The document summarizes the results of a statistical analysis conducted on data from a coffee tasting study. The study examined the influence of coffee bean origin and participant age on taste scores, differences in caffeine content between coffee species, and the effect of age on daily coffee consumption. It was found that coffee bean origin and participant age both influence taste scores. Peru was the most preferred origin overall. Caffeine content differed between species but further analysis was needed. Daily coffee consumption varied most between middle-aged and older participants.

1. Applied Statistics
Prof. Dr. Ir. O. Thas
Group Project
Ameril, Camar (01305028)
Herzallah, Mohammed (01303232)
Ludevese, Christine (01307342)
Nicomel, Nina Ricci (01302593)
Rifai, Ridwan (01302922)
2013 – 2014

2. 1. Statistical Methodology
Being one of the well-known beverages and one of the most important commodities, coffee
has gained its place in the global market. Its taste serves as the primary indicator of the preference of
the consumers. With this, companies involved in coffee marketing are interested in a great number
of factors that may affect the taste of the coffee.
In one case study, a company organized a tasting session in which 40 women were invited to
taste one cup of coffee with distinct characteristics. The participants were requested to give a taste
score to the cup of coffee on a scale of 1 to 20. Additionally, they were asked regarding their age (in
years) and their average coffee consumption per day (in cups). The researchers also have collected
data on the coffee samples and these included the caffeine content of each cup of coffee (in
milligrams), the origin of the coffee beans (i.e. Bolivia, Brazil, Columbia, Peru), the roasting time of
the coffee beans (in minutes), and the species of the coffee plant (i.e. Coffea arabica or Coffea
robusta). It is of primary interest to determine the following: (1) influence of the origin of the coffee
beans and the age of the participants on the taste score; (2) occurrence of the difference in the caffeine
content of the C. arabica and C. robusta plant species and (3) the effect of age on the average coffee
consumption per day of the participants.
Prior to performing any statistical analyses, assumptions on the normality of the residuals or
observations and equality of group variances were assessed using Kolmogorov-Smirnov (KS) test
(with supporting QQ plots) and Modified Levene test, respectively. Two-way Analysis of Variance
(ANOVA) was used to evaluate Question 1 since the influence of two independent variables (i.e.
origin of the coffee beans and age of the participants) on the taste score needs to be examined.
Subsequently, assessments were made whether there is an interaction between the two independent
variables. To find the differences within each factor, Tukey test was used with a family-wise error
rate equal to 5%. As for Question 2, the dataset was first split to assess the assumptions since there
are two species of coffee plant involved. Since it was known that the normality assumption was not
fulfilled and that the data is homoscedastic, Wilcoxon rank-sum test was used for evaluation. Oneway ANOVA was used in Question 3 given that the influence of only one independent variable (i.e.
age) on the average coffee consumption per day of the participants needs to be determined.
All tests were done at a 5% level of significance using TIBCO Spotfire S+ software.
2. Results and Comments
2.1. Question 1
Data points on the QQ plot of the residuals (Figure 1) were alternately found below and above
the line. This may indicate some degree of skewing. For verification, KS test was performed and this
confirmed non-normality with p-value equal to 0.0081 (Table 1). However, since the number of
observations is greater than 30, the Central Limit Theorem may apply and the normality can be
assumed. As for the homoscedasticity assumption, Modified Levene test confirmed the equality of
the variances with p-value equal to 0.7993 (Table 2). Since the assumptions were fulfilled, ANOVA
was then performed to answer Question 1.
Considering Table 3, there is an influence of the origin of the coffee beans and age of the
participants on the taste score since p-values are much less than 0.05. The interaction term is also
significant with p-value equal to 0.0486. This can be supported by the interaction plot (Figure 2)
since the generated lines are not parallel to each other. This means that the influence of the origin of
the coffee beans on the mean taste score depends on the age of the participant and vice versa. Because
of the interaction term, both independent variables must be assessed separately to find the differences.
In Tables 4, 5 and 6, the influence of the origins on the mean taste score was assessed according to
the three age classes. For people younger than 40 years (age class A), there is no significant effect of
origin on the mean taste score. For people aged 40 or older but younger than 60 years (age class B),
only significant differences between (1) Bolivia and Columbia and (2) Brazil and Columbia were
observed. For people aged 60 years or older (age class C), significant differences between (1) Bolivia
and Brazil, (2) Brazil and Columbia and (3) Brazil and Peru were observed. In Tables 7, 8, 9 and 10,
the influence of the age classes on the mean taste score was assessed according to the four origins.
For Bolivia, there is a significant difference between age class B and age class C. For Brazil,

3. significant differences between (1) age class A and age class B and (2) age class A and age class C
were observed. For Columbia, only significant difference between age class A and age class C was
observed. For Peru, there is no significant effect of age class on the mean taste score. From these
results, it can be deduced where the researchers should source their coffee beans from, which is Peru.
This is because regardless of the age of the coffee consumer, same taste score will be given as long
as the origin of the coffee beans is Peru.
2.2. Question 2
The normality of the observations for C. arabica and C. robusta were assessed separately. By
observing the generated QQ plots (Figure 3) and box plots (Figure 4) for both plant species, it is clear
that the observations for C. robusta are normally distributed while those of C. arabica are not. This
can be supported by KS tests (Tables 11 and 12) wherein p-values of 0.5 and 0 were obtained for C.
robusta and C. arabica, respectively. With this, normality assumption was not fulfilled. As for the
homoscedasticity assumption, Modified Levene test revealed that variances of the groups are equal
with p-value equal to 0.6697864 (Table 13). In this case, Wilcoxon rank-sum test was performed and
this showed that HO must be rejected at a 5 % level of significance. Based on this sample, the mean
caffeine content of C. arabica is greater than the mean caffeine content of C. robusta. However, with
p-value equal to 0.0338, it can be inferred that the conclusion is not strong, thus, further analyses
should be done before suggesting which species of coffee should be marketed.
2.3. Question 3
QQ plot of the residuals (Figure 5) clearly shows that residuals do not follow a normal
distribution. For verification, KS test was performed and this confirmed non-normality with p-value
equal to 0.0188 (Table 15). However, since the number of observations is greater than 30, the Central
Limit Theorem may apply and the normality can be assumed. As for the homoscedasticity
assumption, Modified Levene test confirmed the equality of the variances with p-value equal to
0.6697 (Table 16). Since the assumptions were fulfilled, ANOVA was then performed to answer
Question 3.
From Table 17, it can be strongly inferred that at least one age class results in a different
average frequency of coffee consumption per day. At a 5% family-wise level of significance, there
is significant difference between the mean frequency of coffee consumption per day of (1) age class
B and age class C and (2) age class A and age class B. We are 95% family-wise confident that when
the age class is B, the mean frequency of coffee consumption per day will be between 1.38 and 3.53
cups more than when the age class is C. Same interpretation can be done for age class A and age
class B. Moreover, it can also be known from the estimates in Table 17 that the most interesting age
group target is B, followed by C, then by A.
3. Executive Summary
As general remarks, by performing statistical analyses, the researchers concluded that there
is an influence of the origin of the coffee beans and the age of the participants to the taste of the
coffee. The younger age group (i.e. participants younger than 40 years) does not discriminate the
origin of the coffee beans. However, for the middle age group (i.e. participants aged 40 of older but
younger than 60 years) and the older age group (i.e. participants aged 60 or older), the origin of the
coffee beans is a significant factor that affects the taste of the coffee. It is further suggested that Peru
as the origin of coffee beans is the most preferred source.
The mean caffeine content of a more expensive C. arabica is higher than the mean caffeine
content of a cheaper C. robusta. Yet, at 5% level of significance, it is suggested that further analyses
should be done before recommending what species should be the best one for manufacturing coffee
beverage.
The age group of the consumer is important to consider for the marketability of the coffee
product. The middle age group (40 to 59 years old) is the most interesting target consumer since they
are relatively highest in the frequency of consumption. The second interesting one is the older age
group (60 years old and above) and the third interesting group is the younger age group (39 years old
and below) having the higher and lowest frequency of consumption of coffee, respectively.

4. 4. Appendices
4.1. Appendix 1: S+ outputs for Question 1
4.1.1. Assessment of normality assumption
To assess the normality assumption, the Kolmogorov-Smirnov test was used. In this test, the
residuals were considered since the number of observations for each origin is 10, which is a relatively
small number. Additionally, the QQ plot of the residuals was obtained and considered.
H0: Residuals follow a normal distribution.
H1: Residuals do not follow a normal distribution.
Table 1. S+ output of Kolmogorov-Smirnov test.
One sample Kolmogorov-Smirnov Test of Composite Normality
data: residuals in coffee.data
ks = 0.1644, p-value = 0.0081
alternative hypothesis: True cdf is not the normal distn. with estimated
parameters
sample estimates:
mean of x standard deviation of x
0
2.213208
22
0
-4
-2
Residuals
2
4
27
5
-2
-1
0
1
2
Quantiles of Standard Normal
Figure 1. QQ plot of the residuals.
4.1.2. Assessment of homoscedasticity assumption
To assess the homoscedasticity assumption, Modified Levene test was used.
H0: Variances of all groups are equal.
H1: Variances of all groups are not equal.
Table 2. S+ output of Modified Levene test.
***
Modified Levene test ***
Df Sum of Sq Mean Sq F Value
Pr(F)
groep 10
22.675 2.267500 0.601624 0.7993811
Residuals 29
109.300 3.768966

5. 4.1.3. Assessment of interaction effects
H0: There is no interaction between origin and age for average taste score.
H1: There is an interaction between origin and age for average taste score.
Table 3. S+ output of the two-way ANOVA for the interaction assessment.
*** Analysis of Variance Model ***
Short Output:
Call:
aov(formula = taste ~ origin * ageclass, data = coffee.data, na.action =
na.exclude)
Terms:
origin ageclass origin:ageclass Residuals
Sum of Squares 384.0750 194.2043
84.4623 191.0333
Deg. of Freedom
3
2
5
29
Residual standard error: 2.566585
1 out of 12 effects not estimable
Estimated effects may be unbalanced
20
Type III Sum of Squares
Df Sum of Sq Mean Sq F Value
Pr(F)
origin 3 309.5743 103.1914 15.66508 0.00000303
ageclass 2 190.2823 95.1412 14.44300 0.00004441
origin:ageclass 5
84.4623 16.8925 2.56438 0.04868222
Residuals 29 191.0333
6.5874
ageclass
15
10
5
mean of taste -- 0 NA's
21.99+ thru 39
39.00+ thru 59
59.00+ thru 70
Bolivia
Brazil
Columbia
Peru
origin
Figure 2. Interaction plot for origin and age class.

6. 4.1.4. Effects of origin of the coffee beans on the taste score of participants younger than 40
years
H0: There is no effect of the origin of the coffee beans on the taste score of participants younger than
40 years.
H1: There is an effect of the origin of the coffee beans on the taste score of participants younger than
40 years.
Table 4. S+ output of the one-way ANOVA for effects of origin of the coffee beans on the taste
score of participants younger than 40 years.
*** Analysis of Variance Model ***
Short Output:
Call:
aov(formula = taste ~ origin, data = coffee.data.21.99..thru.39, na.action =
na.exclude)
Terms:
origin Residuals
Sum of Squares 54.85714 32.00000
Deg. of Freedom
2
4
Residual standard error: 2.828427
Estimated effects may be unbalanced
Type III Sum of Squares
Df Sum of Sq Mean Sq F Value
Pr(F)
origin 2 54.85714 27.42857 3.428571 0.1357341
Residuals 4 32.00000 8.00000
95 % simultaneous confidence intervals for specified
linear combinations, by the Tukey method
critical point: 3.5638
response variable: taste
intervals excluding 0 are flagged by '****'
Estimate Std.Error Lower Bound Upper Bound
Brazil-Columbia 8.00e+000
3.27
-3.64
19.60
Brazil-Peru 8.00e+000
3.27
-3.64
19.60
Columbia-Peru 8.44e-015
2.31
-8.23
8.23

7. 4.1.5. Effects of origin of the coffee beans on the taste score of participants aged 40 or older but
younger than 60 years
H0: There is no effect of the origin of the coffee beans on the taste score of participants aged 40 or
older but younger than 60 years.
H1: There is an effect of the origin of the coffee beans on the taste score of participants aged 40 or
older but younger than 60 years
Table 5. S+ output of the one-way ANOVA for effects of origin of the coffee beans on the taste
score of participants aged 40 or older but younger than 60 years.
*** Analysis of Variance Model ***
Short Output:
Call:
aov(formula = taste ~ origin, data = coffee.data.39.00..thru.59, na.action =
na.exclude)
Terms:
origin Residuals
Sum of Squares 216.3333 120.6167
Deg. of Freedom
3
16
Residual standard error: 2.74564
Estimated effects may be unbalanced
Type III Sum of Squares
Df Sum of Sq Mean Sq F Value
Pr(F)
origin 3 216.3333 72.11111 9.565658 0.0007429687
Residuals 16 120.6167 7.53854
Estimated Coefficients:
(Intercept) originBrazil originColumbia originPeru
15.5
-0.9
-9.166667
-4.75
95 % simultaneous confidence intervals for specified
linear combinations, by the Tukey method
critical point: 2.861
response variable: taste
intervals excluding 0 are flagged by '****'
Bolivia-Brazil
Bolivia-Columbia
Bolivia-Peru
Brazil-Columbia
Brazil-Peru
Columbia-Peru
Estimate Std.Error Lower Bound Upper Bound
0.90
1.57
-3.5800
5.38
9.17
1.86
3.8500
14.50 ****
4.75
1.68
-0.0603
9.56
8.27
2.01
2.5300
14.00 ****
3.85
1.84
-1.4200
9.12
-4.42
2.10
-10.4000
1.58

8. 4.1.6. Effects of origin of the coffee beans on the taste score of participants aged 60 or older
H0: There is no effect of the origin of the coffee beans on the taste score of participants aged 60 or
older.
H1: There is an effect of the origin of the coffee beans on the taste score of participants aged 60 or
older.
Table 6. S+ output of the one-way ANOVA for effects of origin of the coffee beans on the taste
score of participants aged 60 or older.
*** Analysis of Variance Model ***
Short Output:
Call:
aov(formula = taste ~ origin, data = coffee.data.59.00..thru.70, na.action =
na.exclude)
Terms:
origin Residuals
Sum of Squares 222.6603
38.4167
Deg. of Freedom
3
9
Residual standard error: 2.066039
Estimated effects may be unbalanced
Type III Sum of Squares
Df Sum of Sq Mean Sq F Value
Pr(F)
origin 3 222.6603 74.22009 17.38779 0.0004362847
Residuals 9
38.4167 4.26852
Estimated Coefficients:
(Intercept) originBrazil originColumbia originPeru
7
7.5
-2.75 0.6666667
95 % simultaneous confidence intervals for specified
linear combinations, by the Tukey method
critical point: 3.1219
response variable: taste
intervals excluding 0 are flagged by '****'
Bolivia-Brazil
Bolivia-Columbia
Bolivia-Peru
Brazil-Columbia
Brazil-Peru
Columbia-Peru
Estimate Std.Error Lower Bound Upper Bound
-7.500
1.79
-13.10
-1.91 ****
2.750
1.79
-2.84
8.34
-0.667
1.89
-6.55
5.22
10.300
1.46
5.69
14.80 ****
6.830
1.58
1.91
11.80 ****
-3.420
1.58
-8.34
1.51

9. 4.1.7. Effects of the age class of the participants on the taste score of coffee from Bolivia
H0: There is no effect of the age class of the participants on the taste score of coffee from Bolivia.
H1: There is an effect of the age class of the participants on the taste score of coffee from Bolivia.
Table 7. S+ output of the one-way ANOVA for effects of the age class of the participants on the
taste score of coffee from Bolivia.
*** Analysis of Variance Model ***
Short Output:
Call:
aov(formula = taste ~ ageclass, data = coffee.data.Bolivia, na.action =
na.exclude)
Terms:
Sum of Squares
Deg. of Freedom
ageclass Residuals
115.6
74.0
1
8
Residual standard error: 3.041381
Estimated effects may be unbalanced
Type III Sum of Squares
Df Sum of Sq Mean Sq F Value
Pr(F)
ageclass 1
115.6 115.60 12.4973 0.007674012
Residuals 8
74.0
9.25
95 % non-simultaneous confidence intervals for specified
linear combinations, by the Fisher LSD method
critical point: 2.306
response variable: taste
intervals excluding 0 are flagged by '****'
39.00+ thru 59-59.00+ thru 70
Estimate Std.Error Lower Bound Upper Bound
8.5
2.4
2.96
14 ****

10. 4.1.8. Effects of the age class of the participants on the taste score of coffee from Brazil
H0: There is no effect of the age class of the participants on the taste score of coffee from Brazil.
H1: There is an effect of the age class of the participants on the taste score of coffee from Brazil.
Table 8. S+ output of the one-way ANOVA for effects of the age class of the participants on the
taste score of coffee from Brazil.
*** Analysis of Variance Model ***
Short Output:
Call:
aov(formula = taste ~ ageclass, data = coffee.data.Brazil, na.action =
na.exclude)
Terms:
Sum of Squares
Deg. of Freedom
ageclass Residuals
26.7
12.2
2
7
Residual standard error: 1.320173
Estimated effects may be unbalanced
Type III Sum of Squares
Df Sum of Sq Mean Sq F Value
Pr(F)
ageclass 2
26.7 13.35000 7.659836 0.01727571
Residuals 7
12.2 1.74286
95 % simultaneous confidence intervals for specified
linear combinations, by the Tukey method
critical point: 2.9451
response variable: taste
intervals excluding 0 are flagged by '****'
21.99+ thru 39-39.00+ thru 59
21.99+ thru 39-59.00+ thru 70
39.00+ thru 59-59.00+ thru 70
Estimate Std.Error Lower Bound Upper Bound
5.4
1.450
1.14
9.66 ****
5.5
1.480
1.15
9.85 ****
0.1
0.886
-2.51
2.71

11. 4.1.9. Effects of the age class of the participants on the taste score of coffee from Columbia
H0: There is no effect of the age class of the participants on the taste score of coffee from Columbia.
H1: There is an effect of the age class of the participants on the taste score of coffee from Columbia.
Table 9. S+ output of the one-way ANOVA for effects of the age class of the participants on the
taste score of coffee from Columbia.
*** Analysis of Variance Model ***
Short Output:
Call:
aov(formula = taste ~ ageclass, data = coffee.data.Columbia, na.action =
na.exclude)
Terms:
ageclass Residuals
Sum of Squares 106.1833
69.4167
Deg. of Freedom
2
7
Residual standard error: 3.149074
Estimated effects may be unbalanced
Type III Sum of Squares
Df Sum of Sq Mean Sq F Value
Pr(F)
ageclass 2 106.1833 53.09167 5.353782 0.03884073
Residuals 7
69.4167 9.91667
95 % simultaneous confidence intervals for specified
linear combinations, by the Tukey method
critical point: 2.9451
response variable: taste
intervals excluding 0 are flagged by '****'
21.99+ thru 39-39.00+ thru 59
21.99+ thru 39-59.00+ thru 70
39.00+ thru 59-59.00+ thru 70
Estimate Std.Error Lower Bound Upper Bound
5.67
2.57
-1.910
13.20
7.75
2.41
0.667
14.80 ****
2.08
2.41
-5.000
9.17

12. 4.1.10. Effects of the age class of the participants on the taste score of coffee from Peru
H0: There is no effect of the age class of the participants on the taste score of coffee from Peru.
H1: There is an effect of the age class of the participants on the taste score of coffee from Peru.
Table 10. S+ output of the one-way ANOVA for effects of the age class of the participants on
the taste score of coffee from Peru.
*** Analysis of Variance Model ***
Short Output:
Call:
aov(formula = taste ~ ageclass, data = coffee.data.Peru, na.action =
na.exclude)
Terms:
ageclass Residuals
Sum of Squares 30.18333 35.41667
Deg. of Freedom
2
7
Residual standard error: 2.249339
Estimated effects may be unbalanced
Type III Sum of Squares
Df Sum of Sq Mean Sq F Value
Pr(F)
ageclass 2 30.18333 15.09167 2.982824 0.1156281
Residuals 7 35.41667 5.05952
95 % simultaneous confidence intervals for specified
linear combinations, by the Tukey method
critical point: 2.9451
response variable: taste
intervals excluding 0 are flagged by '****'
21.99+ thru 39-39.00+ thru 59
21.99+ thru 39-59.00+ thru 70
39.00+ thru 59-59.00+ thru 70
Estimate Std.Error Lower Bound Upper Bound
1.25
1.72
-3.81
6.31
4.33
1.84
-1.08
9.74
3.08
1.72
-1.98
8.14

13. 4.2. Appendix 2: S+ outputs for Question 2
4.2.1. Assessment of normality assumption
There are two samples with 20 observations each. The dataset was split first according to species (i.e.
C. arabica and C. robusta) then the normality of both samples was assessed separately.
H0: The observations for C. arabica were obtained from a normal distribution.
H1: The observations for C. robusta were not obtained from a normal distribution.
Table 11. S+ output of Kolmogorov-Smirnov test for C. arabica.
One sample Kolmogorov-Smirnov Test of Composite Normality
data: caffein in coffee.data.arabica
ks = 0.305, p-value = 0
alternative hypothesis:
True cdf is not the normal distn. with estimated parameters
sample estimates:
mean of x standard deviation of x
284.7324
133.3316
H0: The observations for C. robusta were obtained from a normal distribution.
H1: The observations for C. robusta were not obtained from a normal distribution.
Table 12. S+ output of Kolmogorov-Smirnov test for C. robusta.
One sample Kolmogorov-Smirnov Test of Composite Normality
data: caffein in coffee.data.robusta
ks = 0.125, p-value = 0.5
alternative hypothesis:
True cdf is not the normal distn. with estimated parameters
sample estimates:
mean of x standard deviation of x
207.8488
133.0805

14. 400
caffein
500
500
400
300
300
200
200
100
100
0
-1.5
0.0
1.5
-1.5
Normal Distribution
0.0
1.5
Normal Distribution
(a)
(b)
Figure 3. QQ plots of the caffeine content of (a) C. arabica and (b) C. robusta.
600
400
caffein
caffein
600
200
0
arabica
robusta
species
Figure 4. Box plots of the caffeine content of C. arabica and C. robusta.

15. 4.2.2. Assessment of homoscedasticity assumption
H0: Variances of all groups are equal.
H1: Variances of all groups are not equal.
Table 13. S+ output of Modified Levene test.
***
Modified Levene test ***
Df Sum of Sq Mean Sq
F Value
Pr(F)
groep 1
1756.0 1756.021 0.1847069 0.6697864
Residuals 38 361268.6 9507.069
4.2.3. Assessment of the caffeine contents of C. arabica and C. robusta
H0: The mean caffeine content of C. arabica is equal to the mean caffeine content of C. robusta.
H1: The mean caffeine content of C. arabica is greater than the mean caffeine content of C. robusta.
Table 14. S+ output of Exact Wilcoxon rank-sum test.
Exact Wilcoxon rank-sum test
data: x: caffein with species = arabica , and y: caffein with species =
robusta
rank-sum statistic W = 478, n = 20, m = 20, p-value = 0.0338
alternative hypothesis: mu is greater than 0

16. 4.3. Appendix 3: S+ outputs for Question 3
4.3.1. Assessment of normality assumption
H0: Residuals follow a normal distribution.
H1: Residuals do not follow a normal distribution.
Table 15. S+ output of Kolmogorov-Smirnov test.
One sample Kolmogorov-Smirnov Test of Composite Normality
data: residuals in coffee.data
ks = 0.1533, p-value = 0.0188
alternative hypothesis:
True cdf is not the normal distn. with estimated parameters
sample estimates:
mean of x standard deviation of x
5.551115e-018
1.206281
0
-1
Residuals
1
2
14
-2
21
10
-2
-1
0
1
Quantiles of Standard Normal
Figure 5. QQ plot of the residuals.
4.3.2. Assessment of homoscedasticity assumption
H0: Variances of all groups are equal.
H1: Variances of all groups are not equal.
Table 16. S+ output of Modified Levene test.
***
Modified Levene test ***
Df Sum of Sq Mean Sq
F Value
Pr(F)
groep 1
1756.0 1756.021 0.1847069 0.6697864
Residuals 38 361268.6 9507.069
2

17. 4.3.3. Assessment of the differences in coffee consumption among the three age classes
H0: All three age classes result in the same average frequency of coffee consumption per day.
H1: At least one age class results in a different average frequency of coffee consumption per day.
Table 17. S+ output of the one-way ANOVA for the determination if differences in coffee
consumption among the three age classes exist.
*** Analysis of Variance Model ***
Short Output:
Call:
aov(formula = frequency ~ ageclass, data = coffee.data, na.action =
na.exclude
)
Terms:
ageclass Residuals
Sum of Squares 82.85055 56.74945
Deg. of Freedom
2
37
Residual standard error: 1.238454
Estimated effects may be unbalanced
Type III Sum of Squares
Df Sum of Sq Mean Sq F Value
Pr(F)
ageclass 2 82.85055 41.42527 27.00881 5.860174e-008
Residuals 37 56.74945 1.53377
Table 18. S+ output of the Tukey method.
95 % simultaneous confidence intervals for specified
linear combinations, by the Tukey method
critical point: 2.4415
response variable: frequency
intervals excluding 0 are flagged by '****'
21.99+ thru 39-39.00+ thru 59
21.99+ thru 39-59.00+ thru 70
39.00+ thru 59-59.00+ thru 70
Estimate Std.Error Lower Bound Upper Bound
-3.440
0.544
-4.77
-2.110 ****
-0.989
0.581
-2.41
0.429
2.450
0.441
1.38
3.530 ****