LSD and Tukey yardsticks, and one-way ANOVA - SES2003

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Tom Lowe

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Has some problems

4 years, 3 months ago

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Tom Lowe commented 4 years, 3 months ago

Could use some adaptive marking in part e), as the LSD and Tukey yardsticks depend on the value found for the sqrt(RMS) in part a), and which differences are found to be significant depends on the means for the groups found in part d).

Also there is no advice for parts a), b) and c), and the advice for part e) doesn't explain where most of the terms in the calculation of the yardsticks come from (ie the critical values or the sample size of one group).

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Tom Lowe 4 years, 3 months ago

Gave some feedback: Has some problems

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Chris Graham 6 years, 1 month ago

Created this as a copy of LSD and Tukey yardsticks, and one-way ANOVA.

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

There is one other version that you do not have access to.

Question statement

The following data arose in a comparison of the effects of hydration on the time taken (in minutes) to complete a set of exercises. There were three groups of subjects; group 1 (fully hydrated), group 2 (partially hydrated) and group 3 (dehydrated).

Group 1 (fully hydrated)	$\var{r1[0]}$	$\var{r1[1]}$	$\var{r1[2]}$	$\var{r1[3]}$	$\var{r1[4]}$	$\var{r1[5]}$
Group 2 (partially hydrated)	$\var{r2[0]}$	$\var{r2[1]}$	$\var{r2[2]}$	$\var{r2[3]}$	$\var{r2[4]}$	$\var{r2[5]}$
Group 3 (dehydrated)	$\var{r3[0]}$	$\var{r3[1]}$	$\var{r3[2]}$	$\var{r3[3]}$	$\var{r3[4]}$	$\var{r3[5]}$

Give any introductory information the student needs.

			Name	Type	Generated Value

lsd	number	3.58
tukey	number	4.36
sd1	number	2.50
sd2	number	3.10
sd3	number	3.08
vr	number	27.28
w3	list	[ 1, 0, 0 ]
w2	list	[ 1, 0, 0 ]
w1	list	[ 0, 0, 1 ]
mbt	number	230.22
n	integer	18
pmsg	list	List of 5 items
mu3	number	32.5
stderror	number	3.45
sqrms	number	2.91
dfrs	integer	15
m1	number	23.67
m3	number	35.67
m2	number	27.00
btss	number	460.44
stovern	number	15367.3333333333
tss	number	587.11
dfbt	integer	2
tol	number	0.01
yn	list	Nested 3×3 list
ssq	list	[ 3392, 4422, 7680 ]
sig1	number	3
v1	list	[ 1, 0, 0, 0, 0 ]
sig3	number	3
sig2	number	3
cmsg	list	List of 5 items
rss	number	126.67
tsqovern	list	List of 3 items
mu1	number	24.5
g	number	518
r2	list	[ 24, 31, 28, 30, 24, 25 ]
mu2	number	28.5
ss	number	15494
k	integer	3
r3	list	[ 33, 39, 34, 35, 33, 40 ]
mrs	number	8.44
r1	list	[ 22, 27, 23, 25, 25, 20 ]
u	integer	0
t	list	[ 142, 162, 214 ]
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`

3.58

← 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
  Add
2. Gap Gap 1. Number entry
  Add
3. Gap Gap 2. Number entry
  Add
Part e) Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add
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 1	$\var{m1}$
Group 2	$\var{m2}$
Group 3	$\var{m3}$

The differences between the mean values for the groups are:

Between $1$ and $2=\;|\var{m1}-\var{m2}|=\var{abs(m1-m2)}$

Between $2$ and $3=\;|\var{m2}-\var{m3}|=\var{abs(m2-m3)}$

Between $1$ and $3=\;|\var{m1}-\var{m3}|=\var{abs(m1-m3)}$

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 1 and 2	{yn[0][0]}	{yn[0][1]}	{yn[0][2]}
Means of Groups 2 and 3	{yn[1][0]}	{yn[1][1]}	{yn[1][2]}
Means of Groups 1 and 3	{yn[2][0]}	{yn[2][1]}	{yn[2][2]}

Give a worked solution to the whole question.

Use this tab to check that this question works as expected.

There was an error which means the tests can't run:

Part	Test	Passed?
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Choose one from a list
Choose one from a list		Hasn't run yet
Choose one from a list
Choose one from a list		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Match choices with answers
Match choices with answers		Hasn't run yet

This question is used in the following exams:

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LSD and Tukey yardsticks, and one-way ANOVA - SES2003

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Taxonomy: mathcentre

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Tom Lowe commented 4 years, 3 months ago

Tom Lowe 4 years, 3 months ago

Chris Graham 6 years, 1 month ago

Error in variable testing condition

Error

Warning

Generated value: `number`

Parts

Gap-fill

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Error

LSD and Tukey yardsticks, and one-way ANOVA - SES2003

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Tom Lowe commented 4 years, 3 months ago

Tom Lowe 4 years, 3 months ago

Chris Graham 6 years, 1 month ago

Error in variable testing condition

Error

Warning

Generated value: number

Parts

Gap-fill

Generated value: `number`