Measurement Errors

Introduction to Study Skills & Research Methods (HL10040)

Dr James Betts

Lecture Outline:•Measurement Errors Continued

•Types of Errors

•Assessment of Error

•Introduction to Inferential Statistics

•Chi-Squared tests

•Assessment Details.

Measurement Errors• Virtually all measurements have errors

• Reliability and Measurement Error are not the same, rather Reliability infers an acceptable degree of Measurement Error.

Energy Intake (calories per day)

1500 2500 3500 4500 5500

Nu

mb

er

of

Pe

op

le

0

20

40

60

80

100

120

140

160

SD

TotalVariance

This total variance can then be

‘partitioned’

Systematic/Random Error

Skin-Fold Callipers

Hydrostatic Weighing

% Body-fatSubject 1 Subject 2 Subject 3 Subject 4

Body-Fat

0

5

10

15

20

25

Condition

%

Assessment of Error

• Systematic Error

Descriptive Statistics

4 12.00 22.00 16.2500 4.34933

4 8.00 12.00 10.2500 1.70783

4

Hydrostat

Callipers

Valid N (listwise)

N Minimum Maximum Mean Std. Deviation

Assessment of Error• Random

Error

12.00 14.00 16.00 18.00 20.00 22.00

Hydrostat

8.00

9.00

10.00

11.00

12.00

Cal

liper

s

Correlations

1 .527

. .473

4 4

.527 1

.473 .

4 4

Pearson Correlation

Sig. (2-tailed)

N

Pearson Correlation

Sig. (2-tailed)

N

Callipers

Hydrostat

Callipers Hydrostat

Assessment of Error• Systematic &

Random Error

12.00 14.00 16.00

Mean

0.00

5.00

10.00

dif

fere

nce

s

Mean = 4.63

3 points of visual assessment:

-Systematic Error:

-Random Error:

-Nature of error:

12.00 13.00 14.00 15.00 16.00

Mean

0.00

5.00

10.00

dif

fere

nc

es

Mean differenceMean difference

Zero

12.00 13.00 14.00 15.00 16.00

Mean

0.00

5.00

10.00

dif

fere

nc

es

Mean differenceMean difference

Zero

12.00 13.00 14.00 15.00 16.00

Mean

0.00

5.00

10.00

dif

fere

nc

es

Mean differenceMean difference

Zero

12.00 13.00 14.00 15.00 16.00

Mean

0.00

5.00

10.00

dif

fere

nc

es

Mean differenceMean difference

Zero

SystematicVarianceTotal Variance

between trial 1 & trial 2

Dependent Variable

Extraneous/Confounding

(Error) Variables

Independent Variable

Smallest Worthwhile Effect

Re-Run

Introduction to Inferential Statistics

• Before our next lecture you will be conducting some inferential statistics in your lab classes

• All you need to be aware of at this stage is that the ‘P-value’ represents the probability that total variance is not due to primary variance

Gender

62 75.0 -13.0

88 75.0 13.0

150

Male

Female

Total

Observed N Expected N Residual

Goodness of fit χ2 testSPSS Output

Test Statistics

4.507

1

.034

Chi-Square a

df

Asymp. Sig.

Gender

0 cells (.0%) have expected frequencies less than5. The minimum expected cell frequency is 75.0.

a.

Chi-Square Tests

3.270b 1 .071

2.403 1 .121

3.301 1 .069

.120 .060

3.216 1 .073

60

Pearson Chi-Square

Continuity Correctiona

Likelihood Ratio

Fisher's Exact Test

Linear-by-LinearAssociation

N of Valid Cases

Value dfAsymp. Sig.

(2-sided)Exact Sig.(2-sided)

Exact Sig.(1-sided)

Computed only for a 2x2 tablea.

0 cells (.0%) have expected count less than 5. The minimum expected count is 14.50.

b.

Group * Response Crosstabulation

Count

18 12 30

11 19 30

29 31 60

Athletes

Non-Athletes

Group

Total

Do takesupplements

Dont takesupplements

Response

Total

Contingency χ2 test

SPSS Output

Selected Reading• I know error and variance can be confusing topics, try these:

• Atkinson, G. and A. M. Nevill. Statistical methods for assessing measurement error (Reliability) in variables relevant to sports medicine. Sports Medicine. 26:217-238, 1998.

• Hopkins, W. G. et al. Design and analysis of research on sport performance enhancement. Med. Sci. Sport and Exerc. 31:472-485, 1999.

• Hopkins, W. G. et al. Reliability of power in physical performance tests. Sports Medicine. 31:211-234, 2001.

• Atkinson, G., ''What is this thing called measurement error?'' , in Kinanthropometry VIII: Proceedings of the 8th International Conference of the International Society for the Advancement of Kinanthropometry (ISAK) , Reilly, T. and Marfell-Jones, M. (Eds.), Taylor and Francis, London , 2003.

Coursework (60% overall grade)• Your coursework will require you to address

2 of the following research scenarios:

– 1) Effect of Plyometric Training on Vertical Jump

– 2) Effect of Ice Baths on Recovery of Strength

– 3) Effect of Diet on the Incidence of Muscle Injury

– 4) Effect of Footwear on Sprint Acceleration

– 5) Effect of PMR on Competitive Anxiety.

Coursework Outline• For each of the 2 scenarios you will need to:

– Perform a literature search in order to provide a

comprehensive introduction to the research area

– Identify the variables of interest and evaluate the

research design which was adopted

– Formulate and state appropriate hypotheses

– Summarise descriptive statistics in an appropriate

and well presented manner…

Coursework Outline• Cont’d…

– Select the most appropriate statistical test with justification for your decision

– Transfer the output of your inferential statistics into your word document

– Interpret your results and discuss the validity and reliability of the study

– Draw a meaningful conclusion (state whether hypotheses are accepted or rejected).

Coursework Details (see unit outline)• 2000 words maximum (i.e. 1000 for each)

• Any supporting SPSS data/outputs to be appended

• To be submitted on Tuesday 14th December

Assessment Weighting

Evaluation & Analysis (30 %)

Reading & Research (20 %)

Communication & Presentation (20 %)

Knowledge (30 %)

Coursework Details• All information relating to your coursework

(including the relevant data files) are accessible via the unit web page:

www.bath.ac.uk/~jb335/Y1%20Research%20Skills%20(FH10040).html

Web address also referenced on shared area

Mid-Term Test (40% overall grade)• NEXT WEEK• This test will involve short answer questions

covering all the information covered so far• Mostly knowledge recall but will require

understanding and possibly some calculations• Duration = 50 min

So…

Mid-Term Test (40% overall grade)

• Surnames: A-F– Arrive promptly at 08.10 am for start of test at 08.15 am– Exit in silence afterwards

• Surnames: G-Z– Arrive promptly at 09.10 am for start of test at 09.15 am– Exit however you like!