- A second ANOVA examined if nightly expenditure varied across income levels. - The ANOVA results were significant, finding differences in nightly spending across incomes. - Post-hoc tests showed those in the highest income spent significantly more per night than those in lower income categories, as expected.

1. Multivariate Analysis

2. Difference Between F & T Test
T-test is used to estimate population parameter, i.e. population mean, and is also used
for hypothesis testing for population mean. Though, it can only be used when we are
not aware of population standard deviation. If we know the population standard
deviation, we will use Z-test.
F-test is used for finding out whether there is any variance within the samples. F-test is
the ratio of variance of two samples.
Eg. Suppose, in a manufacturing plant there are 2 machines producing same products, and the management
wants to understand, whether there is any variability among the products produced by these two machines.
Researcher will take samples from both the machines and find out the variability, and test it against the null
hypothesis, i.e. the prescribed limit.
F-statistic also forms the basis for ANNOVA.
In regression hypothesis testing the difference is most prominent. T statistic is used to
test the significance of individual coefficients and F-statistic is used to test the overall
significance of the model.

4. What is meant by T-test?
• The t-test compares the actual difference
between two means in relation to the
variation in the data (expressed as the
standard deviation of the difference between
the means).

5. One-Sample T-test
• The one-sample t-test allows us to test whether a sample
mean is significantly different from a population mean. When
only the sample standard deviation is known. Simply, when to
use the one-sample t-test, you should consider using this test
when you have continuous data collected from group that you
want to compare that group’s average scores to some known
criterion value (probably a population mean).
• Often performed for testing the mean value of distribution.
• It can be used under the assumption that sample distribution
is normal.
• For large samples, the procedure performs often well even for
non-normal population.

27. A two tailed paired T test was carried out to test the
difference between the “Inn1” and “Inn2” condition for
significance. Mean value of Inn1 significantly different
than Inn2 t(349)=7.219, p< 0.000
Gain in mean score=0.50571

29. ANOVA: ANALYSIS OF
VARIANCE

30. Analysis of Variance: ANOVA
• One-way ANOVA is a generalised version of the
independent samples t-test: it examines
differences among three or more groups on a
quantitative/numerical
variable.
(numerical/interval/ratio)
•
•
ANOVA stands for analysis of variance.
After ANOVA is conducted, one must determine
which groups differ significantly using post-hoc
or multiple comparisons tests.

31. ANOVA: NOTE
• You have to select a test of homogeneity of
variance to examine equal variances.
• You have then to choose a post-hoc based on
whether equal variances are assumed (Scheffe),
and one based on whether equal variances are
not assumed (Games-Howell).
• Based on results of test of homogeneity of
variance, you will select the more suitable post-
hoc test, if a significant ANOVA result is found.

32. ANOVA Question
• ASK THESE QUESTIONS:
¾How many variables?
¾Which one is the independent variable,
and which one is the dependent variable?
¾What types of variables are they?
¾ ANOVA appropriate?

33. Post-hoc Tests
• Post-hoc tests allow you to determine where
significant differences lie.
When the ANOVA is found
• to be significant, one
must examine which two groups differ
significantly from the total number of groups: so
post-hoc tests look at mean differences between
different
Jamaican,
pairs: e.g. given three groups:
Barbadian, Grenadian, you will
examine differences such as Jamaican versus
Grenadian, Grenadian versus Barbadian, and
Barbadian versus Jamaican.

34. Post hoc tests
• There are many post-hoc tests to choose from
when doing an ANOVA.
Post-hoc tests are done based on whether equal
•
variances are assumed, or not. This assumption
is also for ANOVA (like the t-test).
• The Scheffe post-hoc test should be selected
Games-
if not.
when equal variances assumed but the
Howell post-hoc test should be selected

35. Doing ANOVA
• Using tourism data1:
Does overall satisfaction with the destination
experience vary by age of tourist?
2 variables: satisfaction with destination and
age.
Independent variable = age
Dependent variable
destination
= overall satisfaction with
Age is categorical with more than 2 categories,
and satisfaction is quantitative/numerical.

36. Descriptives
Overall satisfaction with the destination
• The first table in the ANOVA output is similar to that
of the descriptive stats table from the t-test. It shows
the means and standard deviations for each age
group. Mean satisfaction scores based on a five-
point scale ranging from 1(very dissatisfied) to 5
(very satisfied).
N Mean Std. Deviation Std. Error
95% Confidence Interval for
Mean
Minimum Maximum
Lower Bound Upper Bound
18 - 25
26 - 40
41 - 60
Over 60
Total
14
95
134
19
262
3.86
4.03
3.84
3.11
3.86
1.167
.818
.949
1.049
.946
.312
.084
.082
.241
.058
3.18
3.86
3.68
2.60
3.74
4.53
4.20
4.01
3.61
3.97
2
1
1
1
1
5
5
5
5
5

37. Test of Homogeneity of Variances
Overall satisfaction with the destination
• This table (Levene’s test) tests the assumption of
equal variances for the ANOVA – this is the same
assumption found in the t-test but in another table.
Look at the sig. or p-value - the value is .175 which
is above .05. The result indicates that equal
variances assumption is met.
Levene
Statistic df1 df2 Sig.
1.664 3 258 .175

38. • This is the post-hoc tests to see where the differences lie.
You have to focus on the Scheffe post hoc test as the
Levene’s test revealed equal variances (p = .175). You can
see that those over 60 differed significantly from those 26-40,
and 41-60 – they (60+) had significantly lower satisfaction
Multiple Comparisons
Dependent Variable: Overall satisfaction with the destination
(I) Age (J) Age
Mean
Difference
(I-J) Std. Error Sig.
95% Confidence Interval
Lower Bound Upper Bound
Scheffe 18 - 25 26 - 40
41 - 60
Over 60
-.174
.014
.752
.264
.259
.325
.933
1.000
.151
-.92
-.72
-.16
.57
.74
1.67
26 - 40 18 - 25
41 - 60
Over 60
.174
.188
.926*
.264
.124
.232
.933
.512
.001
-.57
-.16
.27
.92
.54
1.58
41 - 60 18 - 25
26 - 40
Over 60
-.014
-.188
.738*
.259
.124
.226
1.000
.512
.015
-.74
-.54
.10
.72
.16
1.38
Over 60 18 - 25
26 - 40
41 - 60
-.752
-.926*
-.738*
.325
.232
.226
.151
.001
.015
-1.67
-1.58
-1.38
.16
-.27
-.10
Games-Howell 18 - 25 26 - 40
41 - 60
Over 60
-.174
.014
.752
.323
.323
.394
.948
1.000
.249
-1.11
-.92
-.33
.76
.94
1.83
26 - 40 18 - 25
41 - 60
Over 60
.174
.188
.926*
.323
.117
.255
.948
.378
.007
-.76
-.12
.22
1.11
.49
1.63
41 - 60 18 - 25
26 - 40
Over 60
-.014
-.188
.738*
.323
.117
.254
1.000
.378
.038
-.94
-.49
.03
.92
.12
1.44
Over 60 18 - 25
26 - 40
41 - 60
-.752
-.926*
-.738*
.394
.255
.254
.249
.007
.038
-1.83
-1.63
-1.44
.33
-.22
-.03
*. The mean difference is significant at the .05 level.

39. ANOVA: Details
• Include the following information in your write-
up:
Means and standard deviations of both groups
(needed when significant difference found)
F-statistic, Between groups df and Within groups
df, and p-value.
Interpretation from the post-hoc tests used;
remember the post-hoc test used is dependent
on the Levene’s test being significant or not.
•
•
•

40. ANOVA Write-up
Sample write-up below:
•
• “A one-way ANOVA was conducted to examine
whether there were statistically significant
differences among tourists in different
relation to their satisfaction with the
age groups
destination.
significant
The results revealed statistically
differences among the age groups, F (3, 258) =
5.34, p = .001. Post-hoc Scheffe tests revealed
statistically significant differences between tourists
over 60 years (M =3.11, SD = 1.05), and those 41-
60 (M = 3.84, SD = .95) and those 26-40 (M =
4.03, SD= .82). Tourists 26-40 yrs and 41-60 yrs
reported significantly higher satisfaction with the
destination compared with tourists over 60 years.
There were no other significant differences
between the other groups”.

41. More ANOVA
• Using tourism data1:
Answer the following questions:
Does satisfaction with prices at the
destination vary across tourists in
income categories.
different
Does
night
total
vary
expenditure per person per
across tourists in different
income categories.