A comparison of the means of two groups (2).

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Christian Lawson-Perfect

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8 years, 9 months ago

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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 (1)..

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 medical researcher is concerned that a new drug may be affecting a patient’s ability to concentrate. She finds six (6) sets of identical twins, randomly gives one a placebo pill (a medically inert and inactive substance) and the other the drug, then measures their reaction times. The data is in the table below:

{object}	A	B	C	D	E	F
Placebo	$\var{r1[0]}$	$\var{r1[1]}$	$\var{r1[2]}$	$\var{r1[3]}$	$\var{r1[4]}$	$\var{r1[5]}$
Drug	$\var{r2[0]}$	$\var{r2[1]}$	$\var{r2[2]}$	$\var{r2[3]}$	$\var{r2[4]}$	$\var{r2[5]}$

Is there a difference in response time between the placebo and the drug?

In other words, test the following null hypothesis:

H0: mean time placebo = mean time drug.

Give any introductory information the student needs.

			Name	Type	Generated Value

attempt	string	hand
d	list	List of 6 items
meandiff	number	-0.033333
mu1	number	0.2
mu2	number	0.25
object	string	Twin set
objects	string	twins
r1	list	List of 6 items
r2	list	List of 6 items
sig1	number	0.025
sig2	number	0.025
stdiff	number	0.045898
t95	number	2.571
thismany	integer	6
tcalc	number	-1.778919
tupper	number	-1.753919
tlower	number	-1.803919
mdupper	number	-0.008333
mdlower	number	-0.058333
stdupper	number	0.070898
stdlower	number	0.020898
outcome	integer	0
sed	number	0.019
test	number	0.0458984386

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
'hand'

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: `string`

hand

This variable doesn't seem to be used anywhere.

Parts

Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add
3. Gap Gap 2. Number entry
  Add
4. Gap Gap 3. Number entry
  Add

Gap-fill

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

Find the mean and standard deviations of the difference between the placebo and drug responses

Calculate differences between placebo and drug responses.

Mean of difference = Gap 0. (input to 3 decimal places )

Standard deviation of difference = Gap 1. (input to 3 decimal places)

Now find the paired t-test statistic using the values you have just calculated =Gap 2. (input 3 decimal places)

Is the null hypothesis rejected? Gap 3. Enter 0 for "No" and 1 for "Yes".

Advice

First, recognise that this is a paired t-test: paired because twins are genetically identical.

So calculate the differences (placebo $-$ drug) between those two observations:

{d}

Note: If you have a graphical calculator, you can enter the two sets of observations into two lists (say L1 and L2), then in the heading (title/label) row for L3 type "=L1 $-$ L2" to get the calculator to work out the differences.

Then calculate the mean difference:

{meandiff}

Then the standard deviation (sd) of the differences:

{stdiff}

Note: You should use your calculator to get both the mean and standard deviation.

The standard error (se) is calculated as:

\[ se = \frac{ sd }{ \sqrt{ n }} \]

It is:

{sed}

Finally, calculate the test statisitic, t-calc, as the mean difference divided by the standard error:

\[ t-calc = \frac{ mean difference }{ se} \]

t-calc = {tcalc}

There are 6 subjects, so 5 degrees of freedom, and the test is two-tailed, so the t-table = 2.571.

If t-calc is greater than 2.571, the null is rejected. As this is a two-tailed test, the sign of t-calc (positive or negative) is ignored.

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
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet

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A comparison of the means of two groups (2).

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Checkpoint description

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: `string`

Parts

Gap-fill

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Error

A comparison of the means of two groups (2).

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: string

Parts

Gap-fill

Generated value: `string`