Download HYPOTHESIS TESTS PROJECT QUESTION Reject H 0

Welcome to .
Week 11 Thurs .
MAT135 Statistics
In-Class Project
What is your favorite diamond
simulant? (1 most-5 least)
What is your favorite white
gem?
Hypothesis Tests
How all the inferential tests
work:
Hypothesis Tests
How all the inferential tests
work:
Excel/your calculator calculates
a probability that you would get
the data you got if the null
hypothesis were true
Hypothesis Tests
How all the inferential tests
work:
Excel/your calculator calculates
a probability that you would get
the data you got if the null
hypothesis were true
If it’s ≤ α-level, reject H0
HYPOTHESIS TESTS
PROJECT QUESTION
The probability
is .03
Do you reject
H0?
HYPOTHESIS TESTS
PROJECT QUESTION
The probability
is .03
Do you reject
H0?
Yup! As long as
your α wasn’t
.01
Hypothesis Tests
CELEBRATE!
Hypothesis Tests
Remember –
Reject the hypothesis if the
statistic is smaller than 0.05
HYPOTHESIS TESTS
PROJECT QUESTION
Reject H0 !
Conclusion?
HYPOTHESIS TESTS
PROJECT QUESTION
Reject H0 !
Conclusion:
The batches do
taste different!
HYPOTHESIS TESTS
PROJECT QUESTION
Which tastes
better?
HYPOTHESIS TESTS
PROJECT QUESTION
For tests of differences
between means, what would
happen if you had a bigger
sample size?
Hypothesis Tests
The p value comes from a
standardized t-distribution:
Questions?
Difference Between Means
We use the t-test when we
have paired data because it is
more powerful
We could use it for other twogroup comparisons, but we
usually use another analysis:
Difference Between Means
Comparing Several Group's
Means:
“ANOVA”
“Analysis of Variance”
Difference Between Means
t-tests can only be used for
comparing two groups
ANOVA can be used to compare
two or more groups
Difference Between Means
A paired t-test is more
powerful
A non-paired t-test is THE
SAME as an ANOVA
(ANOVA’s Excel output page is
better)
Difference Between Means
“ANOVA” stands for
“ANalysis Of VAriance”
Difference Between Means
The analysis assigns the
variability in the data to:
the difference between the
groups
the difference between
individuals
Difference Between Means
Sir Ronald Aylmer Fisher
Difference Between Means
Salaries for Criminal
Justice Jobs
Difference Between Means
There are four classifications
of jobs: probation,
administration, correctional and
patrol
We want to compare the
average salaries to see if they
are the same
ANOVA
PROJECT QUESTION
What would be a good value for
α?
ANOVA
PROJECT QUESTION
α = .05
What would be a good level of
practical significance?
ANOVA
PROJECT QUESTION
What is Ha?
ANOVA
PROJECT QUESTION
Alternative hypothesis Ha:
There are differences in the
salaries of the four job
classifications:
μprobation ≠ μadministration ≠ μcorrectional ≠ μpatrol
What is H0?
ANOVA
PROJECT QUESTION
Null (no difference) hypothesis
H0:
There is no difference in
salaries for the four job
classifications:
μprobation = μadministration = μcorrectional = μpatrol
Difference Between Means
Our strategy:
We hope to disprove H0
and thereby to prove Ha
ANOVA
PROJECT QUESTION
Why can’t you use a t-test for
this data?
Probation
$26,834
$50,748
$39,766
$23,079
$45,883
$51,482
Admin
Correctional
Patrol
$54,780
$41,216
$64,632
$63,447
$23,101
$26,782
$63,687
$27,957
$28,697
$55,653
$53,316
$30,732
$59,299
$32,747
$52,670
$63,063
$21,339
$36,893
ANOVA
PROJECT QUESTION
Clear your TI83/4 data fields
Probation
$26,834
$50,748
$39,766
$23,079
$45,883
$51,482
Admin
Correctional
Patrol
$54,780
$41,216
$64,632
$63,447
$23,101
$26,782
$63,687
$27,957
$28,697
$55,653
$53,316
$30,732
$59,299
$32,747
$52,670
$63,063
$21,339
$36,893
ANOVA
PROJECT QUESTION
Put “Probation” data in L1,
“Admin” data in L2,
“Correctional” in L3 and
“Patrol” in L4
Probation
$26,834
$50,748
$39,766
$23,079
$45,883
$51,482
Admin
Correctional
Patrol
$54,780
$41,216
$64,632
$63,447
$23,101
$26,782
$63,687
$27,957
$28,697
$55,653
$53,316
$30,732
$59,299
$32,747
$52,670
$63,063
$21,339
$36,893
ANOVA
PROJECT QUESTION
“STAT”
“TESTS”
“ANOVA” (at the bottom on my TI83)
ENTER
ANOVA(L1,L2,L3,L4) ENTER
Probation
$26,834
$50,748
$39,766
$23,079
$45,883
$51,482
Admin
Correctional
Patrol
$54,780
$41,216
$64,632
$63,447
$23,101
$26,782
$63,687
$27,957
$28,697
$55,653
$53,316
$30,732
$59,299
$32,747
$52,670
$63,063
$21,339
$36,893
Poof!
Done!
I got:
ANOVA
PROJECT QUESTION
One-way ANOVA
F=5.908580719
p=.0046661234
Factor
df=3
SS=2416783902
MS=805594634
Error
df=20
SS=2726863429
MS=136343171
Sxp=11676.6079
What are
we looking
for?
ANOVA
PROJECT QUESTION
One-way ANOVA
F=5.908580719
p=.0046661234
Factor
df=3
SS=2416783902
MS=805594634
Error
df=20
SS=2726863429
MS=136343171
Sxp=11676.6079
ANOVA
PROJECT QUESTION
What is our
decision?
One-way ANOVA
F=5.908580719
p=.0046661234
Factor
df=3
SS=2416783902
MS=805594634
Error
df=20
SS=2726863429
MS=136343171
Sxp=11676.6079
Reject H0!
ANOVA
PROJECT QUESTION
One-way ANOVA
F=5.908580719
p=.0046661234
Factor
df=3
SS=2416783902
MS=805594634
Error
df=20
SS=2726863429
MS=136343171
Sxp=11676.6079
ANOVA
PROJECT QUESTION
What is our conclusion?
ANOVA
PROJECT QUESTION
What is your conclusion?
We conclude there is a
significant difference between
the average pay of the CJ job
categories
Difference Between Means
Remember –
Reject the null hypothesis if
the statistic is smaller than
0.05
Questions?
Difference Between Means
For the CJ job classifications,
we rejected H0 and concluded
the salaries are different
Difference Between Means
But…
Are they all
different, or is
just one different
or two or …
Difference Between Means
Do a HI-Lo-Close Confidence
Interval graph!
Difference Between Means
From Excel:
Probation
Upper 95% CI 49,571
Lower 95% CI 29,693
Mean
39,632
Admin
63,284
56,692
59,988
Correctional Patrol
43,207
52,532
23,351
27,603
33,279
40,068
ANOVA
PROJECT QUESTION
Which means are different?
ANOVA
PROJECT QUESTION
Is the difference practically
significant?
Difference Between Means
BTW: pre-Excel, this comparison
used to be REALLY hard to do!
Difference Between Means
Yay Excel!
Difference Between Means
PROJECT QUESTION
What would happen if you had a
bigger sample size?
Difference Between Means
PROJECT QUESTION
What would happen if you had a
bigger sample size?
You would be able to show more
statistically significant
differences
Difference Between Means
PROJECT QUESTION
Difference Between Means
t-tests and ANOVAs are
designed to be VERY powerful
for small sample sizes
Difference Between Means
That’s why we include a level of
practical significance
Difference Between Means
Similar to previous tests, the P
comes from a standardized
F-distribution:
Difference Between Means
Because “z” and “t” are based
on 𝒙 , they have similar shapes
F is based on a variance, so it
is in squared units!
Questions?
ANOVA
The ANOVA we just did is
called a “One Factor ANOVA”
ANOVA
The ANOVA we just did is
called a “One Factor ANOVA”
Because there is only one
category (type of job) – called
a “factor”
ANOVA
You can have as many factors
as you want
ANOVA
Excel can handle 2 factors
2 Factor ANOVA
This one is tricky – you have to
have the same number of
observations in each category
M
F
$
$
$
$
Educ Level
HS
Assoc Bachelor's
15,000 $ 25,000 $ 35,000
14,000 $ 24,000 $ 34,000
12,000 $ 35,000 $ 32,000
15,000 $ 43,000 $ 35,000
2 Factor ANOVA
With only one observation it’s
called “without replication”
M
F
$
$
$
$
Educ Level
HS
Assoc Bachelor's
15,000 $ 25,000 $ 35,000
14,000 $ 24,000 $ 34,000
12,000 $ 35,000 $ 32,000
15,000 $ 43,000 $ 35,000
2 Factor ANOVA
With only one observation it’s
called “without replication”
With more than one, it’s called
“with replication”
M
F
$
$
$
$
Educ Level
HS
Assoc Bachelor's
15,000 $ 25,000 $ 35,000
14,000 $ 24,000 $ 34,000
12,000 $ 35,000 $ 32,000
15,000 $ 43,000 $ 35,000
2 Factor ANOVA
An ANOVA table:
ANOVA
Source of
Variation
Total
Gender
Educ Level
Interaction
Within
SS
df
MS
F
1,214,916,667 11
52,083,333 1
52,083,333 7.35
960,166,667 2 480,083,333 67.78
160,166,667 2
80,083,333 11.31
42,500,000 6
7,083,333
p
4%
0%
1%
You survived!
Turn in your homework!
Don’t forget
your homework
due next week!
Have a great
rest of the week!
www.playbuzz.com