# Data analysis

Up to this point, we have just been learning how to read data and make it “tidy”. This was a lot of work. The pay-off is that now the analysis of the data will be much easier and straightforward.

This is intentional. Data cleaning is the messiest and most ambiguous part of data science. A truism is that data cleaning takes 80% of the time of any data science project. However, without this effort, data analysis and visualisation would be similarly messy and time consuming. By cleaning first, we can perform data analysis and visualisation using clean, consistent, well-tested and tidy tools.

## Analysis via summarise

You can perform summary analysis on data in a tibble using the summarise function from the dply package.

summarise will create a new tibble that is a summary of the input tibble, based on grouping and a summarising function. Summarising functions include;

For example, we can calculate the mean average temperature using;

historical_temperature %>%
summarise("average temperature"=mean(temperature, na.rm=TRUE))
# A tibble: 1 x 1
average temperature
<dbl>
1                  9.25

(note that we used na.rm=TRUE to tell the function to ignore NA values)

This has created a new tibble, where the column called “average temperature” contains the mean average temperature.

## Grouping data

Each row of tidy data corresponds to a single observation. We can group observations together into groups using group_by. We can then feed these groups into summaries.

For example, we can group by year and summarise by the mean function to calculate the average temperature for each year;

historical_temperature %>%
group_by(year) %>%
summarise("average temperature"=mean(temperature, na.rm=TRUE))
# A tibble: 362 x 2
year average temperature
<int>                 <dbl>
1  1659                  8.83
2  1660                  9.08
3  1661                  9.75
4  1662                  9.5
5  1663                  8.58
6  1664                  9.33
7  1665                  8.25
8  1666                  9.83
9  1667                  8.5
10  1668                  9.5
# … with 352 more rows

or, we could calculate the average temperature for each month via;

historical_temperature %>%
group_by(month) %>%
summarise("average temperature"=mean(temperature, na.rm=TRUE))
# A tibble: 12 x 2
month average temperature
<fct>                 <dbl>
1 JAN                    3.28
2 FEB                    3.89
3 MAR                    5.35
4 APR                    7.95
5 MAY                   11.2
6 JUN                   14.3
7 JUL                   16.0
8 AUG                   15.6
9 SEP                   13.3
10 OCT                    9.73
11 NOV                    6.08
12 DEC                    4.12

## Filtering data

We can then use the filter, also from dplyr, to filter observations (rows) before we group. For example, we could filter the years in the 18th Century (year<1800 & year>=1700) and calculate the average monthly temperatures then via;

historical_temperature %>%
filter(year<1800 & year>=1700) %>%
group_by(month) %>%
summarise("18th Century"=mean(temperature, na.rm=TRUE))
# A tibble: 12 x 2
month 18th Century
<fct>          <dbl>
1 JAN             2.89
2 FEB             3.80
3 MAR             5.04
4 APR             7.88
5 MAY            11.3
6 JUN            14.5
7 JUL            16.0
8 AUG            15.8
9 SEP            13.5
10 OCT             9.40
11 NOV             5.84
12 DEC             3.89

We could then repeat this for the 21st Century…

historical_temperature %>%
filter(year>=2000) %>%
group_by(month) %>%
summarise("21st Century"=mean(temperature, na.rm=TRUE))
# A tibble: 12 x 2
month 21st Century
<fct>          <dbl>
1 JAN             4.73
2 FEB             4.93
3 MAR             6.60
4 APR             9.08
5 MAY            12.0
6 JUN            14.9
7 JUL            16.8
8 AUG            16.4
9 SEP            14.3
10 OCT            11.2
11 NOV             7.44
12 DEC             5.12

EXERCISE

Use filter, group_by and summarise to create tibbles that contain the average monthly temperatures for the 17th and 21st Centuries. Take the difference of these to calculate the change in average temperature for each month.

Next calculate the minimum and maximum monthly temperatures for the 17th and 21st Centuries. Again, calculate the change in minimum and maximum temperatures for each month.

Finally, what is the average increase in maximum monthly temperatures between the 16th and 21st Centuries?