The document discusses research methods and statistical analysis techniques. It provides information on formulating hypotheses, designing studies to test hypotheses, and interpreting results. Key points covered include defining the null and alternative hypotheses, factors that affect the correlation coefficient, and guidelines for interpreting the magnitude and direction of correlation based on the correlation coefficient value. Examples are provided to illustrate concepts like experimental design, null hypotheses, and positive versus negative correlation.

1. Thursday, 1 December 4, 2014

2. Select a
General
Problem
Conduct
Literature
Review
Exhaustive
Review
Preliminary
Search later
Expanded
Select Specific
Research Problem
Question or hypothesis
Decide Design
And Methodology
Collect
Data
Analyzes
and
Present Data
State Conclusion/
Generalization about Problem
Interpret
Findings
Statistical
Tables
Integrative
Diagrams
Thursday, 2 December 4, 2014

3.  Hypothesis is a prediction about the outcome of the
study.
 After the hypothesis is proposed, a study is designed
to test that hypothesis.
 The data collected in the study enable the
researchers to decide whether the hypothesis is
supported.
 Hypothesis should be clearly and concisely stated
and be testable.

4. For example,
In a study of middle school students, their attitudes
toward school are assessed using questionnaire and
their school performance is measured using their GPA
(Grade Point Average).
One hypothesis in this study may predict that “the
girls’ mean score on the questionnaire would be
significantly higher than the boys’ mean score”, while
another hypothesis may predict “ there is a positive
correlation between students’ scores on the
questionnaire and their GPA”.

5. 1. The alternative hypothesis (HA or H1)
2. The null hypothesis (Ho)
 HA or H1 predicts that there will be some
relationship between variables or difference
between means or groups.
Example:
“ There will be a positive correlation between students;
reading fluency and their reading comprehension
scores.” or “ Students in classes where the teachers
use differentiated instruction will score significantly
higher on the end-of-year spelling test compared
with students in similar classes where teachers do
not use differentiated instruction.”

6.  Ho. Predicts that
“ There will be no positive correlation between
students’ reading fluency and their reading
comprehension scores.” or “ Students in classes
where the teachers use differentiated instruction will
not score significantly higher on the end-of-year
spelling test compared with students in similar
classes where teachers do not use differentiated
instruction.”

7. For example:
We will conduct an experimental study to test the null
hypothesis. This study would be conducted to test the
effect of starting the school day half an hour later on
students’ achievement test scores. In one junior high
school in the district, the students would continue with
the same schedule as in the past years. The null
hypothesis in this study states that “there would be no
difference in the mean scores on an achievement test
between the students in the two junior high schools
who start school at different times.”

8. Another example:
The null hypothesis states that “ there would be no
significant correlation between IQ and depression
score in college students.”
This hypothesis would be tested using a random
sample of two hundred students from one university.
IQ and depression scores of those students would be
obtained and correlated to test the null hypothesis.
Depression: a psychiatric disorder showing symptoms such as persistent
feelings of hopelessness, dejection, poor concentration, lack of energy, inability
to sleep, and, sometimes, suicidal tendencies

9. 1. What is Correlation?
2. Graphing correlation
3. Pearson Product Moment
a. Interpreting the correlation coefficient
b. Hypothesis for correlation
c. Computing Pearson Correlation
4. Factors Affecting the Correlation
5. The coefficient of Determination and
Effect Size

10.  Correlation is the relationship or
association between two or more
numerical variables.
 These variables have to be related to
each other or paired.

11.  Correlation is a statistical technique
used to determine the degree to which
two variables are related.
 In the field of education, the correlation
is used to administer two measures to
the same group of people and then
correlated their scores on one measure
with their score on the other measure.

12.  The strength , or degree of correlation,
as well as the direction of the correlation
(positive or negative), is indicated by a
correlation coefficient.
 The coefficient can range from -1.00,
indicating a perfect negative correlation
to 0.00, indicating no correlation, to
+1.00 indicating a perfect positive
correlation.

13.  Correlation does not imply causation.
 Just because two variables correlate with
each other does not mean that one
caused the other.

14.  Correlation between two measures
obtained from the same group of people
can be shown graphically through the
use of a scatter gram (or a scatter plot)
 A scatter gram (or a scatter plot) is a
graphic presentation of a correlation
between two variables.

16. The figure of this scatter gram
showing a positive correlation
between two variables, X
(number of hours spent
studying) and Y (Final grade in
course).
The points on the scatter gram
in this figure create a pattern
that goes from the bottom left
upward to the top right.
This is typical of a positive
correlation in which an increase
on one variable is associated
with an increase in the other
variable.
The points on this scatter gram
cluster together to form a tight,
diagonal pattern.

17. That as X increases,
Y increases

18. The figure of this scatter gram
showing a negative correlation
between age of car and reliability.
In a negative correlation, an
increase in one variable is
associated with a decrease in the
other variable.

19.  That as X increases, Y decrease
 In statistics books, this part of
relationship is called the direction
of the relationship (i.e., it is either
positive or negative)

20. The scatter gram
contains points that
do not form any clear
pattern and are
scattered widely

21.  That there is no relationship
between X and Y. This means
that neither X nor Y can be used
as a predictor of the other.

22. CCoorrrreellaattiioonn CCooeeffffiicciieenntt
Statistic showing the degree of relation
between two variables

23. SSiimmppllee CCoorrrreellaattiioonn ccooeeffffiicciieenntt ((rr))
 IItt iiss aallssoo ccaalllleedd PPeeaarrssoonn''ss ccoorrrreellaattiioonn
oorr pprroodduucctt mmoommeenntt ccoorrrreellaattiioonn
ccooeeffffiicciieenntt..
 IItt mmeeaassuurreess tthhee nnaattuurree aanndd ssttrreennggtthh
bbeettwweeeenn ttwwoo vvaarriiaabblleess ooff
tthhee qquuaannttiittaattiivvee ttyyppee..

24. SSiimmppllee CCoorrrreellaattiioonn ccooeeffffiicciieenntt ((rr))
 IInn oorrddeerr ttoo uussee PPeeaarrssoonn’’ss ccoorrrreellaattiioonn,,
tthhee ffoolllloowwiinngg rreeqquuiirreemmeenntt sshhoouulldd bbee
ssaattiissffiieedd::
 TThhee ssccoorreess aarree mmeeaassuurreedd oonn aann
iinntteerrvvaall oorr rraattiioo ssccaallee..
 TThhee ttwwoo vvaarriiaabblleess ttoo bbee ccoorrrreellaatteedd
sshhoouulldd hhaavvee aa lliinneeaarr rreellaattiioonnsshhiipp ((aass
ooppppoosseedd ttoo ccuurrvviilliinneeaarr rreellaattiioonnsshhiipp))

25. Interpreting tthhee ccoorrrreellaattiioonn ccooeeffffiicciieenntt
 AAfftteerr oobbttaaiinniinngg tthhee ccoorrrreellaattiioonn
ccooeeffffiicciieenntt,, tthhee nneexxtt sstteepp iiss ttoo
eevvaalluuaattee aanndd iinntteerrpprreett iitt..
 TThhee ssiiggnn ooff tthhee ccoorrrreellaattiioonn ((nneeggaattiivvee
oorr ppoossiittiivvee)) iiss nnoott iinnddiiccaattiivvee ooff tthhee
ssttrreennggtthh ooff tthhee ccoorrrreellaattiioonn..
 AA nneeggaattiivvee ccoorrrreellaattiioonn iiss nnoott
ssoommeetthhiinngg nneeggaattiivvee.. WWhhaatt mmaatttteerrss iiss
tthhee aabbssoolluuttee vvaalluuee ooff tthhee ccoorrrreellaattiioonn..

26. CCoonntt......
 TThhuuss,, aa nneeggaattiivvee ccoorrrreellaattiioonn ooff --00..9933
iinnddiiccaatteess aa ssttrroonnggeerr rreellaattiioonnsshhiipp tthhaann
aa ppoossiittiivvee ccoorrrreellaattiioonn ooff ++00..8800
 TThhee ssiiggnn ooff rr ddeennootteess tthhee nnaattuurree ooff
aassssoocciiaattiioonn
 wwhhiillee tthhee vvaalluuee ooff rr ddeennootteess tthhee
ssttrreennggtthh ooff aassssoocciiaattiioonn..

27.  IIff tthhee ssiiggnn iiss ppoossiittiivvee tthhiiss mmeeaannss tthhee
rreellaattiioonn iiss ddiirreecctt ((aann iinnccrreeaassee iinn oonnee
vvaarriiaabbllee iiss aassssoocciiaatteedd wwiitthh aann iinnccrreeaassee iinn
tthhee ootthheerr vvaarriiaabbllee aanndd aa ddeeccrreeaassee iinn oonnee
vvaarriiaabbllee iiss aassssoocciiaatteedd wwiitthh aa
ddeeccrreeaassee iinn tthhee ootthheerr vvaarriiaabbllee))..
 WWhhiillee iiff tthhee ssiiggnn iiss nneeggaattiivvee tthhiiss mmeeaannss
aann iinnvveerrssee oorr iinnddiirreecctt rreellaattiioonnsshhiipp ((wwhhiicchh
mmeeaannss aann iinnccrreeaassee iinn oonnee vvaarriiaabbllee iiss
aassssoocciiaatteedd wwiitthh aa ddeeccrreeaassee iinn tthhee ootthheerr))..

28.  The value of rr rraannggeess bbeettwweeeenn (( --11)) aanndd (( ++11))
 TThhee vvaalluuee ooff rr ddeennootteess tthhee ssttrreennggtthh ooff tthhee
aassssoocciiaattiioonn aass iilllluussttrraatteedd
bbyy tthhee ffoolllloowwiinngg ddiiaaggrraamm..
strong intermediate weak weak intermediate strong
1- -0.75 -0.25 0 0.25 0.75 1
no relation
perfect
correlation
perfect
correlation
indirect Direct

29. IIff rr == ZZeerroo tthhiiss mmeeaannss nnoo aassssoocciiaattiioonn oorr
ccoorrrreellaattiioonn bbeettwweeeenn tthhee ttwwoo vvaarriiaabblleess..
IIff 00 << rr << 00..22 == NNeegglliiggiibbllee ttoo llooww (( nnoo ccoorrrreellaattiioonn))..
IIff 00..22 ≤≤ rr << 00..44 == LLooww ccoorrrreellaattiioonn..
IIff 00..44 ≤≤ rr << 00..66 == MMooddeerraattee ccoorrrreellaattiioonn..
IIff 00..6600 ≤≤ rr <<00..8800 == HHiigghh ccoorrrreellaattiioonn..
IIff 00..8800 ≤≤ rr << ll == ppeerrffeecctt ccoorrrreellaattiioonn..
Source: Ruth Ravid 2011:120

30. IInntteerrpprreettaattiioonn
DDeeppeennddss oonn wwhhaatt tthhee ppuurrppoossee ooff tthhee ssttuuddyy 
””......iiss…… bbuutt hheerree iiss aa ““ggeenneerraall gguuiiddeelliinnee
• Value = magnitude of the relationship
• Sign = direction of the relationship

31. X X Y Y
How to compute the simple correlation
(coefficient (r
Formula 1
Formula 2
Sx Sy
rXY n
å - -
=
1 ( )( )

32. ::EExxaammppllee
AA ssaammppllee ooff 66 cchhiillddrreenn wwaass sseelleecctteedd,, ddaattaa aabboouutt tthheeiirr
aaggee iinn yyeeaarrss aanndd wweeiigghhtt iinn kkiillooggrraammss wwaass rreeccoorrddeedd aass
sshhoowwnn iinn tthhee ffoolllloowwiinngg ttaabbllee .. IItt iiss rreeqquuiirreedd ttoo ffiinndd tthhee
ccoorrrreellaattiioonn bbeettwweeeenn aaggee aanndd wweeiigghhtt..
serial
No
Age
((years
Weight
((Kg
1 7 12
2 6 8
3 8 12
4 5 10
5 6 11
6 9 13

33. Tasks
1. State the research question!
2. State the hypothesis for correlation!
3. Collect data in a table!
4. Calculate the data by using Pearson Product
Moment!
5. Determine the degree of relationship!
6. Decide whether accept(retain) or reject the
null hypothesis!
7. State the interpretation!

34. These 2 variables are ooff tthhee qquuaannttiittaattiivvee ttyyppee,, oonnee
vvaarriiaabbllee ((AAggee)) iiss ccaalllleedd tthhee iinnddeeppeennddeenntt aanndd
ddeennootteedd aass ((XX)) vvaarriiaabbllee aanndd tthhee ootthheerr ((wweeiigghhtt))
iiss ccaalllleedd tthhee ddeeppeennddeenntt aanndd ddeennootteedd aass ((YY))
vvaarriiaabblleess ttoo ffiinndd tthhee rreellaattiioonn bbeettwweeeenn aaggee aanndd
wweeiigghhtt ccoommppuuttee tthhee ssiimmppllee ccoorrrreellaattiioonn ccooeeffffiicciieenntt
uussiinngg tthhee ffoolllloowwiinngg ffoorrmmuullaa::

35. Tasks
1. State the research question!
2. State the hypothesis for correlation!
3. Collect data in a table!
4. Calculate the data by using Pearson Product
Moment!
5. Determine the degree of relationship!
6. Decide whether accept(retain) or reject the
null hypothesis!
7. State the interpretation!

36. ::EExxaammppllee
AA rreesseeaarrcchheerr iiss ttoo rreesseeaarrcchh tthhee ccoorrrreellaattiioonn bbeettwweeeenn
AAnnxxiieettyy aanndd TTeesstt SSccoorreess.. HHee ccoolllleecctteedd tthhee ssccoorreess aass
ffoolllloowwss::
AAnnxxiieettyy ((XX)) ::1100,, 88,, 22,, 11,, 55,, 66
TTeesstt ssccoorree((YY)) :: 22,, 33,, 99,, 77,, 66,, 55
1. State the research question!
2. State the hypothesis for correlation!
3. Collect data in a table!
4. Calculate the data by using Pearson Product Moment!
5. Determine the degree of relationship!
6. Decide whether accept(retain) or reject the null
hypothesis!
7. State the interpretation!

37. RReeffeerreenncceess Main Sources
Coolidge, F. L.2000. Statistics: A gentle introduction. London: Sage.
Kranzler, G & Moursund, J .1999. Statistics for the terrified. (2nd ed.). Upper Saddle
River, NJ: Prentice Hall.
Butler Christopher.1985. Statistics in Linguistics. Oxford: Basil Blackwell.
Hatch Evelyn & Hossein Farhady.1982. Research design and Statistics for Applied Linguistics.
Massachusetts: Newbury House Publishers, Inc.
Ravid Ruth.2011. Practical Statistics for Educators, fourth Ed. New York: Rowman &
Littlefield Publisher, Inc.
Quirk Thomas. 2012. Excel 2010 for Educational and Psychological Statistics: A Guide
to Solving Practical Problem. New York: Springer.
Other relevant sources
Agresi A, & B. Finlay.1986. Statistical methods for the social sciences. San Francisco,
CA: Dellen Publishing Company.
Bachman, L.F. 2004. Statistical Analysis for Language Assessment. New York: Cambridge University
Press.
Field, A. (2005). Discovering statistics using SPSS (2nd ed.). London: Sage.
Moore, D. S. (2000). The basic practice of statistics (2nd ed.). New York: W. H.
Freeman and Company.
Thursday, December 4, 2014