Perform a one-way ANOVA

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Tom Lowe	said	Has some problems	4 years, 4 months ago
Chris Graham	said	Needs to be tested	6 years, 2 months ago

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Tom Lowe commented 4 years, 4 months ago

Question could do with adaptive marking, as later parts of the question rely on the answers to earlier parts. Also, there is no advice for parts d), e) and f), and the advice for part b) only gives working for the TSS, for the BTSS and RSS it just gives the answer.

There is also no advice for how the standard error in part c) is worked out, and the wording of the question is, to me, confusing. The expression in the statement at the beginning of the question implies to me that the question is asking for the the standard deviation of the entire dataset divided by the square root of the total sample size, which is the standard error of the total mean. However, the question is actually asking for the standard error of the mean of a treatment group, which is the square root of the Mean Square Error (or Residual Mean Square) divided by the square root of the sample size of that treatment group (in this case all treatments have the same sample size). I am not sure if this would be more clear to someone currently taking the module but to me it seems ambiguous.

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Tom Lowe 4 years, 4 months ago

Gave some feedback: Has some problems

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Chris Graham 6 years, 2 months ago

Gave some feedback: Needs to be tested

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Chris Graham commented 6 years, 2 months ago

Vicky added some advice

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Chris Graham commented 6 years, 2 months ago

Needs some advice!

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Chris Graham 6 years, 2 months ago

Gave some feedback: Has some problems

○

Chris Graham 6 years, 2 months ago

Created this as a copy of Perform a one-way ANOVA.

Name	Status	Author	Last Modified
Perform a one-way ANOVA	draft	Newcastle University Mathematics and Statistics	20/11/2019 14:51
One-way ANOVA	draft	Lauren Frances Desoysa	08/10/2018 12:31
Perform a one-way ANOVA	Has some problems	Chris Graham	12/01/2023 10:42

There are 4 other versions that do you not have access to.

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 martial arts "coloured ball" drill, in which the subjects respond to different coloured balls pulled from a bucket with different actions (e.g. kick, punch), as quickly as possible.

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)	$\var{r3[0]}$	$\var{r3[1]}$	$\var{r3[2]}$	$\var{r3[3]}$	$\var{r3[4]}$	$\var{r3[5]}$

Write down the sample mean and standard deviation for each group together with an estimate of the standard error of a mean, $\displaystyle\frac{s}{\sqrt{n}}$ , to 2 decimal places.
Test the null hypothesis that the alcohol consumption does not affect the mean time taken to complete the task.

Give any introductory information the student needs.

			Name	Type	Generated Value

sd1	number	3.44
sd2	number	3.43
sd3	number	2.80
mrs	number	10.50
r2	list	[ 20, 27, 25, 23, 30, 26 ]
vr	number	3.24
mbt	number	34.06
pmsg	list	List of 5 items
stderror	number	1.32
dfrs	integer	15
m1	number	23.67
m3	number	28.33
m2	number	25.17
btss	number	68.11
u	integer	3
tss	number	225.61
dfbt	integer	2
tol	number	0.001
ssq	list	[ 3420, 3859, 4856 ]
sig1	number	3.6
v1	list	[ 0, 0, 0, 1, 0 ]
sig3	number	3.6
sig2	number	3.6
cmsg	list	List of 5 items
rss	number	157.50
tsqovern	list	List of 3 items
mu1	number	22.5
g	number	463
mu3	number	26
mu2	number	25.5
ss	number	12135
k	integer	3
r3	list	[ 30, 25, 27, 27, 33, 28 ]
n	integer	18
r1	list	[ 26, 23, 29, 19, 23, 22 ]
stovern	number	11977.5
t	list	[ 142, 151, 170 ]
v	list	[ 0, 0, 0, 1, 0 ]
n1	integer	6
n2	integer	6
n3	integer	6
pvalue	number	0.068

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
precround(pstdev(r1),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:

This variable doesn't seem to be used anywhere.

Parts

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Part d) Choose one from a list
Part e) Choose one from a list
Part f) Choose one from a list

Gap-fill

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

First fill in this table with the appropriate values, all decimals to 2 decimal places:

	$\overline{x}_i$	$s_i$	$T_i$	$\sum x^2$	$n_i$
Group A	Gap 0.	Gap 1.	Gap 2.	Gap 3.	6
Group B	Gap 4.	Gap 5.	Gap 6.	Gap 7.	6
Group C	Gap 8.	Gap 9.	Gap 10.	Gap 11.	6
			$G=\;$Gap 12.	Sum of Squares=Gap 13.	$N=18$

Note that in doing this you will have supplied the sample means and sample standard deviations for the three groups.

Advice

a)

Here we will work through the top row of the table and compute the values for Group $A$. The other two rows are calculated in the same way.

\[ T = \var{r1[0]}+\var{r1[1]}+\var{r1[2]}+\var{r1[3]}+\var{r1[4]}+\var{r1[5]}=\var{t[0]}. \]

\[\bar{x} = \frac{T}{6}=\var{m1}.\]

\[ \sum{x^2}=\var{r1[0]}^2+\var{r1[1]}^2+\var{r1[2]}^2+\var{r1[3]}^2+\var{r1[4]}^2+\var{r1[5]}^2 =\var{ssq[0]}.\]

\begin{align}
s &= \sqrt{\frac{1}{n-1}\left(\sum_{i=1}^{n}x_i^2 -n\bar{x}^2\right)} \\
&= \sqrt{\frac{1}{5}(\var{ssq[0]}-6\times\var{m1})} \\
&= \var{sd1}.
\end{align}

b)

$\displaystyle TSS$ is the total sum of squares of the ${3}$ groups minus the total sum of the ${3}$ groups divided by the total number of subjects.

\[ TSS =\var{ss}-\frac{\var{g}}{18}=\var{tss}. \]

Similarly

\[ BTSS=\var{btss} \]

\[ RSS=\var{rss} \]

c)

The ANOVA table can be completed from the above values:

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

The estimated standard error of the mean is {{stderror}}.

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:

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Tom Lowe commented 4 years, 4 months ago

Tom Lowe 4 years, 4 months ago

Chris Graham 6 years, 2 months ago

Chris Graham commented 6 years, 2 months ago

Chris Graham commented 6 years, 2 months ago

Chris Graham 6 years, 2 months ago

Chris Graham 6 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: `number`

Parts

Gap-fill

a)

b)

c)

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Perform a one-way ANOVA

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Tom Lowe commented 4 years, 4 months ago

Tom Lowe 4 years, 4 months ago

Chris Graham 6 years, 2 months ago

Chris Graham commented 6 years, 2 months ago

Chris Graham commented 6 years, 2 months ago

Chris Graham 6 years, 2 months ago

Chris Graham 6 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: number

Parts

Gap-fill

a)

b)

c)

Generated value: `number`