Emma's copy of Perform a paired sample t-test,

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Emma Howard

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Emma Howard 7 years, 2 months ago

Created this as a copy of Perform a paired sample t-test, .

Name	Status	Author	Last Modified
Perform a paired sample t-test,	draft	Newcastle University Mathematics and Statistics	20/11/2019 14:51
Adam's copy of Perform a paired sample t-test,	draft	Adam Vellender	22/11/2017 15:38
Emma's copy of Perform a paired sample t-test,	draft	Emma Howard	17/01/2018 13:56

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Question statement

The following data was obtained from $12$ individuals. The observations consist of the time taken to complete a dexterity task using their left and right hands.

{object}	A	B	C	D	E	F	G	H	I	J	K	L
Right	$\var{r1[0]}$	$\var{r1[1]}$	$\var{r1[2]}$	$\var{r1[3]}$	$\var{r1[4]}$	$\var{r1[5]}$	$\var{r1[6]}$	$\var{r1[7]}$	$\var{r1[8]}$	$\var{r1[9]}$	$\var{r1[10]}$	$\var{r1[11]}$
Left	$\var{r2[0]}$	$\var{r2[1]}$	$\var{r2[2]}$	$\var{r2[3]}$	$\var{r2[4]}$	$\var{r2[5]}$	$\var{r2[6]}$	$\var{r2[7]}$	$\var{r2[8]}$	$\var{r2[9]}$	$\var{r2[10]}$	$\var{r2[11]}$

Carry out by hand a paired t-test to test whether there is evidence of a difference in the average times for the left and right hands.

Give any introductory information the student needs.

			Name	Type	Generated Value

pmsg	list	List of 5 items
msg	list	List of 5 items
cmsg1	list	List of 5 items
t999	number	4.437
meandiff	number	2.417
object	string	Individual
sig1	number	2
tvalue	number	2.851
stdiff	number	2.937
sig2	number	2.4
t99	number	3.106
t95	number	2.201
t90	number	1.796
cmsg	list	List of 5 items
d	list	List of 12 items
mu1	number	21.5
r1	list	List of 12 items
r2	list	List of 12 items
mu2	number	24.1
n	integer	12
t	integer	2
v	list	[ 0, 0, 1, 0, 0 ]
pvalue	number	0.016
attempt		Definition of variable `attempt` is empty.

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
[' is less than $0.001$',' lies between $0.001$ and $0.01$',' lies between $0.01$ and $0.05$',' lies between $0.05$ and $0.10$',' is greater than $0.10$']

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: `list`

[ " is less than $0.001$", " lies between $0.001$ and $0.01$", " lies between $0.01$ and $0.05$", " lies between $0.05$ and $0.10$", " is greater than $0.10$" ]

This variable doesn't seem to be used anywhere.

Parts

Part a) Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add
3. Gap Gap 2. Number entry
  Add
Part b) Choose one from a list
Part c) Choose one from a list

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 left and right {attempt}s.

Calculate differences for left {attempt} times – right {attempt} times. Make sure you take the differences this way round.

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

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

Now find the t-test statistic $T$ using the values you have just calculated and input the absolute value $|T|$ here: Gap 2. (3 decimal places).

Advice

The table of differences is given by:

{object}	A	B	C	D	E	F	G	H	I	J	K	L
Right	$\var{r1[0]}$	$\var{r1[1]}$	$\var{r1[2]}$	$\var{r1[3]}$	$\var{r1[4]}$	$\var{r1[5]}$	$\var{r1[6]}$	$\var{r1[7]}$	$\var{r1[8]}$	$\var{r1[9]}$	$\var{r1[10]}$	$\var{r1[11]}$
Left	$\var{r2[0]}$	$\var{r2[1]}$	$\var{r2[2]}$	$\var{r2[3]}$	$\var{r2[4]}$	$\var{r2[5]}$	$\var{r2[6]}$	$\var{r2[7]}$	$\var{r2[8]}$	$\var{r2[9]}$	$\var{r2[10]}$	$\var{r2[11]}$
Differences	$\var{d[0]}$	$\var{d[1]}$	$\var{d[2]}$	$\var{d[3]}$	$\var{d[4]}$	$\var{d[5]}$	$\var{d[6]}$	$\var{d[7]}$	$\var{d[8]}$	$\var{d[9]}$	$\var{d[10]}$	$\var{d[11]}$

We test the following hypothesis:

$H_0:\;\mu_d=0$ versus $H_1:\;\mu_d\neq 0$

$n=\var{n}$ and the mean of the differences is $\overline{d}=\var{meandiff}$.

The variance $V$ of the differences is calculated to be $\var{pstdev(d)^2}$

Hence we have the standard deviation $s_d= \sqrt{V}=\var{stdiff}$ to 3 decimal places.

The paired t-statistic is given by:

\[\begin{eqnarray*} T&=&\frac{\overline{d}-\mu_d}{\frac{s_d}{\sqrt{n}}}\\&=&\frac{\var{meandiff}-0}{\frac{\var{stdiff}}{\sqrt{\var{n}}}}\\&=&\var{tvalue}\end{eqnarray*}\]

(Using the null hypothesis that the means are the same i.e. $\mu_d=0$.)

Hence our test statistic $|T|=\var{tvalue}$.

Looking up this value on the T-distribution table for $t_{11}$

\[\begin{array}{r|rrrrr}&0.20&0.10&0.05&0.01&0.001\\\hline11&1.363&1.796&2.201&3.106&4.437\end{array}\]

We see that the t-statistic {msg[t]} and the table tells us that the $p$ value {pmsg[t]}.

Hence we conclude that we {cmsg[t]} the null hypothesis. There is {cmsg1[t]} evidence of a difference between the average scores of the two groups.

Give a worked solution to the whole question.

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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
Choose one from a list
Choose one from a list		Hasn't run yet
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Emma's copy of Perform a paired sample t-test,

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Taxonomy: mathcentre

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Emma Howard 7 years, 2 months ago

Error in variable testing condition

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Generated value: `list`

Parts

Gap-fill

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Error

Emma's copy of Perform a paired sample t-test,

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Emma Howard 7 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: list

Parts

Gap-fill

Generated value: `list`