Univariate analysis for Ozone
Prepared by Jonathan Godfrey
Basic summary measures
Counts
153 values in all, made up of
68 unique values,
116 observed, and
37 missing values.
Measures of location
| Data |
all |
5% trimmed |
10% trimmed |
| Mean |
42.1293 |
40.8839 |
39.6604 |
Quantiles
|
Quantile |
Value |
| 0% |
Minimum |
1.00 |
| 25% |
Lower Quartile |
18.00 |
| 50% |
Median |
31.50 |
| 75% |
Upper Quartile |
63.25 |
| 100% |
Maximum |
168.00 |
Measures of spread
| Measure |
IQR |
Standard deviation |
Variance |
| Value |
45.25 |
32.9879 |
1088.2005 |
Basic univariate graphs
Histogram
\begin{Schunk}
\begin{figure}
\includegraphics{Ozone/Ozone-Hist-1} \caption[The histogram]{The histogram}\label{fig:Hist}
\end{figure}
\begin{Soutput}
This is a histogram, with the title: Histogram of Ozone
“Ozone” is marked on the x-axis.
Tick marks for the x-axis are at: 0, 50, 100, and 150
There are a total of 116 elements for this variable.
Tick marks for the y-axis are at: 0, 10, 20, and 30
It has 9 bins with equal widths, starting at 0 and ending at 180 .
The mids and counts for the bins are:
mid = 10 count = 37
mid = 30 count = 34
mid = 50 count = 14
mid = 70 count = 15
mid = 90 count = 9
mid = 110 count = 4
mid = 130 count = 2
mid = 150 count = 0
mid = 170 count = 1
\end{Soutput}
\end{Schunk}
Boxplot
\begin{Schunk}
\begin{figure}
\includegraphics{Ozone/Ozone-Boxplot-1} \caption[The boxplot]{The boxplot}\label{fig:Boxplot}
\end{figure}
\begin{Soutput}
This graph has a boxplot 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
This variable has 116 values.
An outlier is marked at: 135 168
The whiskers extend to 1 and 122 from the ends of the box,
which are at 18 and 63.5
The median, 31.5 is 30 % from the left end of the box to the right end.
The right whisker is 3.44 times the length of the left whisker.
\end{Soutput}
\end{Schunk}
Assessing normality
Formal tests for normality
|
Statistic |
P Value |
| Shapiro-Wilk |
0.8787 |
0 |
| Anderson-Darling |
4.5211 |
0 |
| Cramer-von Mises |
0.8033 |
0 |
| Lilliefors (Kolmogorov-Smirnov) |
0.1480 |
0 |
| Pearson chi-square |
73.7241 |
0 |
| Shapiro-Francia |
0.8786 |
0 |
Normality plot
\begin{Schunk}
\begin{figure}
\includegraphics{Ozone/Ozone-NormPlot-1} \caption[The normality plot]{The normality plot}\label{fig:NormPlot}
\end{figure}
\end{Schunk}
Formal tests of moments
|
Statistic |
Z |
P Value |
| D'Agostino skewness |
1.226 |
4.656 |
0.0000 |
| Anscombe-Glynn kurtosis |
4.184 |
2.203 |
0.0276 |