basic statistical tests
DESCRIPTION
The slide for YMEN1806 Introduction to Scientific Thinking and Research Practices.TRANSCRIPT
24/10/2013INTRODUCTION TO SCIENTIFIC THINKING AND RESEARCH PRACTISE
BASIC STATISTICAL ANALYSES AND INTERPRETATION
Takumi [email protected]
University of Lapland, Finland
This slide is available at...http://libero86pooh.wordpress.com/category/research/
OVERVIEW
OVERVIEW
OVERVIEW•Basic Statistical Tests
‣ Compare 2 groups‣ Compare 3+ groups
• Interpretation of the Results‣ Significance and p-value‣ p-value and sample size‣ Effect size
BASIC STATISTICAL TESTS
BASIC STATISTICAL TESTS
BASIC STATISTICAL TESTS
Compare
• T-test
• ANOVA• Multiple comparison
Correlation• Pearson correlation
• Spearman correlation
‣Statistical tests have two main groups.
T-test‘Compare means of two variables’
‣Independent t-teste.g.) TOEFL score in JPN and FIN
‣Dependent t-teste.g.) TOEFL score before and after preparation
Compare
ANOVA (Analysis of Variance)
‘Compare means of three+ variables’‣ Find out the difference in various groups
- e.g.) TOEFL score in JPN, FIN and CHN
※H1= There are difference somewhere in the variables.
cannot find out ‘which group’ have the difference
use Multiple comparison to clarify
Compare
Multiple comparison‘Compare means of three+ variables’
-However, it is different from ANOVA
Compare
0255075
100
JPN FIN CHN0
255075
100
JPN FIN0
255075
100
FIN CHN0
255075
100
JPN CHN
ANOVA Multiple comparison
DATA INTERPRETATION
DATA INTERPRETATION
Statistical significance
p=.0143
Statistical significance
p=.0143?
p-value-Probability of the error
‣so, if p is very low...
possibility for error is very low
➡ The result will be reliable
Statistical significance
Statistical significance
Generally...
p<.05Significant
p-value
Statistical significance
H0H1
p-value
p-value
Statistical significance
H0H1
p= .35 → Not significant
p-value
Statistical significance
H0H1
p= .05* → Significant
p-value
Statistical significance
H0H1
p= .01** → Significant
DATA INTERPRETATION
n M SD Diff. p
AGroup1
p=0.137AGroup2 p=0.137
BGroup1 p=0.015BGroup2
p=0.015
These are 2 different results of t-test.
Q. Which of the tests has larger difference?A? B? or same?
Takeuchi and Mizumoto(2011)
DATA INTERPRETATION
n M SD Diff. p
AGroup1 50 40 10
3.0 p=0.137AGroup2 50 43 10
3.0 p=0.137
BGroup1 100 40 10
3.0 p=0.015BGroup2 100 43 10
3.0 p=0.015
The answer is... the same
because p is just the probability- p is NOT the actual difference
Takeuchi and Mizumoto(2011)
DATA INTERPRETATIONn M SD Diff. p
AGroup1 50 40 10
3.0 p=0.137AGroup2 50 43 10
3.0 p=0.137
BGroup1 100 40 10
3.0 p=0.015BGroup2 100 43 10
3.0 p=0.015
‣ M, SD, and Diff are the same score
Takeuchi and Mizumoto(2011)
DATA INTERPRETATIONn M SD Diff. p
AGroup1 50 40 10
3.0 p=0.137AGroup2 50 43 10
3.0 p=0.137
BGroup1 100 40 10
3.0 p=0.015BGroup2 100 43 10
3.0 p=0.015
‣ M, SD, and Diff are the same score‣ The different thing is sample size➡ p is dependent on sample size
Takeuchi and Mizumoto(2011)
DATA INTERPRETATIONn M SD Diff. p
AGroup1 50 40 10
3.0 p=0.137AGroup2 50 43 10
3.0 p=0.137
BGroup1 100 40 10
3.0 p=0.015BGroup2 100 43 10
3.0 p=0.015
The formula of t (independent)
t = x1 − x22S1
n1+
2S2n2
Takeuchi and Mizumoto(2011)
DATA INTERPRETATION The formula of t (independent)
‣ if n becomes larger, t will get larger
➡ p also gets lower
t = x1 − x22S1
n1+
2S2n2
DATA INTERPRETATION‣ Depending too much on p-value may lead to
FALSE INTERPRETATION➡ Actual difference is also important
So we need the value...- which shows the actual difference- which is independent of sample size
It is important to be able to tell whether it is the sample size or the coefficient that is making the difference. The effect size can do this.
(Cohen, Manion and Morrison, 2007: p.520)
Effect size
• There are several different calculations of effect size, for example (Richardson 1996; Capraro and Capraro 2002: 771): r2, adjusted R2, η2, ω2, Cramer’s V, Kendall’s W, Cohen’s d, and Eta. (Cohen, Manion and Morrison, 2007: p.51)
e.g.) Cohen’s d (frequently used for t-test)
Effect size
Independent of Sample size
d = 1M − 2MpooledSD
Effect sizeIn this result, effect size is...
n M SD Diff. p
A Group1 50 40 103.0 p=0.137A Group2 50 43 103.0 p=0.137
B Group1 100 40 103.0 p=0.015B Group2 100 43 103.0 p=0.015
d = 1M − 2MpooledSD
=310
= 0.3
The ES of A & B are same= Actual difference is same
Takeuchi and Mizumoto(2011)
Effect size
n M SD Diff. p
A Group1 50 40 103.0 p=0.137A Group2 50 43 103.0 p=0.137
B Group1 100 40 103.0 p=0.015B Group2 100 43 103.0 p=0.015
In this result, effect size is...
In Cohen’s d...‣ d=0.3 weak‣ d=0.5 moderate‣ d=0.8 strong
ES is ‘weak’
Takeuchi and Mizumoto(2011)
Effect sizeIn this result, effect size is...
n M SD Diff. p
A Group1 50 40 103.0 p=0.137A Group2 50 43 103.0 p=0.137
B Group1 100 40 103.0 p=0.015B Group2 100 43 103.0 p=0.015
In this result, effect size is...
In Cohen’s d...‣ d=0.3 weak‣ d=0.5 moderate‣ d=0.8 strong
ES is ‘weak’
Takeuchi and Mizumoto(2011)
Summary
• In the quantitative analysis, choosing appropriate test according to the research design will make the result better.
• Statistical analysis is conducted mainly by computer programme (SPSS, etc...), but it is important for the researchers to
ReferencesAmerican Psychological Association. (2010). Publication
manual of the American Psychological Association. Washington, DC: American Psychological Association.
Cohen, L., Manion, L. & Morrison, K. (2007). Research methods in education. London New York: Routledge.
Marczyk, G., DeMatteo, D. & Festinger, D. (2005). Essentials of research design and methodology. Hoboken, N.J: John Wiley & Sons.
Seale, C. (2012). Researching society and culture. London: SAGE.
Takeuchi,O. & Mizumoto, A. (2011). Introduction to effect size and power analysis. Reports of 2011 Studies in Japan Association for Language Education and Technology, Kansai Chapter, Methodology Special Interest Groups (SIG), 47-73.