Chapter_5_Quantity_and_quality.qmd

# Quantity and quality?
## Introduction

Starting from this Chapter, we assume the data for analysis are "tidy"
and are defined as a climatic data frame in R-Instat.

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  ***Fig. 5.1a The Check Data menu***                    
  ------------------------------------------------------ ----------------------------------
  ![](figures/Fig5.1a.png){width="3.071272965879265in"   
  height="2.6721817585301837in"}                         

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This chapter shows different ways to now look at the data. For many
applications this stage can be done quickly, and the work then proceeds
with the analyses described in the following chapters. But omit this
stare at your peril. We often find users have gone immediately to the
analyses they need, only to have to return later to look more critically
at their data.

From now on, in this guide, we will also assume that you are reasonably
comfortable in your use of R-Instat. In Section 5.2 we outline what that
means.

Section 5.3 shows how to get a quick inventory of the data. We also
consider how to tabulate and graph the primary, usually daily, data.
Then Section 5.3 examines the data via boxplots. Boxplots are primarily
an exploratory tool, but can also be used for presentation graphs.

Finally, we consider some formal quality control checks on the data.
What oddities might be in the data and what can be done about them.

## An inventory -- what data do I have?

Open the Rwanda workshop data, Fig. 5.2a. This is from 4 stations and
has already been defined as climatic data as described in Chapter 4.

Use the first menu item in the ***Climatic \> Check Data*** menu, Fig.
5.1a to choose an ***Inventory*** plot, Fig. 5.2b.

In Fig. 5.2b the Data and the Station receivers are completed
automatically. This is because the data frame was defined as Climatic
with these components. If not, then usually:

a.  The data frame was not yet defined as climatic.

b.  You are in the wrong data frame -- change it in the data selector in
    the dialogue in Fig. 5.2b.

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  ***Fig. 5.2a Rwanda workshop data***                                    ***Fig. 5.2b Inventory Dialogue Climatic\>Check Data\>Inventory***
  ------------------------------------------------------- ----------------------------------------------------------------------------------------------------------------------
  ![](figures/Fig5.2a.png){width="3.0161132983377077in"   ![](figures/Fig5.2b.png){width="2.973377077865267in"
  height="3.0161132983377077in"}                          height="2.575567585301837in"}

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In Fig. 5.2b, add the 3 data columns for TMAX, TMIN and PRECIP and press
Ok. The resulting inventory is in Fig. 5.2c.

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  ***Fig. 5.2c Default inventory plot***                  ***Fig. 5.2d Facet by element***
  ------------------------------------------------------- -------------------------------------------------------
  ![](figures/Fig5.2c.png){width="2.9092760279965004in"   ![](figures/Fig5.2d.png){width="3.0269050743657044in"
  height="2.830469160104987in"}                           height="2.839443350831146in"}

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Experiment with the display. For example, in Fig. 5.2d the ***Facet
By***, in Fig. 5.2b has been set to be the ***Element***, rather than
the ***Station***.

One oddity in the data in Fig. 5.2c and 5.2d was the gap in the rainfall
records in the 1980s at 2 of the stations. It is quite common to have
rainfall records in the database without the corresponding temperature
records, but the reverse is odd. The data were exported from the
Clinsoft database and it was not clear why these data were absent. That
is the idea of being able to produce an inventory.

The value of the inventory presentation is that the information on many
stations and elements can be shown together. However, the graphs show
just when data was present or absent. They do not show the actual
values.

They can be supplemented by simple time series plots[^19].

  -----------------------------------------------------------------------
  ***Fig. 5.2e Rwanda temperature data***
  -----------------------------------------------------------------------
  ![](figures/Fig5.2e.png){width="6.066142825896763in"
  height="3.02500656167979in"}

  -----------------------------------------------------------------------

These plots give a useful indication of the data for analysis. One
period in Kamembe Airport is marked in Fig. 5.2e as a cause for concern.
In Fig. 5.2f the interactive plotting, using ***Describe \> View
Graph*** is used to examine this part of the graph in more detail.

  -------------------------------------------------------------------------------------------
  ***Fig. 5.2f Examine the temperature data in more       
  detail***                                               
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  ![](figures/Fig5.2f.png){width="2.9750185914260716in"   
  height="3.30957895888014in"}                            

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Fig 5.2g shows the same time series graph for the rainfall data at each
site. There is a dry period in the year and hence the different years
are clearly visible in these graphs.

  -----------------------------------------------------------------------
  ***Fig. 5.2g Rainfall data at the four stations***
  -----------------------------------------------------------------------
  ![](figures/Fig5.2g.png){width="6.052942913385826in"
  height="2.9319149168853893in"}

  -----------------------------------------------------------------------

The next dialogue is ***Climatic \> Check Data \> Display Daily***, Fig.
5.2h. This produces a lot of output, so we first choose the filter the
data to just the first station, Gisenyi[^20].

When using this dialogue the items on the right (from Station down to
Year) are completed automatically. If not, then you are probably in the
wrong data frame

  ---------------------------------------------------------------------------------------------------------------
  ***Fig. 5.2h Examining daily values***                  ***Fig. 5.2i One year of the data***
  ------------------------------------------------------- -------------------------------------------------------
  ![](figures/Fig5.2h.png){width="2.6560739282589676in"   ![](figures/Fig5.2i.png){width="3.337146762904637in"
  height="2.830469160104987in"}                           height="2.839443350831146in"}

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Complete the dialogue in Fig. 5.2h as shown. We have chosen to recode
zero rainfalls to "---". This is an option so the rainy days are
displayed more clearly in Fig. 5.2i. It indicates the dry period in the
year is usually June and July. The dry period was a feature of Fig.
5.2g.

We have now almost come "full circle". In Fig. 4.4i the rainfall data
from Garoua, Cameroon, were supplied for analysis arranged in a similar
way to the data now shown in Fig. 5.2i. This is a very clear and
sensible layout for the data, but to examine, not to analyse.

The second tab in the same ***Climatic \> Check Data \> Display Daily***
dialogue gives a simple graphical display of the data "by year". An
example of the resulting display is in Fig. 5.2j. The results show both
the missing periods as well as the dry parts of the year.

  -----------------------------------------------------------------------
  ***Fig. 5.2j. Daily rainfall for one station***
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  ![](figures/Fig5.2j.png){width="6.105915354330708in"
  height="2.9670450568678914in"}

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## Using boxplots to check and present data

Open the Dodoma data, using the RDS file from the Climatic \> Tanzania
directory. This is already set as a climatic data frame as described in
Chapter 4. It shows data from a single site, with multiple elements.

Most of the examples in this Section use the special ***Climatic \>
Check Data \> Boxplot*** dialogue. Boxplots are also available through
the main Describe menu (Describe \> Specific \> Boxplot). The results
are the same, but the Climatic Boxplot dialogue is usually simpler to
complete.

  ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
  ***Fig. 5.3a Climatic boxplot dialogue***                  ***Fig. 5.3b Seasonal pattern of sunshine hours***
  ------------------------------------------------------- ----------------------------------------------------------------------------------------------------------------------
  ![](figures/Fig5.3a.png){width="2.6560739282589676in"   ![](figures/Fig5.3b.png){width="2.6560739282589676in"
  height="2.830469160104987in"}                           height="2.830469160104987in"}

  ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

The results, in Fig. 5.3b Show only one value, in September, is odd in
being longer than the day length. Most days in the year have many
sunshine hours, and the median is more than 10 hrs in the data for 6
months, from June to November.

Finding just a single obvious oddity in Fig. 5.3b out of the 20,450
observations is a measure of the high quality of these data. We look in
more detail at how to check for outliers in Sections 5.4 and 5.5. As a
practical measure, setting the value to missing, would hardly affect the
results and may be sensible if the non-computerised records are not
easily available.

As well as being a very useful exploratory method, boxplots are also
often used in the methods section of reports and papers, to present the
data being analysed. Thus they can be presentation as well as
exploratory graphs.

Fig. 5.2b shows the seasonal pattern for the sunshine data. Two simple
changes to the dialogue in Fig. 5.3c show the time series, and hence a
possible trend, is shown in Fig. 5.3d. The second change in Fig. 5.3c is
to use the ***Variable Width*** option, to see which years have many
missing values.

  -------------------------------------------------------------------------------------------------------------
  ***Fig. 5.3c Change to show the time series***         ***Fig. 5.3d***
  ------------------------------------------------------ ------------------------------------------------------
  ![](figures/Fig5.3c.png){width="3.0568897637795276in"   ![](figures/Fig5.3d.png){width="2.9790977690288716in"
  height="3.0768055555555556in"}                         height="3.0134984689413824in"}

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It is possible to show both the seasonality and the time-series
together, as shown in Fig. 5.3e. The resulting figure is a bit crowded
if months are used, so the graph is displayed for each of 4
quarters[^21].

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  ***Fig. 5.3e***
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  ![](figures/Fig5.3e.png){width="6.056246719160105in"
  height="2.9328455818022747in"}

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An example in Chapter 2, Section 2.4, compared the Dodoma station data
on sunshine hours with the estimated values from the satellite data. It
is important to check the quality of the data, whatever the source.
Hence Fig. 5.3f shows the seasonal pattern of the satellite estimates of
sunshine hours.

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  ***Fig. 5.3f Satellite estimates of sunshine at        ***Fig. 5.3g Suspect values mainly in early years***
  Dodoma***                                              
  ------------------------------------------------------ -----------------------------------------------------
  ![](figures/Fig5.3f.png){width="2.9552602799650045in"   ![](figures/Fig5.3g.png){width="2.954428040244969in"
  height="2.915323709536308in"}                          height="2.9476049868766405in"}

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Comparing Fig. 5.3f with Fig. 5.3b (the station data) shows
encouragingly that the distributions seem very similar. However, there
are also a number of values that are clearly longer than the day length
at Dodoma. From discussion with the providers of the data (EUMETSAT) we
learned that the early years may have radiation values (and hence
sunshine hours) that are less reliable. This is confirmed through the
time series plot for the satellite data, in Fig. 5.3g.

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  ***Fig. 5.3h Boxplots for the rainfall***               ***Fig. 5.3i Rainfall on rain days***
  ------------------------------------------------------ ------------------------------------------------------
  ![](figures/Fig5.3h.png){width="3.0212062554680665in"   ![](figures/Fig5.3i.png){width="2.9721916010498686in"
  height="3.0562204724409447in"}                         height="2.9926902887139106in"}

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Boxplots can be used for the rainfall data, as shown in Fig. 5.3i. The
data plotted are just for rain days, with the variable width of each box
indicating the number of rain days. The plot shows the unimodal pattern
of the rainfall from November to April[^22].

  -------------------------------------------------------------------------------------------------------------
  ***Fig. 5.3j Adding a second layer to the plot***               ***Fig. 5.3k Tmax and Tmin plotted together***
  ------------------------------------------------------ ------------------------------------------------------
  ![](figures/Fig5.3j.png){width="2.992442038495188in"   ![](figures/Fig5.3k.png){width="2.970890201224847in"
  height="2.7443383639545056in"}                         height="3.033581583552056in"}

  -------------------------------------------------------------------------------------------------------------

The Dodoma data includes Tmax and Tmin and these can, if required, be
shown together on the same graph. An example is in Fig. 5.3k and one of
the sub-dialogues to facilitate this graph is shown in Fig. 5.3j[^23]
One feature in Fig. 5.3k is the larger variability of the Tmax data in
the rainy season, i.e. from November to April.

Graphs, once saved, can be also combined, using Describe \> Combine
Graphs, as shown in Fig. 5.3l, with all 4 elements shown in Fig. 5.3m

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  ***Fig. 5.3l Combining graphs***               ***Fig. 5.3m The 4 elements in Dodoma***
  ------------------------------------------------------ ------------------------------------------------------
  ![](figures/Fig5.3l.png){width="2.758496281714786in"   ![](figures/Fig5.3m.png){width="3.1666666666666665in"
  height="2.707830271216098in"}                         height="3.1666666666666665in"}

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Other displays of these data are also possible. In Fig. 5.3k we observed
the larger variation of the Tmax data in the rainy months (compared to
both Tmin, and to Tmax in the dry months). This feature is shown more
clearly through density plots as seen in Fig. 5.3p. This uses a dialogue
from the ordinary Describe menu. The results in Fig. 5.3p indicate a
roughly normal-type shape for the data, though with a slightly longer
tail for Tmax in the rainy season[^24].

 -------------------------------------------------------------------------------------------------------------
  ***Fig. 5.3n Producing density plots***               ***Fig. 5.3o Density plots for Tmax and Tmin by month***
  ------------------------------------------------------ ------------------------------------------------------
  ![](figures/Fig5.3n.png){width="2.992442038495188in"   ![](figures/Fig5.3o.png){width="2.970890201224847in"
  height="2.7443383639545056in"}                         height="3.033581583552056in"}

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Often the data frame will include data from more than one station. This
is illustrated briefly with the Rwanda data, from the library, that is
from 4 stations. An example is shown in Fig. 5.3q. It shows relatively
little seasonality, because Rwanda is close to the equator. One feature
of the data is the higher variability and lower temperatures at the
4^th^ stations, which is at a higher altitude compared to the other 3.
For this presentation, in the ***Climatic \> Check Data \> Boxplot***
dialogue, the option is then used to facet by the Station.

  -----------------------------------------------------------------------
  ***Fig. 5.3p Example for multiple stations, Tmin for 4 stations in
  Rwanda***
  -----------------------------------------------------------------------
  ![](figures/Fig5.3p.png){width="6.1667082239720035in"
  height="3.0204975940507435in"}

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## Quality control of temperature (and other) data

The graphical displays in the previous 2 sections have indicated
observations that need checking. The dialogue Climatic \> Check Data \>
Temperatures, Fig. 5.4a, is designed to facilitate this checking. It has
been designed specifically for temperature records, but with a
flexibility to permit it to be used also for other elements.

Fig. 5.4 has been completed for the Dodoma data. Initially with a single
element (Tmax).

 -------------------------------------------------------------------------------------------------------------
  ***Fig. 5.4a Climatic \> Check Data \> QC Temperatures***               ***Fig. 5.4b***
  ------------------------------------------------------ ------------------------------------------------------
  ![](figures/Fig5.4a.png){width="3.123163823272091in"   ![](figures/Fig5.4b.png){width="2.8671358267716536in"
  height="3.504679571303587in"}                         height="2.7212642169728785in"}

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From the previous Section, Fig. 5.3k, Tmax at Dodoma is rarely less than
20°C, and could usefully be checked each time. So, the first
illustration of the dialogue uses the limits 20 and 40 for Tmax.

The results are in Fig. 5.4b. R-Instat has filtered the Dodoma data and
copied the "problem" rows into a new data frame. It shows there were
just 13 occasions with Tmax \<=20 in the record. As shown in Fig. 5.4b,
they include 9^th^ October 1989, when Tmax was equal to Tmin at 15.6°C.

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  ***Fig. 5.4c The available checks***                   ***Fig. 5.4d Checking for consecutive values***
  ------------------------------------------------------ -----------------------------------------------------
  ![](figures/Fig5.4c.png){width="2.7496237970253716in"   ![](figures/Fig5.4d.png){width="3.316666666666667in"
  height="1.6854516622922135in"}                         height="2.6708147419072614in"}

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More checks on the data are available, as shown in Fig. 5.4c. They are
considered in turn:

-   ***Acceptable range*** for each element, as shown in Fig. 5.4a
    and b. This is very simplistic, because it does not allow for
    seasonality in the data.

-   ***Same*** examines consecutive days and, with the default setting,
    indicates whenever 4 days or more have the same value. The idea is
    that when many consecutive values are identical, it is possible they
    were simply copied in, and not measured on each day. An example of
    the results is in Fig. 5.4e.

-   ***Jump*** notes whenever 2 consecutive days are different by more
    that the threshold amount. The default is that any difference (jump)
    of more than 10°C deserves further examination.

-   ***Difference*** is only available when 2 elements have been
    included, usually Tmax and Tmin. The default is to note whenever
    Tmax \<= Tmin, but the difference could be altered.

-   ***Outlier*** is the most complex and relates the value to the
    boxplot outliers. A boxplot is conceptually fitted for each month at
    each station and the outliers are then noted. The traditional limit
    for boxplots has a coefficient of 1.5[^25], as used in all the
    figures in Section 5.3. We find, with the large samples in climatic
    data, this gives too many outliers, many of which are not
    particularly surprising. We therefore usually use 2.5 or 3 (instead
    of 1.5) as the multiplying value.

You may choose to do multiple checks at the same time. We consider them
in turn. Each time the dialogue is used, it produces a new data frame.

In Fig. 5.4d we specify the ***Same*** check, for both Tmax and Tmin
together.

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  ***Fig. 5.4e Results from the Same check***            ***Fig. 5.4f Jump of more than 10°C***
  ------------------------------------------------------ -----------------------------------------------------
  ![](figures/Fig5.4e.png){width="2.9792082239720035in"   ![](figures/Fig5.4f.png){width="3.028753280839895in"
  height="2.8092530621172354in"}                         height="2.7992268153980753in"}

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The results are in Fig. 5.4e. The first occurrence was in July 1965 when
Tmax was 26.0°C on 4 consecutive days, while in October 1969 Tmin was
consecutively 17.4°C. The results, in Fig. 5.4e also include further
columns to note how many consecutive days and whether they were for Tmax
or Tmin. In this case there were only 7 occurrences of the event, giving
28 rows in total, so these extra columns are not so important.

Fig. 5.4f shows the results from the test for jumps of more than 10°C.
Here the logical column was always TRUE for Tmax, i.e. this event did
not occur for Tmin. Sometimes Tmax drops because of rainfall, and this
column is automatically included in the filtered data. The results in
Fig. 5.4f include the size of the jump.

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  ***Fig. 5.4g Tmax within 1°C of Tmin***                ***Fig. 5.4h Outiers from corresponding boxplots***
  ------------------------------------------------------ -----------------------------------------------------
  ![](figures/Fig5.4g.png){width="2.6875459317585304in"   ![](figures/Fig5.4h.png){width="3.334831583552056in"
  height="1.1320406824146982in"}                         height="2.499064960629921in"}

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In the next check, the limit is set to 1°C. There are then, Fig. 5.4g,
just 4 days when Tmax is within 1 degree of Tmin.

The final check is equivalent to the boxplot outliers. The threshold in
producing Fig. 5.4h was set to 2.5 and there were still 150 outliers to
investigate. There are effectively 4 tests here, i.e. whether either
Tmax or Tmin are too low, or too high. These correspond to the settings
of the logical columns in Fig. 5.4h. Thus the first 3 rows all indicate
a low value of Tmax, while the 4^th^ row is a low value for Tmin.

Readers may be concerned in having to check 150 values. Our view is that
these data are of high quality. This is 150 values out of more than
40,000 (i.e. over 20,000 days for each of Tmin and Tmax), so less than
0.5% of the values to be checked! Not bad.

## Quality control for rainfall records

The system for checking rainfall data is similar to that for the
temperatures, described in Section 5.4.

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  ***Fig. 5.5a***                                       ***Fig. 5.5b***
  ----------------------------------------------------- -----------------------------------------------------
  ![](figures/Fig5.5a.png){width="3.053068678915136in"   ![](figures/Fig5.5b.png){width="2.846933508311461in"
  height="2.969220253718285in"}                         height="3.6387970253718285in"}

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We continue with the Dodoma data. Two checks are undertaken in the
dialogue in Fig. 5.5a. First is to note all values more than 100mm and
second is to note when any 2 consecutive non-zero values are the same.

Some of the results (after reordering columns for clarity) are in Fig.
5.5b. There are 83 rows of data, from 6 occasions with more than 100mm
(all look plausible) and 38 occasions when 2 consecutive days had the
same rainfall. Looking at the results in Fig. 5.5b, perhaps the low
values e.g. 0.3mm on 2 consecutive days is not so surprising, but 19.2mm
on both the 5^th^ and 6^th^ January 1967 deserves further investigation.

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  ***Fig. 5.5c Same values after a filter***             ***Fig. 5.5d Checking for dry months***
  ------------------------------------------------------ ------------------------------------------------------
  ![](figures/Fig5.5c.png){width="2.9309733158355207in"   ![](figures/Fig5.5d.png){width="3.0435115923009626in"
  height="3.479775809273841in"}                          height="3.0732534995625547in"}

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The data in Fig. 5.5b are just in an ordinary data frame, so we check
more closely by filtering out the values of 1mm or less. The results are
in Fig. 5.5c. There are just 16 occasions, most of which are shown in
Fig. 5.5b with exactly the same amount on 2 days. One way this arises is
when the data are computerised initially on the wrong day. They are then
transferred to the previous day, but the original is not deleted. A
check with the paper records is all that is needed.

The next option in Fig. 5.5a is called "Consecutive". This checks on the
number of consecutive rain days. In some places a large number is rare.
But sometimes temperature columns may be entered mistakenly. This then
appears as many consecutive "rain" days, with relatively similar amounts
on the successive days.

The next option is called Dry Month and is shown in Fig. 5.5d. The
explanation is given for Dodoma, where the rainy season is from November
to April. The other months may be totally dry. If January (in the middle
of the rainy season) is totally dry, then probably it was missing and
recorded mistakenly as zero each day. What is more complicated is
November (the usual start of the season) and April (the usual end). If
November is totally dry, then it could be true and a late start to the
season. Or the data are missing. The same goes for April.

  -----------------------------------------------------------------------------------------------------------
  ***Fig. 5.5e***                                      ***Fig. 5.5f***
  ---------------------------------------------------- ------------------------------------------------------
  ![](figures/Fig5.5e.png){width="3.11877624671916in"   ![](figures/Fig5.5f.png){width="2.7583595800524936in"
  height="3.303284120734908in"}                        height="3.0145352143482063in"}

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The results are in Fig. 5.5e. Right-click on the month column and use
the Levels/Labels dialogue, Fig. 5.5f to give the results in Fig. 5.5g.
This shows the zeros are primarily in November, but December is zero in
2 years. There are no zero months in January to April.

One way to find which years to investigate, is the make the year column
in Fig. 5.5e into a Factor and then use the same Levels/Labels dialogue.
The results are in Fig. 5.5h, showing the first years are 1935. 1936,
1943, while the frequency of 31 in 1952 idicates that was one of the
years when December was zero.

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  ***Fig. 5.5g It is a November/December problem***      ***Fig. 5.5h These are the years***
  ------------------------------------------------------ -----------------------------------------------------
  ![](figures/Fig5.5g.png){width="2.5220581802274715in"   ![](figures/Fig5.5h.png){width="2.729306649168854in"
  height="3.516259842519685in"}                          height="3.521013779527559in"}

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The final option is the outliers, using the limits from the skew
boxplot. In Fig. 5.5i we omit the zero values and set the skewness
weight to 3. This has identified just 3 possible outliers, and each is
only just above the corresponding limit, see Fig 5.5j.

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  ***Fig. 5.5i Settings for the rainfall outliers***    ***Fig. 5.5j Possible outliers from skew boxplot***
  ----------------------------------------------------- -----------------------------------------------------
  ![](figures/Fig5.5i.png){width="2.978626421697288in"   ![](figures/Fig5.5j.png){width="3.272315179352581in"
  height="1.497422353455818in"}                         height="0.9956594488188977in"}

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