| Level | Mean | Standard deviation | n | Standard error |
|---|---|---|---|---|
| 5 | 23.61538 | 22.22445 | 26 | 4.358573 |
| 6 | 29.44444 | 18.20790 | 9 | 6.069301 |
| 7 | 59.11538 | 31.63584 | 26 | 6.204298 |
| 8 | 59.96154 | 39.68121 | 26 | 7.782126 |
| 9 | 31.44828 | 24.14182 | 29 | 4.483024 |
The ratio of the largest group standard deviation to the smallest is 2.18
This graph has 5 boxplots printed vertically
with the title:
"" appears on the x-axis.
"" appears on the y-axis.
Tick marks for the y-axis are at: 0, 50, 100, and 150
Group 5 has 26 values.
An outlier is marked at: 115
The whiskers extend to 1 and 45 from the ends of the box,
which are at 11 and 32
The median, 18 is 33 % from the lower end of the box to the upper end.
The upper whisker is 1.3 times the length of the lower whisker.
Group 6 has 9 values.
An outlier is marked at: 71
The whiskers extend to 12 and 39 from the ends of the box,
which are at 20 and 37
The median, 23 is 18 % from the lower end of the box to the upper end.
The upper whisker is 0.25 times the length of the lower whisker.
Group 7 has 26 values.
There are no outliers marked for this group
The whiskers extend to 7 and 135 from the ends of the box,
which are at 35 and 80
The median, 60 is 56 % from the lower end of the box to the upper end.
The upper whisker is 1.96 times the length of the lower whisker.
Group 8 has 26 values.
There are no outliers marked for this group
The whiskers extend to 9 and 168 from the ends of the box,
which are at 28 and 84
The median, 52 is 43 % from the lower end of the box to the upper end.
The upper whisker is 4.42 times the length of the lower whisker.
Group 9 has 29 values.
An outlier is marked at: 96 78 73 91
The whiskers extend to 7 and 47 from the ends of the box,
which are at 16 and 36
The median, 23 is 35 % from the lower end of the box to the upper end.
The upper whisker is 1.22 times the length of the lower whisker.
Warning in dotplot.formula(Ozone ~ Month, xlab = "Ozone", ylab = "Month"):
The dotplot command is a wrapper for stripchart, and is not a base R
function.
This graph has 5 dotplots printed horizontally
with the title:
"" appears on the x-axis.
"" appears on the y-axis.
Tick marks for the x-axis are at: 0, 50, 100, and 150
the data that range from 1 to 168 has been broken into 6 bins.
The counts are:
5: 18 7 0 0 1 0
6: 5 3 1 0 0 0
7: 5 7 9 4 1 0
8: 7 6 7 3 2 1
9: 19 6 2 2 0 0
The p value for Month is 0
The ratios of the group standard deviations to the overall standard deviation
(groups ordered by increasing mean) are:
0.76 0.62 1.08 1.35 0.82
Df Sum Sq Mean Sq F value Pr(>F)
Month 4 29438 7359 8.536 4.83e-06 ***
Residuals 111 95705 862
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
37 observations deleted due to missingness
Bartlett test of homogeneity of variances
data: Ozone by Month
Bartlett's K-squared = 13.451, df = 4, p-value = 0.00927
Fligner-Killeen test of homogeneity of variances
data: Ozone by Month
Fligner-Killeen:med chi-squared = 19.341, df = 4, p-value =
0.0006736
For term Month the comparisons which are significant at 5% are:
7 and 5 with a difference of 35.5 and P-value of 3e-04
8 and 5 with a difference of 36.35 and P-value of 2e-04
7 and 9 with a difference of 27.67 and P-value of 0.0062
8 and 9 with a difference of 28.51 and P-value of 0.0043
Tukey multiple comparisons of means
95% family-wise confidence level
factor levels have been ordered
Fit: aov(formula = Ozone ~ Month, data = airquality2)
$Month
diff lwr upr p adj
6-5 5.8290598 -25.6630930 37.32121 0.9858842
9-5 7.8328912 -14.1594735 29.82526 0.8603562
7-5 35.5000000 12.9158068 58.08419 0.0002795
8-5 36.3461538 13.7619606 58.93035 0.0001869
9-6 2.0038314 -29.0666371 33.07430 0.9997676
7-6 29.6709402 -1.8212127 61.16309 0.0749128
8-6 30.5170940 -0.9750588 62.00925 0.0622826
7-9 27.6671088 5.6747440 49.65947 0.0061535
8-9 28.5132626 6.5208979 50.50563 0.0043387
8-7 0.8461538 -21.7380394 23.43035 0.9999733
