LSD and Tukey yardsticks, and one-way ANOVA

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Newcastle University Mathematics and Statistics

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Newcastle University Mathematics and Statistics 9 years, 2 months ago

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Name	Status	Author	Last Modified
LSD and Tukey yardsticks, and one-way ANOVA	draft	Newcastle University Mathematics and Statistics	20/11/2019 14:51
LSD and Tukey yardsticks, and one-way ANOVA - SES2003	Has some problems	Chris Graham	23/11/2022 13:16
LSD and Tukey yardsticks, and one-way ANOVA - Mock Test - SES2003	Needs to be tested	Chris Graham	04/03/2019 10:28

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Question statement

The following data arose in a comparison of the effects of alcohol on the time taken to complete a task. There were three groups of subjects; Group A had no alcohol, Group B had two units over 1 hour and Group C had 4 units over 1 hour. The responses are the times (in seconds) taken to complete a word-matching task.

Group A (0 units)	$\var{r1[0]}$	$\var{r1[1]}$	$\var{r1[2]}$	$\var{r1[3]}$	$\var{r1[4]}$	$\var{r1[5]}$
Group B (2 units)	$\var{r2[0]}$	$\var{r2[1]}$	$\var{r2[2]}$	$\var{r2[3]}$	$\var{r2[4]}$	$\var{r2[5]}$
Group C (4 units)	$\var{r3[0]}$	$\var{r3[1]}$	$\var{r3[2]}$	$\var{r3[3]}$	$\var{r3[4]}$	$\var{r3[5]}$

Give any introductory information the student needs.

			Name	Type	Generated Value

lsd	number	3.44
tukey	number	4.20
sd1	number	2.97
sd2	number	3.62
sd3	number	1.26
vr	number	19.73
w3	list	[ 1, 0, 0 ]
w2	list	[ 0, 1, 0 ]
w1	list	[ 1, 0, 0 ]
mbt	number	154.50
n	integer	18
pmsg	list	List of 5 items
mu3	number	32
stderror	number	3.20
sqrms	number	2.80
dfrs	integer	15
m1	number	23.00
m3	number	33.00
m2	number	29.50
btss	number	309.00
stovern	number	14929.5
tss	number	426.50
dfbt	integer	2
tol	number	0.01
yn	list	Nested 3×3 list
ssq	list	[ 3218, 5287, 6542 ]
sig1	number	3.4
v1	list	[ 1, 0, 0, 0, 0 ]
sig3	number	3.4
sig2	number	3.4
cmsg	list	List of 5 items
rss	number	117.50
tsqovern	list	[ 3174, 5221.5, 6534 ]
mu1	number	22
g	number	513
r2	list	[ 24, 29, 28, 33, 29, 34 ]
mu2	number	28
ss	number	15047
k	integer	3
r3	list	[ 34, 31, 32, 34, 33, 34 ]
mrs	number	7.83
r1	list	[ 26, 19, 26, 20, 24, 23 ]
u	integer	0
t	list	[ 138, 177, 198 ]
w	list	Nested 3×3 list
v	list	[ 1, 0, 0, 0, 0 ]
n1	integer	6
n2	integer	6
n3	integer	6
pvalue	number	0.000

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
precround(2.131*sqrms*sqrt(2/n1),2)

JME function reference

Description

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `number`

3.44

← Depends on:

n1
sqrms

→ Used by:

Advice
"Part e)" → "Gap 0." - Minimum accepted value
"Part e)" → "Gap 0." - Maximum accepted value

Parts

Part a) Gap-fill
1. Gap Number entry
  Add
Part b) Choose one from a list
Part c) Choose one from a list
Part d) Gap-fill
1. Gap Gap 0. Number entry
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2. Gap Gap 1. Number entry
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3. Gap Gap 2. Number entry
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Part e) Gap-fill
1. Gap Gap 0. Number entry
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2. Gap Gap 1. Number entry
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3. Gap Gap 2. Match choices with answers
  Add

Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

You are given the following ANOVA table for this data:

Source	df	SS	MS	VR
Between Treatments	$\var{dfbt}$	$\var{btss}$	$\var{mbt}$	$\var{vr}$
Residual	$\var{dfrs}$	$\var{rss}$	$\var{mrs}$	-
Total	$\var{n-1}$	$\var{tss}$	-	-

Input $\sqrt{RMS}$ here: Unnamed gap to 2 decimal places.

This will be used to calculate the LSD and Tukey yardstick values later.

Advice

Using the Yardsticks

The mean values for each group are:

	$\overline{x}_i$
Group A	$\var{m1}$
Group B	$\var{m2}$
Group C	$\var{m3}$

The differences between the mean values for the groups are:

Between $A$ and $B=\;|\var{m1}-\var{m2}|=\var{abs(m1-m2)}$

Between $B$ and $C=\;|\var{m2}-\var{m3}|=\var{abs(m2-m3)}$

Between $A$ and $C=\;|\var{m1}-\var{m3}|=\var{abs(m1-m3)}$

We compare these differences with the LSD and Tukey yardsticks:

LSD yardstick = $2.131\times\var{sqrms}\times\sqrt{2/\var{n1}}=\var{lsd}$ to 2 decimal places, where $\var{sqrms}$ is the value of $\sqrt{RMS}$ found above.

Tukey yardstick = $3.67\times\var{sqrms}\times\sqrt{1/\var{n1}}=\var{tukey}$ to 2 decimal places.

If the difference of the means:

is greater than the Tukey yardstick we say that there is evidence of a definite significant difference.

less than the Tukey yardstick but greater than the LSD yardstick we say that there is evidence of a possible significant difference.

is less than the LSD yardstick then we say that there is no evidence of a significant difference.

Hence we have the following for the groups:

Pairs of Groups	Definite Significant Difference	Possible Significant Difference	No Significant Difference
Means of Groups A and B	{yn[0][0]}	{yn[0][1]}	{yn[0][2]}
Means of Groups B and C	{yn[1][0]}	{yn[1][1]}	{yn[1][2]}
Means of Groups A and C	{yn[2][0]}	{yn[2][1]}	{yn[2][2]}

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This question is used in the following exams:

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Taxonomy: mathcentre

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Newcastle University Mathematics and Statistics 9 years, 2 months ago

Error in variable testing condition

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Generated value: `number`

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Gap-fill

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LSD and Tukey yardsticks, and one-way ANOVA

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Newcastle University Mathematics and Statistics 9 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: number

Parts

Gap-fill

Generated value: `number`