A comparison of the means of four groups (1).

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Christian Lawson-Perfect

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Christian Lawson-Perfect 8 years, 9 months ago

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Keith McGuinness 9 years, 8 months ago

Created this as a copy of A comparison of the means of three groups (2)..

Name	Status	Author	Last Modified
Paired t-test after treatment.	Ready to use	Bill Foster	01/06/2016 09:47
Christian's copy of Paired t-test after treatment.	Ready to use	Christian Lawson-Perfect	01/06/2016 10:06
A comparison of the means of two groups (1).	Ready to use	Keith McGuinness	01/06/2016 09:47
A comparison of the means of two groups (2).	Ready to use	Keith McGuinness	01/06/2016 09:47
Testing an hypothesis about the mean of a group (1).	Ready to use	Keith McGuinness	01/06/2016 09:47
Testing an hypothesis about the mean of a group (2).	Ready to use	Keith McGuinness	01/06/2016 09:47
Summary statistics (1).	Ready to use	Keith McGuinness	01/06/2016 09:47
A comparison of the means of two groups (3).	Ready to use	Keith McGuinness	01/06/2016 09:47
A comparison of the means of two groups (4).	Ready to use	Keith McGuinness	01/06/2016 09:47
A comparison of the means of three groups (1).	Ready to use	Keith McGuinness	01/06/2016 09:47
A comparison of the means of three groups (2).	Ready to use	Keith McGuinness	01/06/2016 09:47
A comparison of the means of four groups (1).	Ready to use	Keith McGuinness	01/06/2016 09:47
Simon's copy of Paired t-test after treatment.	draft	Simon Thomas	05/06/2019 14:44

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Question statement

A biologist studied the effects of season and population density (number of animals in the area) on egg production in a marine snail [5]. A partially completed analysis of the study is shown below. State appropriate null hypotheses, then complete the analysis and draw conclusions about these null hypotheses, and about the effects of density and season.

Give any introductory information the student needs.

			Name	Type	Generated Value

cval	number	0.569
dfamong	integer	2
dftotal	integer	17
dfwithin	integer	15
fratio	number	84.263
ftable	number	3.68
grp1	list	List of 6 items
grp2	list	List of 6 items
grp3	list	List of 6 items
mean1	number	54.100
mean2	number	70.383
mean3	number	59.633
msamong	number	411.3272222222
mswithin	number	4.8814444444
object	string	Athlete
objects	string	Athletes
outcome	integer	1
s1	number	67797.8938888889
s2	number	68693.77
s3	number	68620.5483333333
sig1	integer	3
slip	number	0.025
ssamong	number	822.6544444444
sstotal	number	895.8761111111
sswithin	number	73.2216666666
sumallx	number	1104.7
sumsq1	number	17569.94
sumsq2	number	29745.35
sumsq3	number	21378.48
sumx1	number	324.6
sumx2	number	422.3
sumx3	number	357.8
treat1	number	54.5
treat2	number	70
treat3	number	60.5
tuk12	number	16.283
tuk12sig	integer	1
tuk13	number	5.533
tuk13sig	integer	1
tuk23	number	10.75
tuk23sig	integer	1
tukse	number	0.902
tukssd	number	3.310
tukval	number	3.67
var1	number	1.816
var2	number	4.494
var3	number	8.335

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
precround(max([var1,var2,var3])/sum([var1,var2,var3]),3)

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`

0.569

← Depends on:

This variable doesn't seem to be used anywhere.

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Gap-fill

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

Summary statistics

Calculate means and variances for both groups: variance ( $s^2$ ) is just the standard deviation ( $s$ or $sd$ ) squared.

Note: All values, except df and outcome, should be given to 3 decimal places.

Mean 1 = Gap 0.; Mean 2 = Gap 1.; Mean 3 = Gap 2.

Variance 1 = Gap 3.; Variance 2 = Gap 4.; Variance 3 = Gap 5.

n1 = 6; n2 = 6; n3 = 6

Cochran's value = Gap 6.

(Normally, we would compare the Cochran's value to the table (0.707) and transform the data if required, but this makes this too complicated, so we will assume that the calculated value is always lower than the table value.)

In the next part, you enter the values for the intermediate terms.

Advice

Summary statistics

Calculate means and variances for both groups: variance ($s^2$) is just the standard deviation ($s$ or $sd$) squared.

Mean 1 = {mean1}; Mean 2 = {mean2}; Mean 3 = {mean3}

Variance 1 = {var1}; Variance 2 = {var2}; Variance 3 = {var3}

Cochran's value = {cval}; Table value = 0.707. If Cochran's value > 0.707, transformation of the data may be required. (This will be ignored in this example because it would greatly complicate the code.)

n1 = 6; n2 = 6; n3 = 6

Intermediate terms

Caalculate the following:

Sum of Group 1 = {sumx1}; Sum of Group 2 {sumx2}= ; Sum of Group 3 = {sumx3}

Sum of all values = {sumallx}

Sum of squares of all values = {s2}

Calculate the S terms:

S1 = {s1}

S2 = {s2}

S3 = {s3}

Complete the ANOVA table

Fill in the values (3 decimal places, except for df).

Source	SS	df	MS	F-ratio
Among	{ssamong}	{dfamong}	{msamong}	{fratio}
Within	{sswithin}	{dfwithin}	{mswithin}
Total	{sstotal}	{dftotal}

Outcome

Is the null hypothesis (all means equal) rejected? A 0 means "no" and a 1 means "yes".

Outcome = {outcome}

Complete Tukey's test

1. Find the appropriate q-value (k = 3, df = 15):

table q = {tukval}

2. Calculate the standard error (square-root(MSwithin/n)):

SE = {tukse}

3. Calculate the smallest significant difference (SSD or Least Significant Difference, LSD):

SSD = {tukssd}

4. Calculate the differences between all pairs of means (ignore the sign):

Mean 1 - Mean 2 = {tuk12}
Mean 1 - Mean 3 = {tuk13}
Mean 2 - Mean 3 = {tuk23}

5. Compare each difference to the SSD. If the difference is greater than SSD, then the means differ. Enter 0 below if the means are equal and 1 if they differ:

Mean 1 - Mean 2 = {tuk12sig}
Mean 1 - Mean 3 = {tuk13sig}
Mean 2 - Mean 3 = {tuk23sig}

Note that this test can give inconclusive results.

Give a worked solution to the whole question.

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

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A comparison of the means of four groups (1).

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

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Christian Lawson-Perfect 8 years, 9 months ago

Keith McGuinness 9 years, 8 months ago

Error in variable testing condition

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Generated value: `number`

Parts

Gap-fill

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Error

A comparison of the means of four groups (1).

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Christian Lawson-Perfect 8 years, 9 months ago

Keith McGuinness 9 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: number

Parts

Gap-fill

Generated value: `number`