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A film which ultimately examines how societies condone bullying and the alienation of those perceived as different. Indie Cork, Ireland. Offline, Birr, Ireland.
The production of descriptive statistics is a straightforward matter, most statistical packages producing all the statistics one could possibly desire, and a choice has to be made over which ones to present. These then have to be included in a paper in a manner that is easy for readers to assimilate. There may be constraints on the amount of space available, and it is in any case a good idea to make statistical display as concise as possible. This article reviews the statistics that might be used to describe a sample of older people, and gives tips on how best to do this in a paper for publication in Age and Aging.
It builds on a previously published paper [ 1 ]. The values observed in a group of subjects, when measurements of a quantitative characteristic are made, are called the distribution of values. Graphical displays can be used to show the detail of the distribution in a variety of ways, but they take up a considerable amount of space.
A precis of two key features of the distribution, its centre and its spread, is usually presented using descriptive statistics. The centre of a distribution can be described by its mean or median, and the spread by its standard deviation SD , range, or inter-quartile range IQR.
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Definitions and properties of these statistics are given in statistical textbooks [ 2 ]. Figure 1 a shows an idealised symmetric distribution for a quantitative variable. The mean might be used here to describe where the centre of the distribution lies and the SD to give an idea of how spread out values are around the centre.
SDs are particularly appropriate where a symmetric distribution approximately follows the bell-shaped pattern shown in Figure 1 a which is called the normal distribution. Presentation of the mean and SD invites the reader to calculate the normal range and think of it as covering most of the distribution of values. Another reason for presenting the SD is that it is required in calculations of sample size for approximately normally distributed outcomes, and can be used by readers in planning future studies. A graphical display of approximately normally distributed real data age at admission amongst study participants is shown in Figure 1 c: with relatively small sample size a smooth distribution such as that shown in Figure 1 a cannot be achieved.
The mean For familiar measurements, such as age, there is additional value in presenting the range, the minimum and maximum values attained.
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Knowing that the study included people aged between 65 and years is immediately meaningful, whereas the value of the SD is more difficult to interpret. Idealised and real data distributions.
The median is often recommended as the preferred statistic to describe the centre of a skewed distribution, but the mean can be helpful. If the attribute being described takes only a limited number of values, the medians of two groups can take the same value in spite of substantial differences in the tails.
In these circumstances, the mean can be sensitive to an overall shift in distribution while the median is not. When a comparison of cost based on length of stay is to be made, presenting means of the skewed distributions facilitates calculation of cost savings per subject by applying unit cost to the difference in means. Figure 1 b suggests that the value with highest frequency might be a useful descriptor of the centre of a distribution.
In practice, this can prove awkward: depending on the precision of measurement there may be no value occurring more than once. It is clear from Figure 1 b that no single number can adequately describe the spread of a skewed distribution because spread is greater in one direction than the other. The range from 1. Another possibility is the IQR from 3. The SD may be presented even though a distribution is skewed, and could be useful to readers for approximate power calculations, but the normal range derived from the mean and SD will be misleading.
The participants reported the diagnosis of an average of 2. There are perhaps too many attributes age, gender, marital status, employment status, educational level, living arrangements, nationality, personal income and number of chronic conditions being described in the excerpt above: it would be easier to assimilate this information from a table. Where there are too many characteristics to be described in text, or several sub-groups of participants are being compared, tabular presentation becomes more convenient.
An example summarising the distribution of 11 categorical variables and 2 quantitative variables in the 2 phases of a before—after evaluation of the introduction of a care pathway for hip fracture [ 4 ] is presented in Table 1.
The categorical variables so-called because they indicate which of several categories a participant falls in are best described by the number and percentage in each category. It is best to give the number as well as the percentage, unless a study is very large, to emphasise that percentages are estimated with imprecision.
Unless a very large sample is available, the information conveyed by the decimal places in a percentage is spurious accuracy. Displayed with two decimal places it becomes No other values between Even were a large enough sample available to distinguish between percentages of This artefact can occur in the final digit however many decimal places are presented. Table 1. The distributions of the two quantitative variables in Table 1 are described by mean SD and range. The statistics being presented should be stated in the context of the table, here in the left hand column, and could differ across variables.
If the same statistics are presented for all the variables in a table they can be indicated in the column headings or title. We can see that the distribution is skewed because the mean is much closer to the minimum than the maximum, and, if the normal range is calculated, the upper limit does not approach the high values in either phase. A choice arises when describing the distribution of an ordinal variable indicating ordered response categories, such as ambulation score in Table 1.
If the variable takes many distinct values, it can be treated as a quantitative variable and described in terms of centre and spread: ordinal variables often extend from the minimum to maximum possible values and in this case stating the range is not helpful. The meaning of the extremes should be stated in the context of the table to aid interpretation of results. With only five categories the latter approach was adopted for ambulation score.
The success of an organization is closely linked to the freedom that its employees have to express their views and ideas. A company which treats questions to senior management as insubordination is bound to create a culture of fear. If people Read more. Dental Assistant vs. Dental Hygienist. Basics of Negotiation for Beginners. Types of Small Business Loans.