CONTENTS
CONTENTS 2
Preparing and Interpreting Statistical Reports 4
Well-Designed Statistical Reports 4
Considerations for a Report 4
Preparation: Background, Uses and Users 4
Structure 4
Language 4
Informative Titles or Headlines 5
Key messages 5
Context 5
Interpretation 5
Standards for Statistical Reports 5
Condensing Data 5
Stages 5
Measures of Central Tendency 6
Mean 6
Mode 6
Median 6
Measures of Spread or Variation 6
Standard Deviation 6
Variance 6
Presenting Information 6
Reference Tables 7
Charts 7
Bar Charts 7
Line Charts 7
Pie Charts 8
Population Pyramids 8
Scatter Plots 8
Maps 8
New and Other Ways of Visualization 8
Dynamic Visualizations 8
Animation and Video 8
Spark Lines 9
Cloud Tags 9
Infographics 9
Scenarios in Relationship between Factors 9
Correlation 9
Magnitude and Truthfulness 9
Explanatory or Predictor Variable 9
Declining Number of Enrollees in UK Education 10
Appendix 11
Figure 1: Sample image of a demonstration table in the body text of a report. 11
Figure 2: Sample image of a reference table in a report. 12
Figure 3: Sample image of bar charts in the body text of a report. 13
Figure 4: Sample image of line charts in the body text of a report. 14
Figure 5: Sample image of pie charts in the body text of a report. 15
Figure 6: Sample image of a population pyramid in the body text of a web report. 16
Figure 7: Sample image of scatter plot in the body text of a web report. 17
Figure 8: Sample image of a density map in a report. 18
References 19
Preparing and Interpreting Statistical Reports
Well-Designed Statistical Reports
Considerations for a Report
There are several considerations for writing a report. The UK Statistics Authority (2009) recommends seven points to consider. These are: (1) preparation: background, uses and users; (2) structure; ((3) language; (4) an informative title; (5) key messages; (6) context; and, (7) interpretation.
Preparation: Background, Uses and Users
One of the most important things to understand before starting the report is the background of the report or the research. Every research has question being asked or a hypothesis being tested. The purpose of the report is to answer the question in a conclusive manner.
The answer to the research question is supposed to serve a particular purpose. The report has its use. The way the report is written should keep that in mind to avoid digressing into other directions. A market research report is supposed to serve certain marketing purposes. Economic, social and other policy research reports is supposed to help in policymaking.
The specific use of the report would determine who the uses of the report would be. As there could be so much data gathered for the report, knowing the user would determine the kind and level of language that has to be used and the specific areas to be highlighted and to focus on.
Structure
Different kinds of reports follow different kinds of structure. Basically, there are generic structures followed: one for the academe which include academic papers and government reports, and another for journalism intended for the general public.
Academic reports are structured like a pyramid. They begin with an introduction, builds up it story with the details, and ends with the conclusion. They may contain some amount of technical details and explanatory notes within the body. These reports are after all trying to explain what would lead to the conclusion. The report usually begins with an abstract summarizing the message of the report. An introduction follows summing up the purpose of the project, expectations, hypothesis and methodology. The findings are discussed and wrapped with a conclusion.
In contrast, journalism reports are an inverted pyramid. They begin with a summary, conclusion and most important details. The paper is then filled with a lot of helpful information and later with some details that are nice to know but not essential to understand the matter under study.
Language
There is no argument that statistical reports should be written in very clear and accurate language. Inaccurate use of word could lead to the reader’s incorrect understanding of the report. It thus goes without saying that a statistical report should be well written.
Informative Titles or Headlines
For a journalism report, only one title—the title of the article—would serve the purpose. For academic papers, section heads should be treated as important as titles themselves. These section heads should indicate clearly what the section would contain. It should capture the essence of the section without having to go through that portion in its entirety.
Key messages
The report should not contain every detail and data covered in the research. Again, the focus should revolve on the purpose and uses of the report. Key details and messages should be discussed. These messages could serve as the outline of the report. They may also be used to guide the writing of the section heads or titles.
Context
The context should take into consideration the users of the report. The report should be able to explain what the research was done in the first place, what the findings are useful for, and why the reader should be interested in these findings. Data and information gathered for a report can have many and varied uses. So, it is important to focus on fewer kinds of users and thus adjust the report accordingly.
Interpretation
As with context, it is important to keep the users in mind. An important guideline in the interpretation of data is to avoid conjecture and opinion. Excessive use of adjectives and superlatives could introduce extreme biases into a report and these should be avoided. The interpretation of the research findings should be as objective as possible.
Standards for Statistical Reports
The UK Statistics Authority (2012) issued a statement concerning the standards that government agencies should follow in writing statistical reports. The standards has five points concerning writing:
Include an impartial narrative in plain English that draws out the main messages from the statistics;
Include information about the context and likely uses of the statistics;
Include information about the strengths and limitations of the statistics in relation to their potential use;
Be professionally sound; and,
Include, or link to, appropriate metadata.
Condensing Data
Data and findings of a research are very numerous and can be very difficult to make sense of. All these information need to be organized and condensed into more meaningful. Condensing the data usually follow three stages.
Stages
Exploring the data is the first stage of research analysis and report writing. The writer tries to grasp to extent and indications of the data. The process also includes organizing the data and determining which statistical methods should be used for analysis.
Building a model and testing these models is the second stage. Many models can actually be applied to analyze the data. The most appropriate one will have to be chosen.
The application of the selected model is applied to the data. This is the third stage and it is also called the deployment stage. The application of the model aims to predict the predict as to where the data would lead to.
Basic analysis of data usual involves the measures of central tendency and the measures of spread or variance.
Measures of Central Tendency
The frequency distribution of data usually converge at a certain point. These are measured in terms of the mean, the mode and the median.
Mean
The mean is the average of all the data gathered. It is simply the total amount divided by the total number in the population.
Mode
The mode is the point that has the highest frequency of data occurrence. It is essentially the point that has the highest count of the data occurrence.
Median
Spread from highest to lowest, the median is the central or middle point all the data regardless of the frequency of the occurrence of the values. It refers to middle position in the array of values and does not consider the specific value of each data entry.
Measures of Spread or Variation
Data tend to be converge at a central point and spread out toward the highest and toward the lowest values. This spread is estimated by standard deviation and variance.
Standard Deviation
Standard deviation determines how diverse the data in the set is. It estimates how close to the center or how spread out from the center the array of values. The standard deviation is the square root of the variance.
Variance
Variance is another index or measure of the spread of data from the convergence point. It is the square of the standard deviation. The standard deviation can be derived the getting the square root of the variance.
Presenting Information
Not all information can be presented clearly in text or prose form. Data need to be summarized and presented in a form that people could easily understand. Visualization is thus important. Visualization helps organization in easily readable from. It also condenses data in an already interpretative form. For instance, bar charts make it easy to compare data side by side.
The UNECE (2009) classifies and recommends three common ways of visualizing data: (1) tables, (2) charts and (3) maps.
Statistical reports today are not always presented in print form. After all, there are new technology and new media. Data could now be prepared, processed and presented in ways that were not possible in the past. Publishing and distributing statistical report could now be done forms other in print—including such media as the internet and social networking site, audio-visual presentations, video, among others.
Under each classification of visualization forms are several ways of presenting data.
Using a table is a way of presenting numeric (or also text) in an organized and systematic form. (New technology has allowed the use of graphics in tabular format.) These are usually detailed information that is confusing to present as text and too detailed to present in chart form.
A good table should have the following elements to guide the reader in the presentation of the data: a table number (if there are more than one table in the report) and title; column headers at the top; row stubs; footnotes and other explanatory notes at the bottom; and, a source line at the most bottom part of the table identifying where the data had been obtained.
There are two types of tables: (1) presentation or demonstration tables; and, (2) reference tables.
Presentation Tables
Presentation or demonstration tables are small tables inserted in the body text of a report. It is small enough to fit the format of the body and short enough to be understood at one glance.
Reference Tables
Reference tables are large table formats. While it is usually large, it is still a summary of all data gathered in the research. These tables are usually found in the appendices of reports.
Charts
Statistical data can sometimes be better illustrated as charts. They can show in compact form summaries of a large amount of data or express a key message or finding. Charts are used for several reasons. First is for comparison, especially with regard to relative sizes. Second is to show changes over time. Third is to show frequency distribution—to show how a phenomenon occurs in different segments of the population. Fourth is to show correlation, to show how variables are linked together. Fifth is to show the share of anything in a given population.
Bar Charts
Bar charts are used to compare figures of different categories or groups. They may be presented in either horizontal or vertical form. Stacked bars can also be used. They show percentage shares or cumulative data of different groups under different categories.
Line Charts
Line charts are used for used for time and other continuous series of data. They show a phenomenon or developments are progressing through time or through increasing independent variable. More than one line can be presented in a chart. Each line is distinguished from each other by a different design—e.g., dots or dashes—and each representing a different dependent variable against the same independent variable. Time or the independent variable is usually plotted on the horizontal axis. Lines convey the idea of movement. Thus, line charts are usually used for data that is continuously growing or moving toward a certain direction, either in time or value.
Pie Charts
Pie charts are useful when one wants to show the percentage distribution of a variable across several parts. The pie is usually the 100% total of the different parts. A pie chart can accommodate only a few variable or segments. As much as possible, the segments should not be more than six. Otherwise, the segments may be very difficult to see. They are most useful when one has to show the importance of certain segments to a whole or to provide an overview of a given situation.
Population Pyramids
Populations pyramids are a combination of two horizontal bar charts. Two classes of data with numerous sub-groups are compared. The vertical axis is in the center of the chart and the data for the two classes being compared are plotted in opposite directions on the horizontal axis. A common use of the population charts is to compare the male and female segments of the population across subgroups like age.
Scatter Plots
Scatter plots is a line graph with point scattered around line. The line (which may not necessarily be visible represents a certain norm or standard through time. The scatter points represents how the data perform along that line. The line can also be derived from the scatter points through linear regression. The central line can be likened to the mean in a data array; the scatter may be likened to the standard deviation. Unlike the mean or standard deviation that are fixed, scatter plots are a data series.
Maps
Maps are usual when one wants to present the distribution or dispersion of data in a geographic location. They visualize geographical visual patterns. They quickly convey at glance distribution and patterns that may not be obvious in charts or tables. Maps have come to greater use today because of computer software and technology. Color or varying density of dots is an important component of maps. Different colors or shades of a color can distinguish characteristics in different areas of the map. It is important that the regions in a map are clearly distinguished from one another.
New and Other Ways of Visualization
New technology and media has allowed new ways for the visualization of statistical information. Video and new forms of graphics are now being used. Also, there are now other ways of publishing and distributing statistical reports. The can come in the form of audio-visual presentation (like PowerPoint), a documentary video, a section in a website, and many other ways.
Dynamic Visualizations
On the internet, users can now custom-design their own tables using data for their own specific purposes. Different summary tables can be made out using data from the provided reference tables or database.
Animation and Video
Animation and video are now particularly useful to show transitions, changes, growth, and other data undergoing transformation through time or some other independent variable. With the help of new technology, these kinds of presentation can now be produced on the computer and distributed on the internet easily.
Spark Lines
Spark lines are essentially line charts presented in very small sizes to fit body text or inserted inside tables. They show certain patterns of movements from point to another without having to show many numbers.
Cloud Tags
Cloud tags are highlighted or enlarged texts within the body text. These tags may use color different from the text. These have become common and have practical use on the internet. They can draw attention readers’ attention themselves. Usually, they are hyperlinked to other places on the internet. Clicking on the tags would lead readers to explanatory notes or other references important to the topic. These tags with hyperlinks are particularly useful. They lead a user to other references not initially indicated in the text of a report.
Infographics
Infographics in the form the item the data is referring to. For instance, statistics about housing could be displayed in the form of a house. Differences in amounts, size or values are presented in varying sizes of the graphic element.
Scenarios in Relationship between Factors
It is not enough to collate and organize information. It is important that the report goes beyond averages and variances. To serve fully its purpose, the report must provide information on how the findings could forecast certain phenomenon.
An analysis must be made on how the different variables relate to each other. How the variables are correlated must be established.
Correlation
The correlation between variables can be positive or negative. A positive one (+1) correlation means that the variables are100%, correlated. An increase in one variable corresponds with an exact amount of increase in the other variable. As the correlation increase the impact of one variable to the other diminishes until it becomes a negative correlation. A negative correlation means that an increase in one variable corresponds to a decrease in another. A negative one (-1) means that the variables are completely negatively correlated. An increase in one variable corresponds to a an equivalent decrease in the other.
Magnitude and Truthfulness
The magnitude as well as truthfulness of this relationship needs to be estimated. The magnitude would indicate the intensity of the impact if certain variables are manipulated; the truthfulness measures the validity of future estimates using samples. It provides a level of confidence or the probability that such an event would also take place in the population as it had in the sample.
Explanatory or Predictor Variable
If a research aims to be able to provide a theory on how to predict certain events, the report should be identify which variables are explanatory, independent or predictor and which are dependent, in particular the dependent variable that will be controlled or manipulated. This is particularly important in policymaking. For instance, would higher education necessarily bring about higher incomes? Higher education in this case is the explanatory variable. Then, would higher government funding get more people to attain higher education?
The interaction among variables needs to be studied thoroughly. The relationship among variables is more complex. In the real world, many variables work together to affect events. It is a combination variables with positive and negative correlations working or fighting each other. All of these may need to be studied simultaneously. Only with such information can correct judgment be made in policy-making, especially in choosing which variables needs to be manipulated.
According to Whitaker and Mitchell, correlation among variables can be estimated six ways:
1. Simple linear relationships between two continuous variables;
2. Simple relationships between two categorical variables;
3. Multiple linear relationships between continuous variables;
4. Multiple relationships between categorical variables;
5. Nonlinear relationships; or,
6. Time-dependent or lagged relationships.
Simple linear relationships, multiple linear relationships and time-dependent relationships are of particular relevance in policymaking.
Declining Number of Enrollees in UK Education
In the school-years 2011-2012 and 2012-2013, the number of students studying has been declining after a steady though slow growth from 2003-2011. The decline seems to be occurring at all levels, in all age groups, and across genders. By age group and level, undergraduates over 30 years old showed the biggest drop during the period. Among regions, the decline is particularly more pronounced among English schools in the UK. Enrollment in certain subject areas—computer science, historical and philosophical studies, languages, education and subjects allied to medicine—also declined. The figures did not seem to indicate shifts into other forms of education. Even distance learning reflected a drop. The data available did not have much information about income brackets.
The decline does not seem to be the result of UK’s education financial support to universities. After all, from 2003 to 2011, enrollment steadily increased until 2011-2012 school-year. Other variables may be causing the problem.
It is unlikely that decline could be the result of attitude or behavior change. The attainment of higher education results in higher income in later life. Most people would thus want to pursue higher education.
The decline seems to be stemming from students inability to go to school. This could be happening for several reasons. One, more and more students can no longer afford to UK schools. This may be a belated impact of the Euro Crisis which is still plaguing the Eurozone.
Two, more and more students may not be meeting admission requirements. Some may not be applying anymore as they know they would not pass. It is a remote possibility, but the matter should be explored. The decline and removal of grammar schools in the country could be having an effect on later education.
An area that may be explored may be with regard to subsidies or low-interest, long-term loans to students, instead of grants to schools. Only selected students—usually the best and the brightest—benefit to grants given to schools. Providing loans to ordinary students might help arrest the continued decline in enrollment.
Appendix
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