This document provides an overview of inferential statistics and statistical tests that can be used, including correlation tests, t-tests, and how to determine which tests are appropriate. It discusses the assumptions of parametric tests like Pearson's correlation and t-tests, and how to check assumptions graphically and using statistical tests. Specific procedures for conducting correlation analyses in Excel and SPSS are outlined, along with how to interpret and report the results.

1. Inferential
Statistics
Research Methods

2. Outline
• What Statistical Tests to Use?
• Correlation Tests
• t-Tests
• To play around with the data, please download
the file: Statistics-Inferential.xlsx
 Download from https://goo.gl/eY8j6N or
http://www.filehosting.org/file/details/491184/Statist
ics-Inferential.xlsx
 Scan the QR code or

3. What
Statistical
Tests to Use?

4. Decision on the Statistical Tests
• Depends on
 The design of the research
• To see the relationship of the variables?
• To see if there are any changes in the participants
after certain treatment?
• Etc.
 Can the results be generalized?
• Assumptions – conclusions – actions

5. Why checking assumptions?
• Assumption is important
 assumption  conclusion  action
 Correct assumption  correct conclusion 
correct action

6. Case: I couldn’t meet Ast today at 1.30 PM
• Assumptions
 12-1 PM  official lunch time in SWCU
 Everybody needs lunch
 Classes at FLL usually go from 11 AM – 1 PM then
from 2-4 PM
• Conclusions
 Every lecturer in SWCU will have lunch at 12-1 PM
 Every lecturer may teach 11 AM – 1 PM then from 2-4
PM
• Action
 See Ast between 1-2 PM

7. But…
• Assumptions
 Ast hates me for God knows what reasons
• Conclusions
 He will not see me at all
• Action
 That’s probably why he refuses to see me at 1.30
PM today.

8. How do you know your assumptions are right?
• It’s regulation/convention
 But are you sure it’s regulated in SWCU and FLL?
• It’s what usually happens in SWCU and FLL
 Offices are closed between 12-1 PM
 Lecturers are seen at campus cafes having lunch
during 12-1 PM
 Schedule of classes
• Where did your assumption go wrong?
 How can you be so sure that Ast hates you?

9. What has Ast to do with ResMeth?
• Assumption must be correct, otherwise the
conclusion will not be correct
• What made your conclusion wrong in the
case of Ast?
 Feelings and not what NORMALLY happens
either by regulation/convention in the
POPULATION (SWCU/FLL)
• Remember NORMAL DISTRIBUTION?

10. Looking back at previous meetings…
• The aim of doing quantitative research is to
generalize the results for the population
• Assumption
 Population  normal distribution
 Sample  normal distribution
• Conclusion
 If my sample is normally distributed, I can expect to
generalize it to the population
• Action
 My research recommendations can be applied in the
population

11. Parametric vs. Non-Parametric Tests
• Some statistical tests are parametric tests based on
the normal distribution
• A parametric test  requires parametric data from
one of the large catalogue of distributions that
statisticians have described (regulation/convention)
• Parametric data  certain assumptions must be
true.
 A parametric test for NON parametric data  inaccurate
results
• very important  check the assumptions before
deciding which statistical test is appropriate

12. Correlation
Tests

13. • Positively related  one up, the other up
• Not related at all  same no matter what
• Negatively related  one up, the other
down
How 2 variables could be related?

14. Correlational Tests
• Parametric Test
 Pearson’s Product Moment Correlation
• Non-Parametric
 Spearman’s Correlation Coefficient
 Kendall’s tau (τ)
• To decide:
 Check the assumptions
 1 assumption violated  non-parametric

15. What are the underlying assumptions?
1. Related pairs
2. Scale of measurements
3. Normality
4. Linearity
5. Homoscedasticity
Testing:
1 & 2  design of the research
3-5  testable using graphic & tests

16. Related Pairs
• Data must be collected from related pairs
• 1 data from one variable, 1 data from the
other variable
• E.g. Relationship between gender and
English competence
 Arif has data for gender “male” and for English
competence “84 points”

17. Scale of Measurements
• Interval or ratio
• Do you still remember what they are?
 Continuous
 Not categorical
• E.g. Arif
 Gender  nominal (categorical)
 Competence  ratio (continuous)
• One assumption violated!
 Go to non-parametric (Spearman’s or Kendall’s)

18. Warning!
• Difference in literature
 Coakes (2005)  both variables must be
continuous - interval
 Field (2009)  interval or one variable can be
categorical – binary
• I’m inclined to Coakes
 The scatterplot when one variable is interval and
the other is binary is not homoscedasticity (I’ll
show you later why this matters)

19. Normality
• In MSExcel – (complicated!)
 Histogram
0
2
4
6
8
10
12
14
46 47 52 74 79
Series1
Poly. (Series1)

20. Normality & Linearity
• In SPSS (relatively easier)
 Together with descriptive statistics report &
linearity
• Test by:
 Graphic
 Normality tests

21. Normality and Linearity
• Analyze | Descriptive Statistics | Explore
 Select the variable you want to test
 Statistics: tick
• Descriptives
 Plots: tick
• Histogram
• Normality plots with tests

22. Normality
• From Kolmogorov-Smirnov (K-S) & Shapiro-Wilk
(S-W)
 Sig. <.05  significantly different from normal
distribution
 competence sig. = .008 <.05  data not normal
 Shapiro – Wilk is more powerful (maybe K-S sig, S-W
not sig.)

23. Normality
• Graphic – Histogram
 not bell-shaped  not
normal
• Psst.. Normality line
here is added as a
guide.
 How? Try right clicking
the graphic & edit the
content. Find this icon
in the bar:

24. Normality
• Is your data normally distributed?
0
2
4
6
8
10
12
14
46 47 52 74 79
Series1
Poly. (Series1)

25. Linearity
• How your data for
each variable falls
in a linear line
• MS Excel – not
possible
• SPSS – yes!
 See the test of
normality

26. Homoscedascity
• How your data clustered into certain areas
when two variables are related
• To see if they have similar variance along
the linear line
• Why this is important?
 Not wide difference between data
 Too wide --> not normal

27. Homoscedasticity
• MS Excel – not possible
• SPSS – yes!
 Graph | Legacy Dialogs |
Scatter/Dot | Simple Scatter
 Choose the two variables for
X axis and Y axis
• Psst.. Linear line here is
added as a guide.
 How? Try right clicking the
graphic & edit the content.
Find this icon in the bar:

28. Homoscedasticity
Gender vs. Competence
• Heteroscedasticity
• Not normal
Competence vs. Graduation
• Homoscedasticity
• Maybe normal
Can’t do categorical variable!
Coakes wins!

29. Once you’ve done all of this assumption checking…
• Select the correlational test the data falls
into
• Our correlational tests are bivariate
correlation
 Between 2 variables
• We’re not dealing with partial correlation
(between 2 variables plus one or more
controlling variables)  later when you’re
more ‘grown up’ in statistics

30. • Pearson product-moment correlation
(standardized measurement)
 Symbol : r or R
 -1 to +1
 To measure size of the effect
• ± 0.1  small effect
• ± 0.3  medium effect
• ± 0.5  large effect
•
How do we measure relationships?

31. Pearson’s Correlation Coefficient
• Using MS Excel – Data | Data Analysis |
Correlation
• Downsides
 Only for Pearson’s, not Spearman’s or Kendall’s
 No indicator of significance of relationship
 Only the strength of correlation coefficient
Competence Graduation
Competence 1
Graduation 0.954149422 1

32. • Analyze | Correlate |
Bivariate
• Input the variables
used in Variables
• Default: Pearson
• Options: Spearman
and Kendall
• One- vs. two-tailed
 One-tailed 
directional
hypothesis (the more
x, the more y)
 Two-tailed  not
sure
Bivariate Correlation (Using SPSS)

33. • Interpretation of
the result table
 ** significant
correlation
 r value  Pearson
Correlation value
 Significant or not
 Sig. <.05
• What does this
numbers mean?
Pearson’s Correlation Coefficient

34. • Correlation result ≠ causality
• Third-variable problem
 Maybe there is an influence of third variable
• Direction of causality
 No clear indication which variable causes the
other variable to change
Warning: Causality!!!

35. • Non-parametric statistic
 Not normal data distribution, etc.
 Not interval data  ordinal data
• Interpretation of the result table
 ** significant correlation
 rs -- Correlation coefficient value
 Significant or not  Sig. <.05
Spearman’s Correlation Coefficient

36. • Non-parametric statistic
 Small data set which when it is ranked it has
many scores with the same rank
 More accurate generalization than Spearman’s
• Interpretation of the result table
 ** significant correlation
 τ – Correlation coefficient value
 Significant or not  Sig. <.05
Kendall’s tau (τ)

37. • Tell:
 How big
 Significant value
• Important Notes:
 No zero before the decimal point for correlation
coefficient (for example -- .87 NOT 0.87)
 Correlation coefficient in different letters (r, rs, or τ)
 One-tailed must be reported
 Standard criteria for p value (probabilities) -- .05, .01
and .001
How to Report Correlation Coefficients

38. • Pearson’s
 There is a significant correlation between X variable
and Y variable, r = .87, p (one-tailed) <.05
• Spearman’s
 X variable is significantly correlated with Y variable,
rs = .87 (p <.01)
• Kendall’s
 There was a positive relationship between X variable
and Y variable, τ = .47, p<.05
Example of Reports

39. t-Tests

40. What is it for?
• Looking at the effect(s) of one variable to
another
• By systematically changing some aspect of
that variable
• To compare two means of the data

41. Comparing 2 means of data
• Between-group, between-subjects or
independent design
 DIFFERENT participants to different
experimental manipulations
• A repeated-measures design
 SAME participants to different experimental
manipulations at different points in time

42. Comparing 2 Means Using t-Tests
Different participants
Between groups, between subjects, or independent
design
Single Sample
From one sample
compared to the
population
Test scores of a group in
a semester compared to
previous group’s scores
Independent or
Two- Sample
Two samples with
different conditions
Test scores of 2 groups
with different teachers
after a semester
Same participants
Repeated measures
design
Paired- or
Dependent sample
From two samples
of the same
condition
The scores of a group
before and after a
semester

43. Assumptions of the t-tests
1. Scale of Measurement – continuous interval
2. Random sampling
3. Normality
4. Additional for Independent t-test
1. Independent of groups – inclusion into one group
only, and not the other group
2. Homogeneity of variance – Levene’s test
(presented in SPSS results for independent t-test)

44. Single Sample t-Test
• Comparing the mean of a
data set with a set means
of other aggregate data
• MS Excel  no!
• SPSS  Analyze |
Compare Means | One
Sample t-Test
 Input the Test Variable
compared
 Input the Test Value
(aggregate data)

45. Single Sample t-Test: Results & Report
• Reporting:
There is no significant difference in the graduation grade
between this year’s participants with previous year’s
participants ( t(19) = .493, p>.05), although this year’s
participants have slightly higher grade (Mean Difference =
1.4)
Significant  sig. <.05
t positive  this data > previous aggregate data

46. Using MS Excel for Other t-Tests
• Only for
 Paired-sample T-Test
 Independent T-Test
• Assuming equal variance
• Assuming non-equal variance
 Reject or accept the null hypothesis  there is
no difference of means in the two variables

47. Paired-Samples t-Test
• Comparing the means of the same group
participants under two conditions
• Samples  two sets of data, but paired
(from the same participants)
• E.g. The pre-test vs. post-test scores of a
group participants
• E.g. The scores of a group participants after
being taught using picture vs. film

48. Paired-Sample t-Test in MSExcel
• H0 = there is no difference
between the two groups
• Data | Data Analysis | t-
Test: Paired two Sample
for Means | Select Variable
1 & 2 | Select Output
Range
• P (T<=) two-tail <t Critical
two-tail = reject H0
 What’s the result?
• t Stat is minus 
the pre (competence) <the post (graduation)

49. Paired-Samples t-Test in SPSS
• Analyze | Compare
Means | Paired-
Samples T-Test |
Input the two
variables

50. Results
• Paired-Samples Statistics
• Paired-Samples Correlations
 Pearson’s  r and sig. (r  see effect,
significant  <.05)
• Paired-Samples Test
 Mean = difference of means between groups
 t value = minus  first variable has smaller mean
 df = sample size – 1 (degree of freedom)
 Sig. = significant  p <.05

51. Results
Pearson’s r
significant  sig. <.05
Correlation  size of
effect
significant  sig. <.05
t minus  first variable has smaller mean

52. Reporting on Results
On average, the participants has significantly
higher scores on variable graduation grade (M=
71.40, SE = 2.001), than on variable competence
score (M= 67.95, SE = 2.328, t(19) = .00, p<.05)
with large effect r = .954)
 Legend
• M – mean
• SE – standard error
• t (19) – df
• r – this formula (large effect)

53. Independent T-test
• Compare the means of two groups’ participants
in two different conditions
• The groups are independent of each other
 MS Excel – always assume unequal variances or
do F-Test Two Sample for Variance to decide if they
are equal/unequal, then choose appropriate
independent t-test
 SPSS -- checked using Levene’s test in the results of
independent t-test
• E.g. the scores of two groups’ participants after
being taught using pictures vs. film

54. Independent T-test using MSExcel
• Data | Data Analysis | t-Test:
Two-Sample Assuming
Unequal Variances | Select
Variable 1 & 2 (by group) |
Select Output Range
• H0 = there is no difference
between the two groups
• P (T<=) two-tail <t Critical
two-tail = reject H0
 What’s the result?
• t Stat is minus 
Pictures group < film group

55. Independent T-test Using SPSS
• Analyze | Compare
Means |
Independent-
Samples t-Test |
Insert the test
variable & grouping
variable

56. Results
• Group Statistics
• Independent Samples Test
 Homogeneity of Variances using Levene’s test –
should be NOT significant (groups are similar)  sig
>.05  See sig. of equal variances assumed
(otherwise See not assumed)
 Mean = difference of means between groups
 t value = minus  first group has smaller mean
 df = sample size – 1 (degree of freedom)
 Sig. = significant  p <.05

57. Results
Sig. > .05  group is similar
(good!)  equal variances
assumed
significant  sig. >.05
Mean Difference minus  first group
has smaller mean

58. Reporting on Results
• On average, participants that were taught
using film had higher scores (M=72,
SE=2.921), than those taught using pictures
(M=70.80, SE=2. 878). This difference was
not significant t(18)=-.773, p>.05.
• Legend – same as in dependent t-test

59. Confused?
• Ask now 
• Ask me – F 505 by appointments
• Email me – neny@staff.uksw.edu
• Twit me -- @nenyish
• This presentation file is available at: