ANOVA

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Xiaodan Leng 5 years, 10 months ago

Created this as a copy of ANOVA.

Name	Status	Author	Last Modified
Small sample t-test on sample mean	Ready to use	Frank Doheny	21/02/2023 07:50
Two sample t-test: comparison of means	Ready to use	Frank Doheny	07/10/2021 10:29
Two sample t-test: paired data	Ready to use	Frank Doheny	07/10/2021 10:24
Z-test on sample mean	Ready to use	Frank Doheny	04/10/2021 21:48
Z-test on sample proportion	Ready to use	Frank Doheny	04/10/2021 22:24
Two sample Z-test on proportions	Ready to use	Frank Doheny	07/10/2021 10:40
Chi-square goodness of fit test	Ready to use	Frank Doheny	21/02/2023 07:39
Chi-square test: contingency tables	Ready to use	Frank Doheny	08/10/2021 14:55
ANOVA	Ready to use	Frank Doheny	21/02/2023 07:50
One sample t-test -SES	Has some problems	Lauren Frances Desoysa	25/06/2018 09:49
Perform a one-sample t-test	Needs to be tested	Lauren Frances Desoysa	11/11/2024 14:22
Colin's copy of Two sample t-test: paired data	draft	Colin Whitehead	25/06/2018 15:31
David's copy of Z-test on sample mean	draft	David Goulding	18/09/2018 16:33
Resting heart rate statistics	draft	David Goulding	18/09/2018 16:54
Catherine's copy of Z-test on sample proportion	draft	Catherine Palmer	13/03/2022 22:33
STAT7008 Hypothesis test, single sample, two sided t-test on sample mean	draft	Catherine Palmer	25/11/2020 19:04
Charlie's copy of STAT7008 Hypothesis test, single sample, two sided t-test on sample mean	draft	Charlie Earle	09/12/2018 12:34
Two sample t-test: Paired data	Should not be used	Brad Allison	11/06/2020 14:14
Brad's copy of Two sample t-test: comparison of means	draft	Brad Allison	12/06/2019 12:40
Brad's copy of Two sample t-test: paired data	draft	Brad Allison	13/06/2019 14:01
ANOVA	draft	Xiaodan Leng	11/07/2019 00:17
Chi-square test: contingency tables	draft	Xiaodan Leng	11/07/2019 00:17
Chi-square goodness of fit test	draft	Xiaodan Leng	11/07/2019 00:17
Z-test on sample proportion	draft	Xiaodan Leng	11/07/2019 00:18
Z-test on sample mean	draft	Xiaodan Leng	11/07/2019 00:18
Two sample Z-test on proportions	draft	Xiaodan Leng	11/07/2019 00:19
Two sample t-test: paired data	draft	Xiaodan Leng	11/07/2019 00:19
Two sample t-test: comparison of means	draft	Xiaodan Leng	11/07/2019 00:20
Small sample t-test on sample mean	draft	Xiaodan Leng	11/07/2019 00:20
Chi-square goodness of fit test	Ready to use	Ben Parker	24/02/2023 11:16

There are 51 other versions that do you not have access to.

Question statement

An experiment was designed to test whether students’ learning is affected by background sound. Twenty-four students were randomly separated into three groups of eight. All students study a passage of text for 30 minutes.

Group 1 study with music playing at a constant volume in the background. Group 2 study with recorded conversations playing in the background and group 3 study with no sound at all. After studying, all students take a multiple-choice test on the material.

Their scores are given below:

Group 1	Group 2	Group 3
{r1[0]}	{r2[0]}	{r3[0]}
{r1[1]}	{r2[1]}	{r3[1]}
{r1[2]}	{r2[2]}	{r3[2]}
{r1[3]}	{r2[3]}	{r3[3]}
{r1[4]}	{r2[4]}	{r3[4]}
{r1[5]}	{r2[5]}	{r3[5]}
{r1[6]}	{r2[6]}	{r3[6]}
{r1[7]}	{r2[7]}	{r3[7]}

Test the hypothesis that the students' average marks are unaffected by the background sounds.

Give any introductory information the student needs.

			Name	Type	Generated Value

scenario		Error evaluating variable scenario: No definition of 'sum' of correct type found.
decision_matrix		Error evaluating variable decision_matrix: Variable `scenario` is not defined.
f_u	number	3.82
r2	vector	Vector with 8 components
r3	vector	Vector with 8 components
sum_r1	number	464
sum_r3	number	686
sum_r2	number	458
r1	vector	Vector with 8 components
total_sum_r	number	1608
r1sqd	number	28036
r2sqd	number	28952
r3sqd	number	59598
ss_betw	number	4221.00
ss_within	number	4629.00
test_statistic	number	9.57
f_l	number	0.025
msb	number	2110.5
msw	number	220.43

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
sum(map(abs(test_statistic)<x,x,[f_l,f_u]))

JME function reference

Error

Error evaluating variable scenario: No definition of 'sum' of correct type found.

Description

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

← Depends on:

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
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3. Gap Gap 2. Number entry
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4. Gap Gap 3. Number entry
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5. Gap Gap 4. Number entry
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6. Gap Gap 5. Number entry
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7. Gap Gap 6. Number entry
  Add
Part b) Choose one from a list

Gap-fill

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

Fill in the appropriate values in the table below, correct to one decimal place

	Sum of squares	degrees of freedom	mean square	F
Between	Gap 0.	2	Gap 2.	Gap 4.
Within	Gap 1.	21	Gap 3.

Correct to 2 decimal places, enter the lower table statistic: F = Gap 5.

Correct to 2 decimal places, enter the upper table statistic: F = Gap 6.

Advice

In this example we are comparing the means of three distict samples, we therefore must use the analysis of variance test (ANOVA)

$H_0:$ Students' average marks are unaffected by different background sounds.

$H_1:$ Students' average marks are affected by different background sounds.

	Group 1	Group 2	Group 3
${n_i}$	8	8	8
$\sum{x_i}$	{sum_r1}	{sum_r2}	{sum_r3}
$\sum{x_i^2}$	{r1sqd}	{r2sqd}	{r3sqd}

We need to evaluate the sum of squares between the samples $S_b$ , and the sum of squares within the samples $S_w$ .

$S_b=\sum\left(\frac{(\sum{x_i})^2}{n_i}\right)-\frac{(\sum{x_{i,j}})^2}{n_t}$ where ${n_i}$ is the number of data values in sample $i$ and ${n_t}$ equals the total number of data values.

$S_b=\frac{(\var{sum_r1})^2}{8}+\frac{(\var{sum_r2})^2}{8}+\frac{(\var{sum_r3})^2}{8}-\frac{(\var{total_sum_r})^2}{24}$

$S_b=\var{ss_betw}$

$S_w=\sum\left(\sum{x_i^2}-\frac{(\sum{x_i})^2}{n_i}\right)$

$S_w=\left(\var{r1sqd}-\frac{(\var{sum_r1})^2}{8}\right)+\left(\var{r2sqd}-\frac{(\var{sum_r2})^2}{8}\right)+\left(\var{r3sqd}-\frac{(\var{sum_r3})^2}{8}\right)$

$S_w=\var{ss_within}$

	Sum of Squares	deg. of freedom	Mean square	F
Between	$\var{ss_betw}$	2	$\var{msb}$	$\var{test_statistic}$
Within	$\var{ss_within}$	21	$\var{msw}$

The F-table values will have $F_{2,21}=2, 21$ degrees of freedom.

The lower cut-off point is found using $\frac{1}{F_{21,2}}$

Significance	0.05
Lower limit	0.025
Upper limit	4.42

Compare the test statistic with the F-table values and choose your conclusion.

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
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Choose one from a list
Choose one from a list		Hasn't run yet

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Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Checkpoint description

Xiaodan Leng 5 years, 10 months ago

Error in variable testing condition

Error

Warning

Generated value:

Parts

Gap-fill