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Statistical Table & Statistical Graph

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Statistical Table & StatisticalGraph

Zhang Guozhen

School of Public Health

Xinjiang Medical University

- Statistical description is a kind of fundamental work for statistical inference, which describes the feature of the sample.
- The main forms for description are tables, graphs and numerical indexes.
- Statistical tables and graphs are two kinds of forms made of point, line, area and number.
- They can show the information of data directly. So they are widely used in medical practice.

§1 Statistical Tables

Example1 125 children were tested in county B and 9 cases were found In this study, 221 children were tested in county A and 4 cases were found suffering from rachitis; the prevalence rate was 18.10 per thousand.; the prevalence rate was 72.00 per thousand. 248 children were tested in county C and 2 cases were found; the prevalence rate was 8.00 per thousand…..

- Very tired and verbose.
- Difficult to remain any impression

Table 1 Rachiotis prevalence rates in 5 counties

- Clearimpression !
- Easy to compare each other !

- The main contents must be emphasized, simple and understood easily.
- Primary and secondary contents as well as arrangement must be clear

- Title:generalize the contents, including time and site. The title is located on the top of the table and a sequence No. is on the left of the title.
- Horizontal item:indicate the subjects investigated, usually located in the left of the table.
- Vertical item:indicate statistical index including the units, usually located in the right and upper of the table.

Table 1 Rachiotis prevalence rates in 5 counties

- Lines (horizontal only):
- Top and bottom (dark): define the range of table
- Others (light): separate items and figures.
- Not suitable to having too many lines. The vertical lines and skew lines can’t be allowed.

- Figures:require to use Arabian number in the statistical table and the decimal must be accordant. The empty cells can’t be allowed.
- Notes:usually use star mark “ ” to express notes,
and the mark “ ” usually put on the bottom of

the table.

Table 1 Table title

Top line

Item line

Total line

Bottom line

- Simple table:One variable only
- Combinative table: More than 2 variables

- Row item: Subject
- Column item: Predicate
- The table read as:
- The group of HBsAg carriers has 1457 persons tested, among which 46 positive with positive rate 3.16%.
- 2. The group of HB patients has 1224 persons tested, among which 161 positive with positive rate 13.15%.

Example 2

The mental score and other factors related to coronary heart disease were researched in certain area. The results were shown in table 5

- Too much content was put in a table, especially, the measurement data and numeration data were put in a table.
- Many blank space in table because of incompatible content in different column.
- Inversion of row item and column item
- Too much content, complex ranks, data inappropriately arranged in table

Solution：dividing it into two tables, table 6,7

- Title: Not exactly fit the content
- Content:
Too much;

Mix of important and many non-important ones

- Items:Inappropriately arranged
- Figures:
Total and subtotals; Digits and decimals

- Lines: Using vertical lines and oblique lines

What’s wrong with the following table?

§2 Statistical Graphs

- advantage: data visualization and remaining impression.
- The purpose of using graphic displays is to give a quick overall impression of the data, which is sometimes difficult to obtain with numeric measures.

type：Different graphs according to different purposes and types of data

bar graph, histogram, percent bar chart,

pie chart, line graph, scatter plot ,statistical map, stem-leaf plot, box plot, residual plot

Basic requirements:

- Axis: Y-axis (vertical) and X-axis (horizontal).
- Legend:explain meaning of colors or patterns.
- Title:under the graph; content, time, place.

Principle

- Select the proper graph according to different aim of study and the character or feature of data.
- Title: including time , place and main content .
below the graph

- Index and unit are shown in the Y-axis and X-axis. The point of intersection commonly is 0. The ratio of Y-axis to X-axis is 5：7 properly.
- Different lines and colors indicate different statistical value of subjects. Marginal data is attached to the graph.
- Legends are the notes of a statistical graph, usually located on the right top corner or located between the bottom of the graph and the title.

legend

Vertical item (unit)

legend

Graph body

0

Horizontal item (unit)

Fig 1 The basic structure of a statistical graph

- bar chart
- pie chart
- percent bar chart
- line graph
- Histogram
- Scatter Diagram

- Compare figures of different populations
- Display the comparison among similar and relative independent data
- Often used to compare the level of the variable at several locations
- simple bar chart or complex bar chart

Example 3 Mortality rates of main cause of death are shown in figure 1.

Bar chart is selected because the cause of death is interdependent indexes. Simple bar chart , only classified by the cause of death .

Figure 2 mortality rate of main cause of death (/100,000)

Fig.3 Average cost of outpatients for several treatments in a hospital in 1994 and 1997

- Label both axes clearly
- Leave space between bars
- Leave space between the left-most bar and the vertical axis
- When possible, begin the vertical axis at 0
- All bars should be the same width

- Describe percentages of all the parts of population
- Indicate the proportion
- The 360o angle at the centre is apportioned to each item in the total in proportion of its magnitude .

- Give clear, complete title
- Label all sections clearly
- use a legend or key

- Order by frequency
- Start at top (12:00)
- Move clockwise from start

Fig.4 The pie chart

10%

40%

15%

17%

18%

Fig.5 Percentages of the reasons for re-addiction (xx place,1996)

A pie chart is good for making relative comparisons among pieces of a whole.

Compare frequencies of a category variable

- Indicate the proportion

Fig. 6 Mother’s education manner in group of drug addicts and group of controls. (xx place, 1996)

Describe the changing of Y with X (time) -- tendency

Fig. 7 Incidence rates of stomach cancer in a city

- Used for expressing a phenomenon changes with the time and condition, or one phenomenon changes with another phenomenon.
- Its horizontal axis and vertical axis are all arithmetic rules.

Fig.8 example of line graph

- Used for expressing the developing velocity (relative number) of a phenomenon changes with the time ,condition, or another phenomenon.
- Unlike a general line graph, its horizontal axis is arithmetic rule and vertical axis is logarithmic rule.

Left: The absolute difference of mortality rates ~ Year

Right: The absolute difference of log (mortality rate)

Suitable line graphs in different situation

- Describe a frequency distribution of continuous Quantitative Data
- A histogram is a diagram in which:
- The horizontal scale represents the value of the variable marked at interval boundaries.
- The vertical scale represents the frequency or relative frequency in each interval

Fig.9 Age distribution of first attack among 215 cases

A histogram is the continuous data analogue of the bar chart.

- It is a picture of the number of observations in each of the class intervals
- The bars are adjacent or touching, which reflects the continuity of the data
- Equal width intervals are strongly recommended
- Area (width x height) of bar represents proportion
in the interval

Some guidelines for constructing histograms :

- The graph title should be a complete description of the graph
- Clearly label both the horizontal and vertical axes
- label either endpoints or midpoints on horizontal axis

- Include all intervals, even when “empty”
- Break axes when necessary
- Use equal class widths

Describe the relationship between two numerical variables.

Is the relationship linear or non-linear?

Fig 10 Relationship between temperature and deaths due to bronchitis and pneumonia.

- A nice table can save a lot of words, show the fundamental characteristics and their relationship clearly.
- Comparing to statistical tables, nice looking statistical plots are even more intuitive and understandable.
- Contrarily, a poor organized table or a messy plot may sicken people.

Thank you!