A comparison of the means of three 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 two groups (4)..

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 researcher is testing the effect of a new warm-up (WU) regime on sprint times. She divides her 18 volunteers into 3 groups (of 6 each): one group does no warm up; one group does a short warm up routine; the third group does a long warm up routine. She then records sprint times for each person. The data is given below (numbers are times in seconds).

No warm up: {grp1[0]}, {grp1[1]}, {grp1[2]}, {grp1[3]}, {grp1[4]}, {grp1[5]}
Short: {grp2[0]}, {grp2[1]}, {grp2[2]}, {grp2[3]}, {grp2[4]}, {grp2[5]}
Long: {grp3[0]}, {grp3[1]}, {grp3[2]}, {grp3[3]}, {grp3[4]}, {grp3[5]}

Is there a difference in average sprint time among the groups?

In other words, test the following null hypothesis:

H0: The mean sprint time is the same for all treatment groups.

Give any introductory information the student needs.

			Name	Type	Generated Value

cval	number	0.414
dfamong	integer	2
dftotal	integer	17
dfwithin	integer	15
fratio	number	88.081
ftable	number	3.68
grp1	list	[ 15, 16, 14, 17, 14, 15 ]
grp2	list	[ 13, 13, 12, 11, 11, 11 ]
grp3	list	[ 19, 21, 19, 19, 21, 20 ]
mean1	number	15.167
mean2	number	11.833
mean3	number	19.833
msamong	number	96.8888888889
mswithin	number	1.1
object	string	Athlete
objects	string	Athletes
outcome	integer	1
s1	number	4386.7222222222
s2	number	4597
s3	number	4580.5
sig1	integer	1
slip	number	0.025
ssamong	number	193.7777777778
sstotal	number	210.2777777778
sswithin	number	16.5
sumallx	number	281
sumsq1	number	1387
sumsq2	number	845
sumsq3	number	2365
sumx1	number	91
sumx2	number	71
sumx3	number	119
var1	number	1.367
var2	number	0.967
var3	number	0.967
wulong	integer	20
wunone	integer	15
wushort	integer	12
tukval	number	3.67
tukse	number	0.428
tukssd	number	1.571
tuk12	number	3.334
tuk13	number	4.666
tuk23	number	8
tuk12sig	integer	1
tuk13sig	integer	1
tuk23sig	integer	1

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`

0.414

← Depends on:

var1
var2
var3

→ Used by:

This variable doesn't seem to be used anywhere.

Parts

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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 three groups (1).

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Taxonomy: mathcentre

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Taxonomy: Context

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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 three 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`