want to know whether students
from these 4 majors have different degrees of
interest in hiking. For si
Hypothesis Testing I
Hypothesis Testing
hypothesis testing refers to the statistical test
which uses sample data to evaluate a hypothesis
about a population
Researchers want to draw a general conclusion the hypothetical variable would change the results
Regression
Predicting from Correlated
Variables
premise: there is a correlation between 2 variables
The same question in the previous lecture
Now we already know that the hours spent on
exercise is correlated with happiness
Conceptually, suppose in the fu
Normal Distribution
Z Score
by itself, a raw score or X value provides very little
information about how that particular score
compares with other values in the distribution
e.g., a score of X = 76
if the raw score is transformed into a z-score, the
val
Effect Size and Power
First go back to the situation of one score
(Sample size =1)
Cutoff point
Samples that make the
test insignificant
Samples that make the
test significant
Population 1: The group in some condition
effect
Population 2: The group not in
Descriptive Statistics
Central Tendency
a number that indicates where the center of the
distribution tends to be located
give you an overview of a set of data with a number
Measures of central tendency
Mode
Mean (also known as ordinary average)
Median
PSYC 2010
Introduction to Statistics
Dr. Kitty Y. F. Fung
Sample and Population
Population
~ entire group we wish to draw conclusions about
e.g., all university students in Hong Kong
Sample
~ a subset of the population we select to represent
the entire po
Hypothesis Testing II
What is the most common practical problem with
the one-score hypothesis testing technique we
introduced earlier?
Often the one score observed is not sufficient for
us to accept the research hypothesis even if the
research hypothesis
Psychology 2010, Introduction to Statistics
Lecture 6:
Instructor
Teaching Assistant
Liqiang Huang
Kelvin, Lui Fai Hong
Review
A single observation might not be
statistically significant (red arrow) , but a
larger sample could make the test
significant (g
Psychology 2010, Introduction to Statistics
Lecture 3:
Instructor
Teaching Assistant
Liqiang Huang
Kelvin, Lui Fai Hong
Review
Two important description of a distribution
Central Tendency
Variability
Median Mean Mode
Variance
Standard deviation
Review
Raw
Psychology 2010, Introduction to Statistics
Lecture 11:
Instructor
Teaching Assistant
Liqiang Huang
Kelvin, Lui Fai Hong
This type of data can not be handled by
using the previous methods because we are
not comparing means of 2 or more groups,
but are try
Psychology 2010, Introduction to Statistics
Lecture 7:
Instructor
Teaching Assistant
Liqiang Huang
Kelvin, Lui Fai Hong
Review
Population 1
Population 2
Review
The distribution
of means
The distribution
of means
Cut-off point
When the distance between the
Psychology 2010, Introduction to Statistics
Lecture 2:
Instructor
Teaching Assistant
Liqiang Huang
Kelvin, Lui Fai Hong
Review
Comparison
Nominal/
Categorical
Rank-order
Equal-Interval
No
Calculation
(Arithmetic)
No
Yes
Yes
No
Yes
Review
Tom
17
Mike
18
An
Psychology 2010, Introduction to Statistics
Lecture 9:
Instructor
Teaching Assistant
Liqiang Huang
Kelvin, Lui Fai Hong
Review
1-sample t-test: In general, are red dots
on the right side of the blue line?
Paired t-test: In general, is the red dot
on the r
Psychology 2010, Introduction to Statistics
Lecture 8:
Instructor
Teaching Assistant
Liqiang Huang
Kelvin, Lui Fai Hong
Review
Review
There is an important difference between
Population variance and Best estimation
of Population Variance from the sample
P
Psychology 2010, Introduction to Statistics
Lecture 13:
Instructor
Teaching Assistant
Liqiang Huang
Kelvin, Lui Fai Hong
Outline
Descriptive statistics
Inferential statistics
Correlation and regression
Chi-square test
Finding the appropriate test
Central
Psychology 2010, Introduction to Statistics
Lecture 12:
Instructor
Teaching Assistant
Liqiang Huang
Kelvin, Lui Fai Hong
Review
8
6
4
2
0
0
2
4
6
8
10
We need to capture the trend of the
correlation (usually described as a straight
line) and use it to mak