Statistical Table & Statistical
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Statistical Table & Statistical Graph. Zhang Guozhen School of Public Health Xinjiang Medical University. Statistical Tables and Graphs. Statistical description is a kind of fundamental work for statistical inference, which describes the feature of the sample.

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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 Tables and Graphs

  • 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


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


Put into a table

Table 1 Rachiotis prevalence rates in 5 counties

  • Clearimpression !

    • Easy to compare each other !


Principles of Making Tables

  • The main contents must be emphasized, simple and understood easily.

  • Primary and secondary contents as well as arrangement must be clear


Construction of Statistical Table

  • 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.


Basic Structure of Statistical Table

Table 1 Table title

Top line

Item line

Total line

Bottom line


Types of Statistical tables

  • Simple table:One variable only

  • Combinative table: More than 2 variables


Simple Table

  • 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%.


Combinative Table


Table 4 the result of HBsAg of persons at different age group in city or country at certain area in certain year


Announcements of Making Statistical Table

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


Table 5 compare of the risk factor of patients with coronary heart disease


Problems in above Table

  • 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


Table 6 compare of the risk factor of patients with coronary heart disease (X±S)

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


Table 7 compare of the risk factor of patients with coronary heart disease


Frequent Mistakes in Tables

  • 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


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.


Basic Structure of a Statistical Graph

legend

Vertical item (unit)

legend

Graph body

0

Horizontal item (unit)

Fig 1 The basic structure of a statistical graph


Content

  • bar chart

  • pie chart

  • percent bar chart

  • line graph

  • Histogram

  • Scatter Diagram


Bar Chart

  • 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


Guidelines for Bar Charts

  • 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


Pie Chart

  • 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 .


Guidelines for Pie Charts:

  • 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.


Percent Bar Chart

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)


Line Graph

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

Fig. 7 Incidence rates of stomach cancer in a city


General Line Graph

  • 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


Semi-logarithmic 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.


Semi-logarithmic Line Graph

Left: The absolute difference of mortality rates ~ Year

Right: The absolute difference of log (mortality rate)

Suitable line graphs in different situation


Histogram

  • 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


Scatter Diagram

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.


Summary

  • 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!


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