. Q. 1. I am interested in exploring the pattern of my data over time and suspect that there is seasonality in the incidence of pneumonia over time. Can you recommend some ideas on suitable graphs?

A. You can make a good start by considering the resource Seasonality. This particular resource encourages the use of box-plots to represent your data. Also, please see the note item 4., later in this solution to see how you may access some relevant practise data. You can learn more about the anatomy of a box-plot and how to construct one using SPSS by referring to Q.’s 13 to 15 and the corresponding solutions on the WordPress MedStats page GRAPHICAL PRESENTATION OF DATA.

As you have data collected across different time-points,the relationships in your data are likely to be influenced by a range of factors. These include seasonality (reflected by periodic behaviour within a given time interval), trends (influencing the extent to which this periodic behaviour may change monotonically over time) and confounding factors, such as temperature and humidity and error variation. This explains why it is useful to decompose the data so as to pull out the influence which is specifically due to seasonality. To access some very good training for this purpose within SPSS, follow the steps below.

1. Select the option ‘Topics’ from the menu ‘Help’.

2. Enter the search term ‘seasonal decomposition’ in the search box and then hit the return key on your computer keyboard (or perform an equivalent operation).

3.  Double-click on the first return you receive and consider the training material at the links to the first three listed topics provided in the main window.

4. Note the instructions at the third of these links for accessing the relevant SPSS spreadsheet, catalog.sav, for the worked example.

NB. The above data have been adapted so that you also create a box-plot with individual months along the x-axis (or category axis) and sales of men’s clothing (scale variable) on the vertical axis.

The topic of time series analysis is much more comprehensive than the uninitiated could hope to take on board during the conduct of a short research project. Nevertheless, there are a range of exploratory analyses, including those above, that can be performed using study data to inform future work.

In addition, it is helpful to consider scatter-plots of continuous variables over time where you suspect  that these variables are potential confounding factors explaining some of the patterns in your data. For this purpose, you should aim to work on the raw data. For example, if you have monthly temperature readings over time, don’t just plot mean temperature by month but make sure you break down the monthly readings according to year as well. This will help in the identification of trends, bleeps and seasonality more accurately. Excel is very suitable for this purpose, although it lacks the functionality which SPSS affords for a full time series analysis. There is plenty of information in the Statistics index on making friends with Excel charts. Please refer to the MedStats WordPress page Excel – handy guides, tutorials and tips if you need further help in this area. Once you have explored your data in this way, you may wish to move on to consider assessing correlation (if your graphs suggest the existence of a correlation). On referring to the MedStats WordPress page CORRELATION COEFFICIENTS – LINEAR AND NON-LINEAR , you will find a list of FAQs that cover this area in detail. Assessing correlation at this stage will inform a future study in which the importance of your suspected confounding variables can be taken into consideration based on your findings.

· Q. 2. I am trying to decide on a seasonality index for quantifying incidence of pneumonia.  Can you recommend some suitable choices?

A. One of the most accessible choices is the winter/summer ratio and its variants (see section 3.2.2 of Chapter 3 in Roland Rau’s electronic book Seasonality in Human Mortality: A Demographic Approach). Variants of this index can arise if you feel that it is not specifically winter and summer which you wish to compare. Your graphs should help here (see solution to Q. 1, above) and you should aim to be flexible!

· Q. 3. What are the main limitations of the winter/summer ratio of which I should be aware when writing up the discussion section of my report.

A. I have designed the document Limitations of the winter/summer ratio (and its variants) as a seasonality index to assist you (see below). I hope you find it helpful! 

· Q. 4. Can you recommend a good method for obtaining a 95% confidence interval for the winter/summer ratio?

I would recommend the Wilson (1927)* “score” method. The C-P method is more conservative (i.e. delivers a wider confidence interval (CI) than the Wilson method.

The first block of the following Excel spreadsheet calculates the Wilson confidence interval for a proportion: ciproportion.xls. You can download the spreadsheet (by saving it) and insert your own frequencies to obtain the required confidence limits. If you use the spreadsheet online, please don’t save your changes. 

 By way of illustration, consider the data for monks represented in Figure 3.4 of section 3.2.2 of Chapter 3 in Roland Rau’s electronic book Seasonality in Human Mortality: A Demographic Approach.

1. There appear to have been approximately 113 deaths in January to March and 69 in July to September, leading to a winter/summer ratio of 113/69 (or, 1.638).

2. The total number of deaths over the periods of interest (January to March and July to September) is 182.

3. In turn, the proportion of deaths which occurred in January to March is 113/182 (or, 0.621).

4. You ought to use the fraction obtained for your data at step 3 within the above Excel template. In the above example, this fraction includes a numerator of 113 and a denominator of 182 (or ‘113’ out of ‘182’). You will see the expression ’81 out of 263′. So it is necessary to replace the ’81’ and 263′ in the component of the template labelled Wilson score method by ‘113’ and ‘182’, respectively.

5. The CI limits will update automatically, giving you a new interval of (0.5486, 0.6882).

6. But this is a CI for the incidence 113/182 and what you are after is CI for the winter/summer ratio. To obtain the latter from the former, use the formulae provided below.

winter/summer ratio limit = limit for the incidence/(1- limit for the incidence).

7. In our example, the corresponding calculations are

left-hand limit: winter/summer ratio limit = 0.5486/(1- 0.5486) = 1.215

right-hand limit: winter/summer ratio limit = 0.6882/(1- 0.6882) = 2.207.

8. Thus, we can report a summer/winter ratio of 0.621 (95% CI = (1.215, 2.207)).

9. Now it’s your turn!

 Thanks are due to Professor Robert Newcombe, Professor of Statistics, Cardiff University for providing the above Excel template and for suggesting the above example.

*Access the original paper which presents the Wilson score method: Wilson EB (1927) Probable inference, the law of succession, and statistical inference

.Q 5 I wish to determine whether my hospital waiting times data are stable over time. Can you recommend a convenient procedure for doing this?

A. There is a helpful video tutorial available on the essentials of constructing Control Charts using the statistical software programme Minitab. Please click on  Using control charts to obtain advice on the relevant steps.

Time Series Analysis by Margaret MacDougall is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.