Measurement Errors Introduction to Study Skills & Research Methods (HL10040) Dr James Betts.

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– i.e.

Measured Score = ‘True’ Score ErrorTherefore inherently linked to SD

• 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 This variability between methods is

caused by both systematic and error factors

Direct Record

Retrospective Recall

SD

TotalVariance

(SD2)

This total variance can then be

‘partitioned’

SystematicVariance

ErrorVariance

Caused by systematic error

Caused by random error

Types of Errors• Systematic Error

– Any variable causing a consistent shift in the mean in a given direction

e.g. Retrospective diet records tend to omit the snacks between meals

• Random Error– The fluctuation of scores due to chancee.g. Innaccurate descriptions of the food consumed

Systematic Error

Skin-Fold Callipers

Hydrostatic Weighing

% Body-fatSubject 1 Subject 2 Subject 3 Subject 4

10 12 8 11

17 22 14 12

Random Error

Skin-Fold Callipers

Hydrostatic Weighing

% Body-fatSubject 1 Subject 2 Subject 3 Subject 4

14 18 10 9

11 15 21 17

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

Evidence of bias between means

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 r2 = 0.278

r = 0 infers lots of error

r = 1 infers no error In general, good agreement

requires r > 0.7

Assessment of Error• Systematic &

Random ErrorCallipers HydroStat. 10.00 17.00 12.00 22.00 8.00 14.00 11.00 12.00 14.00 11.00 18.00 15.00 10.00 21.00 9.00 17.00

Assessment of Error• Systematic &

Random ErrorCallipers HydroStat. Difference Mean 10.00 17.00 7.00 13.50 12.00 22.00 10.00 17.00 8.00 14.00 6.00 11.00 11.00 12.00 1.00 11.50 14.00 11.00 -3.00 12.50 18.00 15.00 -3.00 16.50 10.00 21.00 11.00 15.50 9.00 17.00 8.00 13.00

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

The “Bland-Altman” Plot 3 points of visual assessment:

-Systematic Error: are points evenly distributed about the zero line?

-Random Error: do points deviate greatly from the mean line?

-Nature of error: is the error consistent left-right?

Examples of Bland-Altman Plots

12.00 13.00 14.00 15.00 16.00

Mean

0.00

5.00

10.00

Mean difference

Zero

Examples of Bland-Altman Plots

12.00 13.00 14.00 15.00 16.00

Mean

0.00

5.00

10.00

Mean difference

Zero

Examples of Bland-Altman Plots

12.00 13.00 14.00 15.00 16.00

Mean

0.00

5.00

10.00

Mean difference

Zero

Examples of Bland-Altman Plots

12.00 13.00 14.00 15.00 16.00

Mean

0.00

5.00

10.00

Mean difference

Zero

Examples of Bland-Altman Plots

12.00 13.00 14.00 15.00 16.00

Mean

0.00

5.00

10.00

Zero

Why is Error Important• Measurement Error is clearly of importance when

evaluating the agreement between two measurement tools

• A consideration of error is also relevant when attempting to establish intervention effects/treatment differencesi.e. where some of the variance between trials is due to the

independent variable...

Total Variance between trial 1

& trial 2

SystematicVariance

ErrorVariance

Dependent Variable

Extraneous/Confounding

(Error) Variables

Independent Variable

SystematicVarianceTotal Variance

between trial 1 & trial 2

SystematicVariance

ErrorVariance

Dependent Variable

Extraneous/Confounding

(Error) Variables

Independent Variable

Primary Variance

So researchers strive to increase the proportion of variance due to IV.

Total Variance between trial 1

& trial 2

SystematicVariance

Error Variance

Dependent Variable

Extraneous/Confounding

(Error) Variables

Independent Variable

Primary Variance

So researchers strive to increase the proportion of variance due to IV.

Increase control

Maximise effect

(20 pints?)

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

i.e. P = 0.01 infers a 99 % probability variance in the DV is not due to pure chance

(i.e. 1 % likelihood of your result occurring if there is in fact no effect)

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

i.e. P = 0.10 infers a 90 % probability variance in the DV is not due to pure chance

(i.e. 1 % likelihood of your result occurring if there is in fact no effect)

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

In exercise science, we must be at least 95 % sure that our effect is due more than pure chance before

concluding a ‘significant’ difference.

i.e. P 0.05

n.b. this DOES NOT mean that you will find this result in 95/100 test-retests or that your false positive rate is 5 %

n.b. this DOES NOT mean that you will find this result in 95/100 test-retests or that your false positive rate is 5 %

Quantitative Analysis of Nominal Data

• Recall that nominal data infers that variables are

dichotomous, i.e. belong to distinct categories

e.g. Athlete/Non-Athlete, Male/Female, etc.

• We know that such qualitative data can be coded

quantitatively to allow a more objective analysis

• Nominal data does not require any consideration

of normality and is analysed used a Chi2 test.

The Chi-Squared Test

• Goodness of fit χ2 test– A comparison of your observed frequency counts

against what would be expected according to the null hypothesis

i.e. null hypothesis infers equal dispersion (50:50)

• Contingency χ2 test– A comparison of two observed frequency counts

Goodness of fit χ2 test• Is a leisure centre used more by males than by

females?– n =150

Observed Frequency

Expected

Frequency

Male 62 75

Female 88 75

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. P-value AKA significance level

i.e. significant difference in the proportion of users

according to gender

Contingency χ2 test• Are elite athletes more likely to take nutritional

supplements than non-athletes– n =60

Do take supplements

Do not take supplements

Athletes 18 12

Non-athletes 11 19

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

This is the test of interest

i.e. no significant difference in the proportion of users

according to group

Assumptions for Chi-Squared

• Although ND not required…

• Cells in the table should all be independent

i.e. one person could have visited the leisure centre twice

• 80 % of the cells must have expected frequencies greater than 5 and all must be above 1

i.e. the more categories available, the more subjects needed

• Cannot use percentages

i.e. a 15:45 split cannot be expressed as 25%:75%

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 Thursday 11th 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-H– Arrive promptly at 11.10 am for start of test at 11.15 am– Exit in silence afterwards

• Surnames: I-Z– Arrive promptly at 12.10 am for start of test at 12.15 am– Exit however you like!

J.Betts@bath.ac.uk