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