# How To: Analyse & Present Data

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2 EXAMPLE 2: Audit criteria: All patients should attend a pre-op clinic Exception: emergency operation Results: Yes = 32, No = 13 and N/A (emergency) = 32 = 32 4 x 32 patients attended a pre-op clinic 18 did not, but of these were emergencies (exception criteria) Therefore 32/4 (71%) met the standard B. NUMERICAL DATA Some of the data items you collect are likely to be numerical values, e.g. age, length of stay in hospital, blood glucose level etc. Lists of numbers like this can be summarised using measures of central tendency and dispersion: Measures of central tendency look at the middle/common values in a list of data items: the mean, median and mode. Measures of dispersion look at how spread the data is: the range. MEASURES OF CENTRAL TENDENCY The mean is the average value, calculated as: Sum of all the values Number of values The table below shows data about length of stay (LOS) on three wards: Length of Stay (days) Number of patients discharged Ward 1 Ward 2 Ward For Ward 1, the mean is: (1x4) + (2x8) + (3x12) + (4x18) + (x) + (6x18) + (7x12) + (8x8) + (9x3) = 11 = The mean LOS on ward 1 is days (rounded to nearest whole day). If the same formula were used to calculate the means for wards 2 and 3, you will find that for each ward, the mean LOS is days. However, the mean is not always the best measure of central tendency. The LOS for all three wards is illustrated on the graph below. The mean suggests that the data is the same for all three wards, however the graph indicates that this is not the case. The problem with the mean is what it does not tell us. 9 UHBristol Clinical Audit Team Version 3 Page 2 of 8

3 Length of Stay Number of patients discharged Ward 1 Ward 2 Ward 3 Day The data collected for Ward 1 is almost perfectly symmetrical, with the graph illustrating that the data follows the shape of a bell curve. Data that conforms to this shape is known as parametric data. In this instance the mean is an appropriate measure of central tendency. The data for Wards 2 and 3 is non-parametric. Their graphs do not form a symmetrical curve. Describing their notable features, Ward 2 has a significant proportion of patients with a LOS of 3 days together with a number of patients staying 9 or days. Ward 3 has a peak LOS of 6 days. It can be seen that using the mean alone with non-parametric data is not very informative. The median and mode can help to convey the missing information. The mode is the most commonly occurring value. For Ward 2 this is 3 days and for Ward 3 it is 6 days. This should be obvious from both the raw data and the graph. If the highest occurrence is shared by more than one value you could either state them all as modal values, or none. For example, if for Ward 3 there were patients discharged on both day and day 6 you could either say there were 2 modal values of and 6, or that there was no mode. The median is the mid-point of all the values. For Ward 2, we have data on 67 patients. If we made a list of LOS, placed in order from the lowest to the highest, the mid-point would be the 34 th value i.e. there are 33 values below and above this. The 34 th value relates to a patient who was discharged after days, so this is the median. For Ward 3, we have data on 42 patients, i.e. there is no single mid-point. In this case, take the average of the 21 st and 22 nd value (there are values below and above these two values). The 21 st value relates to a patient who was discharged after days and the 22 nd value relates to a patient who was discharged after 6 days, so the median is. days (+6 divided by 2). Unless you are well versed in statistics, we would advise that you use all three measures of central tendency, or show the information using a graph. In general, quote median rather than mean for non-parametric data. Not all lists of numerical data should be analysed in this way. For example, if your standard is The patient will be considered medically fit for surgery if temperature <38 C and you collect a list of temperature data, it would not be meaningful to present the mean, median and mode temperature. What you are interested in here is the percentage of cases that met the standard i.e. the percentage of surgical cases with temperature <38 C. MEASURES OF DISPERSION As well as stating the mean, median and mode, it is also good practice to provide some indication of how spread the data is. The range states the lowest and highest values. In our example: Ward 1 has a range of 1-9 days Ward 2 has a range of 1- days Ward 3 has a range of 1-8 days 9 UHBristol Clinical Audit Team Version 3 Page 3 of 8

4 A more subtle way of expressing dispersion is to use quartile range. This involves listing your values from lowest to highest, as per calculating the median, and then dividing the values into four equal parts or subranges. The range you are interested in lies between the second and third quarter (or quartile ). So, for example, some more LOS data: Ward C: In this case the range is 1-38 days, but the quartile range is -9 days The quartile range is useful in taking out outlying data (data some distance away from the mean/median/mode), as in the case of Ward C above and Ward 2 in our first example. Ward 2 has the largest range but a comparable quartile range to Wards 1 and 3: Ward 1 - range 1-9 days; quartile range 4-6 days Ward 2 - range 1- days; quartile range 3-7 days Ward 3 - range 1-8 days; quartile range 4-7 days ANALYSING DATA AGAINST STANDARDS If your standard statement was Patients should be discharged by the end of their th day following surgery, using LOS data for ward 2, you find that 4 out of the 67 discharged patients had a LOS of days or less. You would write this as 4/67 (67%) patients met the standard. C. FREE-TEXT DATA If you include an open question in your data collection form, you will obtain free-text data. In order to analyse this data you should group comments into themes or categories, i.e. as if you were creating tick-box options for the data collection form. You might also want to consider reproducing some comments verbatim in your report, if they are particularly pertinent. DRAWING CONCLUSIONS The end stage of your analysis is concluding how well the standards were met and, if applicable, identifying reasons why the standard was not met in all cases. These reasons might be agreed to be acceptable, i.e. could be added to the exception criteria for the standard in future, or will suggest a focus for improvement. In theory, any case where the standard (criteria or exceptions) was not met in % of cases suggests a potential for improvement in care. In practice, where standard results were close to %, it might be agreed that any further improvement will be difficult to obtain and that other standards, with results further away from %, are the priority targets for action. This decision will depend on the topic area, in some life or death type cases, it will be important to achieve %, in other areas a lower result might still be considered acceptable. 2. DISPLAYING DATA CONTINUOUS DATA A set of data is said to be continuous if the values/observations belonging to it may take on any value within a finite or infinite interval. You can count, order and measure continuous data. For example height, weight, temperature, the amount of sugar in an orange, the time required to run a mile. 9 UHBristol Clinical Audit Team Version 3 Page 4 of 8

5 Continuous data fits on a numerical scale. Examples of continuous data include: Temperature: 34, 3, 36, 37, 38, etc. Days post-op: 1, 2, 3, 4,, 6, 7, 8, etc. Age: 16, 17, 18, 19,, 21, etc. Generally when displaying continuous data, it would be appropriate to use charts that allow you to lay out this numerical scale and plot data against it e.g. scatter graphs, box and whisker plots, etc. CATEGORICAL DATA Categorical data is data that can be sorted according to non-overlapping (mutually exclusive) categories, whereby each subject in a sample can only fit into one category. For example: Gender: Male/ Female Age group: 16-, 21-, 26-3, etc. Standard met: Yes / No The usual type of data resulting from a clinical audit is categorical data and would most commonly be represented as a bar chart or a pie chart. PIE CHARTS AND BAR GRAPHS Bar or pie charts are most commonly used in clinical audit to illustrate compliance with audit standards, however there are certain circumstances where one or the other is better. Pie charts - Show proportion, e.g. percentage compliance with standard. A pie chart would be inappropriate if, for example, it was being used to illustrate type of treatment in cases where patients are likely to have had more than one treatment. In this instance the pieces of the pie would add up to the total number of treatments rather than the total number of patients, which could be misleading and is not very meaningful in itself. Bar/column charts - Generally used to show frequency, e.g. number of patients seen by different staff: nurse, Specialist Registrar, Consultant, etc. For example if the audit criteria stated that all patients seen in A&E meeting certain criteria should be seen by a consultant, you might want to show what grade of staff saw the patients if it was not the consultant. Versions of Bar charts (stacked or comparative) - Show more than one standard/ question per chart, e.g. multiple results on one graph, bars divided to show percentages, etc. EXAMPLE 3: Pie Charts, Bar Graphs & Comparative Bar Graphs Was Standard 1 met? Was Standard 1 met? n = Fully % Partially % Number of patients 3 n = Not met 3% Fully Partially Not met 9 UHBristol Clinical Audit Team Version 3 Page of 8

6 Were the standards met? Fully Were the standards met? n = Number of patients n = Partially Not met Standard 1 Standard 2 Standard 3 Percentage of patients % 9% 8% 7% 6% % 4% 3% % % % Standard 1 Standard 2 Standard 3 Not met Partially Fully CREATING GOOD CHARTS Good charts should focus on getting your message across, rather than creating fancy, and distracting, images. Clutter should be avoided and the charts clearly labelled. REMEMBER: Do not use graphs just for the sake of it. EXAMPLE CHART 1: 37/4 members of staff (93%) took personal protective equipment on domiciliary visits Did member of staff take personal protective equipment with them? Yes 3 No 37 A chart might be considered unnecessary to illustrate the above data. It is always important to consider whether or not people need to see a graphical representation of the data, in some cases simply expressing the data as x/n (y%) is sufficient. In a project with a lot of standards producing a chart for every single one may confuse rather than clarify the results. People may not remember which image related to which standard. 9 UHBristol Clinical Audit Team Version 3 Page 6 of 8

8 PATIENT ENGAGEMENT For advice on Patient Involvement, including designing structured surveys and questionnaires contact Paul Lewis, Patient Involvement Facilitator, tel. (117) or For advice on Patient Involvement, including unstructured surveys and focus groups contact Tony Watkin, Public Involvement Lead, tel. ( or Surveys MUST be approved by the Trust's Questionnaire, Interview and Survey (QIS) Group. Proposals should be submitted to Paul Lewis using the QIS proposal form. The proposal form is available [online] via A copy of the UHBristol Covering Letter template is available [online] via the internal intranet site RESEARCH For advice on research projects contact the Research & Development Department, tel. (117) or LITERATURE REVIEWS For advice on literature reviews contact the Learning Resource Centre, tel or SAMPLE SIZES The Sample Size Calculator is available [online] via: 9 UHBristol Clinical Audit Team Version 3 Page 8 of 8

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