{"id":671,"date":"2017-06-25T15:06:12","date_gmt":"2017-06-25T14:06:12","guid":{"rendered":"https:\/\/marriott-stats.com\/nigels-blog\/?p=671"},"modified":"2019-02-09T10:32:00","modified_gmt":"2019-02-09T10:32:00","slug":"uk-weather-trends-1-spring-2017","status":"publish","type":"post","link":"https:\/\/marriott-stats.com\/nigels-blog\/uk-weather-trends-1-spring-2017\/","title":{"rendered":"UK Weather Trends #1 – Spring 2017"},"content":{"rendered":"

Meteorologists define spring in the UK to be the period from March to May so spring is now over and we are officially in summer.\u00a0 I have decided to create a series of posts which I will publish at the end of each season showing how that season compares to the weather record.\u00a0 The 2017 spring turned out to be the 2nd warmest on record.<\/p>\n

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Analysis of trends is a key skill that all statisticians and analysts need to have.\u00a0 Indeed I run a training course on Identifying Trends & Making Forecasts <\/a>as I have learned over my 25 years as a professional statistician that skills in this area are nowhere near where they should be.\u00a0 By publishing this series of posts about trends in weather and other fields, I hope you will learn something you will be able to apply elsewhere.<\/p>\n

As my weather tracker series <\/a>shows, weather cannot be thought of as a univariate data set.\u00a0 We define weather as a combination of temperature, sunshine and rainfall which makes weather a multivariate data set.\u00a0 There are many ways of displaying multivariate data but one of the first questions that has to be asked is how do we compare 3 variables that use 3 different numerical scales i.e. degrees Celsius, hours and millimetres?\u00a0 The answer is to convert the scales of all 3 variables into a new common scale using a procedure known as STANDARDISATION.<\/p>\n

Standardisation works as follows.\u00a0 For each year within each variable, we first subtract the average for that variable to get the difference from the average.\u00a0 Then we divide by the standard deviation of that variable.\u00a0 For example, if the average spring temperature over the last 50 years is 7.6 degrees Celsius and the standard deviation is 0.8 degrees Celsius, then the STANDARDISED spring temperature for 2017 will be +1.9 since the actual average 24 hour UK spring temperature was 9.1 degrees Celsius i.e. (9.1 – 7.6)\/0.8 = +1.9.<\/p>\n

Notice that by dividing by the standard deviation, we convert the scale of any variable to a scale which measures the variable as Number of Standard Deviations Above\/Below the Mean value.\u00a0 So spring 2017 was almost 2 standard deviations above the average.\u00a0 If you are familiar with the properties of the Normal Distribution<\/a>, you will know that if your variable follows a normal distribution, then 95% of the data points will lie within +\/- 2 standard deviations of the mean and 5% of the data points will lie without +\/- 2 standard deviations of the mean.\u00a0 So our +1.9 for the STANDARDISED spring temperature for 2017 does suggest that 2017 was unusual (but not exceptional) and indeed spring 2017 was the 2nd warmest on record beaten only by 2011 as shown in the chart below.<\/p>\n

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Standardised variables (also known as Z-SCORES) aid interpretation of data in many ways.\u00a0 If the standardised value is positive, it means that the value is above your average or expected value.\u00a0 If it is negative, then the value is below your expected value.\u00a0 The chart above suggests that our spring temperatures have been following a rough 25 year cycle e.g.<\/p>\n