Methods of Data Presentation

Dra. Abat

FCM/Neurotrans

1.To describe the different scales of measurements of variables.2.To discuss the various methods of summarizing collected data.3.To discuss the methods of presenting collected data.

degree or precision with which a characteristic is measured

also determines which statistical methods maybe used to analyze the data.Types: 1. NOMINAL SCALE 2. ORDINAL 3. INTERVAL 4. RATIO 5. NUMERICAL

Categories/scales Description ExamplesNOMINAL classifies subject

into one of a number of qualitative classes

sex, religion, nationality

ORDINAL similar to nominal but classes can be ranked

Social class Professionnutritional status

INTERVAL exact distance between 2 categories can be determined but zero point is arbitrary

Temperature

RATIO similar to interval but zero point is fixed

Age, height,weight

NOMINAL SCALE names, labels, or tags are given to distinguish one

measurement from the other. Measurements on this scale does not include any

notion of magnitude of the individual measurements. Ex. Outcome of disease: survival or death Admission status: in patient, outpatient Psychiatry patients: psychotic, neurotic, manic

depressive, Schizophrenics Types of DM: Type I , Type 2

ORDINAL SCALE an observation is measured based on an inherent order

among categories. Observations are still classified as with nominal scales

but some observations have “ more” or “greater than” other observations.

Ex. Patient’s condition upon admission in the hospital:

critical, severe, moderate light. Nutritional status of children: mild , moderate,

severe Staging of hypertension Staging of TB by X-ray- Minimal , moderate, far

advance

INTERVAL SCALE characterized by a numerical unit of measurements such

that the difference between any two measurements is explicitly known in terms of an interval between two points on the scale.

A peculiar characteristic of this scale is that both unit of measurement and the zero point ( origin of the starting point ) of the scale are arbitrary and only fixed by conventions.

Ex. Temperature – Celsius or Fahrenheit 37-39 etc.Ordinal scale can be made to look like an interval scale by assigning score to the various measurement

RATIO SCALE has all the characteristic of the interval scale as well as a

true or absolute zero so that the ratio between two values on the scale is a meaningful measure of the relative magnitude of the 2 measurements.

Ex. Height in cm weight in kg.

NUMERICAL SCALES - Quantitative observations in which the differences between the

numbers have meaning in the numerical scale are also called quantitative observations because they measure the quantity of something.

Types of numerical data:A) Continuous scale- values on the continuum , can assume

integral or fractional values . ex. Age, ht, wt, blood chemistry, length of time of

survival, B ) Discreet- values equal to integers or whole numbers

ex. # of boys, # of fractures , # of pregnancies, # of deaths or morbidity from a certain disease

A. TextualB. Semi-textualC. TabularD. Graphical Presentation

A. Tabular1. More compact2. Easier to understand esp. when comparing figures3. Appears more orderly4. Can present large sets of information5. Point out trends, comparisons and interrelationships

Parts of Statistical Table 1. Table number 2. Title 3. Head note 4. Column headings 5. Row headings/stubs 6. Body of table 7. Footnote 8. Source of data

Table number numbered consecutively using Arabic numerals

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Session Objectives

Scales of Measurement

Data Presentation

TRANSER GROUP NAME

Title complete information:what,who,where,when self-explanatory may use additional information (headnote)

Column headings basis of classification of the columns or vertical

series of figures should be centered capitalization of headings,including row headings Row headings or stubs indicate the basis of classification of the rows or

horizontal series of figuresBody

intersection of a row and a column in a table is called a cell

figures within the cells should be aligned by decimal points

may contain extra columns or rows for marginal totals

Footnotes - small letters are used ;usually placed beside

figures in the table. placed immediately below the bottom rule of the

tableSource of data

obligatory if source is not original placed after the footnotes or bottom rule of the

table should not be placed as a footnote to the page

Table Title--A table title gives an overview of the information displayed in the table. The title is given at the top of the table.

Row/Column Labels--The label of each row or column indicates what type of information is contained in that row or column. The table shown here has 2 columns of information, each with a label.

Individual Cells--Each cell is defined by its row and column location. In the example,the cell outlined is in the fourth row, first column.

Relationship of cells within a row or column--Often we want to determine if there is a trend within a row or column. For example, do the values increase as we move up or down a row or column?

Example:

The Relationship BetweenTicket Prices and Attendance at First Union University

1. What is the attendance when ticket price is $15 dollars? The answer is 9 thousand.

2. What is the relationship between ticket prices and attendance? As ticket prices increase, attendance decreases. The point where no one will buy a ticket is at a cost of $25.

3. What is the optimal ticket price? Give a reason for your answer. The optimal ticket price is $15. At a ticket price of $15 the money taken in from ticket sales is $135 thousand, which is the greatest amount. Even though more people attend at a lower price, the amount of money is less than $135 thousand.

It should be simple,clear and direct Clean,uniform and professional look

1. Positioning of the table immediately after the text where it is first cited should never be placed before its mentioned/cited

in the textlarge tables which could not fit in the conventional vertical position maybe positioned horizontally or in facing pages

2. Uniformity of style Standardize a particular design for a single report Creates a feeling of “normal expectation” on the

part of the reader Unnecessary confusion results if the format of one

table differs from the other format of other tables within the same report

3. Numbers of variables presented Two or at the most three variables

4. Self-explanatory Can understand the content without referring to

textual explanations. Title must be complete and concise Units of measure should be clearly indicated Codes, abbreviations and symbols that are not

common should be explained in footnotes5. Rules

lines which separate rows or columns within a table Closely-spaced double rules are used for the top

rule of the table and succeeding rules, including the bottom ones are single-ruled

Codes, abbreviations and symbols that are not common should be explained in footnotes

horizontal rules should separate the column headings from the figures

Vertical rules used for closely-spaced figures

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Pointers in Construction of a Table

DATA PRESENTATION

TRANSER GROUP NAME

A census conducted in Brgy X in Cavite City by IRRI in 1988, showed that there were 272 females aged between 15-44 years old. Of these 75 or 28% were less than 20 yrs old, 107 or 39 % were between 20 and 29 while 91 or 33 % were between 30 & 44. Approx. 77% or 181 of women had married at least once. Among the 15-19 age group , only of 7 of the women or 8% ever get married . The proportion of the ever married women increased sharply in the 20-29 age group to 81% or 87 women. For the 30-44 age group , the number of ever married women was 89 or 98% of the women in the age bracket.

Common type of table used to summarize counts of observation Components of the table: a. Class limits

b. Class boundariesc. Class midpointd. Cumulative frequencye. Relative

f. cumulative frequency

a. Class limitslower class limit upper class limit

EXAMPLE: weight in kg No. of Mothers

28-34 935-41 13742-48 30649-55 19656-62 7563-69 3770-76 977-83 484-90 391-97 1

b. Class boundaries

True lower class limit True upper class limit

c. Class midpoint

- value which divides the class into 2 subclasses of equal width sum of the class boundaries divided by 2

28 + 34 / 2 = 31

weight in kg No. of Mothers Class midpoint

28-34 9 3135-41 137 3842-48 306 4549-55 196 5256-62 75 59 63-69 37 6670-76 9 7377-83 4 8084-90 3 8791-97 1 94

CUMULATIVE FREQUENCY

d. Cumulative frequency

sum of all class frequencies preceding a given class and the frequency of the class under consideration

Example:

weight in kg no. of Mothers Class midpoint cum.freq 28-34 9 31 935-41 137 38 14642-48 306 45 452 49-55 196 52 648 56-62 75 59 72363-69 37 66 76070-76 9 73 769 77-83 4 80 77384-90 3 87 77691-97 1 94 777

e. Relative frequency

class frequency divided by the total number of observations expressed in percentage

EXAMPLE:weight in kg no. of Mothers Class midpoint cum.freq relative freq 28-34 9 31 9 1.2 35-41 137 38 146 17.6 42-48 306 45 452 39.4 49-55 196 52 648 25.2 56-62 75 59 723 9.7 63-69 37 66 760 4.8 70-76 9 73 769 1.2 77-83 4 80 773 0.5 84-90 3 87 776 0.4 91-97 1 94 777 0.1

sum of all relative frequencies preceding a given class and the relative frequency of the class under consideration allows us to see how many observations, in relative terms lie below a certain class.

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CUMULATIVE FREQUENCY

GRAPHICAL PRESENTATION

TRANSER GROUP NAME

Pointers TITLE

it should be self-explanatory Clear and concise title- what,when where,source of data if secondary Position of title is a matter of choice,although in technical papers, it is below the chart

SCALES it should be properly labeled identify the entities being measured along horizontal as well vertical axis. scale graduations should be clearly indicated

Grid or Guide rulings Used to guide the eye Should be drawn lightly Use minimally Should be neat and businesslike quality Simple and devoid of unnecessary trimmings and draftsmanship Simplest graphs are the most effective Basis of classification is generally represented on the horizontal scale while frequencies, whether absolute or relative , are placed along the vertical Vertical scale should always start with zero. Use of color for emphasis or to differentiate between items Equal distances between tick marks on an axis should represent equal numerical units.

What is a BAR GRAPH?

A bar graph is a visual display used to compare the amounts or frequency of occurrence of different characteristics of data. This type of display allows us to:

compare groups of data, and To make generalizations about the data quickly.

When reading a bar graph there are several things we must pay attention to: the graph title, two axes, including axes labels and scale, and the bars. Since bar graphs are used to graph frequencies or amounts of data in discrete groups, we will need to determine which axis is the grouped data axis, as well as what the specific groups are, and which is the frequency axis.

Things we must pay attention to: graph title two axes, including axes labels and scale bars

Since bar graphs are used to graph frequencies or amounts of data in discrete groups, we will need to determine which axis is the grouped data axis, as well as what the specific groups are, and which is the frequency axis.

Price of Corn versus Quantity Demanded

Graph Title--overview of the information being presented in the graph. The title is given at the top of the graph.

Axes and their labels--Each graph has two axes. The axes labels tell us what information is presented on each axis. One axis represents data groups, the other represents the amounts or frequency of data groups.

Grouped Data Axis--The grouped data axis is always at the base of the bars. This axis displays the type of data being graphed.

Enrollment in Introductory Courses at Union University

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TRANSER GROUP NAME

1. Which course has the most students enrolled in it? 2. Order the courses by enrollment from lowest to highest. 3. The enrollment in Econ is approximately how many

times bigger than the enrollment in Chem.? 4. Approximately how many students were enrolled in the

course with the most students? 5. Approximately how many more students are in Econ

than in Physics?

CIRCLE GRAPHS

- Pie charts, are a type of graph used to represent a part to whole relationship. Properties of Circle Graphs:

They are circular shaped graphs with the entire circle representing the whole.

The circle is then split into parts, or sectors. Each sector represents a part of the whole. Each sector is proportional in size to the amount each

sector represents, therefore it is easy to make generalizations and comparisons.

Properties of Circle Graphs: Circular shaped graphs with the entire circle

representing the whole. It is then split into parts, or sectors. Each sector represents a part of the whole. Each sector is proportional in size to the amount each

sector represents, therefore it is easy to make generalizations and comparisons.

Revenue Sources for the Federal Government

Circle Graphs

Graph Title--gives an overview of the information displayed in the graph. The title is given at the top of the graph.

Sectors--Each sector represents one part of the whole. The size of each sector represents its fraction of the whole.

Sector Labels--The label of each sector indicates the category of information it refers to, and may also give numeric data (often a percentage) so we know the size of each sector.

LINE GRAPHS

A line graph is used to show the relationship between two variables, the independent variable and the dependent variable. The variables being compared go on the two axes of the graph

The independent variable always goes on the horizontal axis, called the x-axis.

The dependent variable always goes on the vertical axis, or y-axis.

A SCATTERPLOT or SCATTERPOINT DIAGRAM is often employed to identify potential associations between two QUANTITATIVE variables

A positive association upward trend (positive slope)

e.g. where higher incomes correspond to higher education levels and lower incomes correspond to fewer years of education.

A negative association would be indicated by the opposite effect (negative slope)e.g. where the most highly educated individuals would have lower incomes than the least educated individuals.

Or, there might not be any notable association, in which case a Scatterplot would not indicate any trends whatsoever. The following plots demonstrate the appearance of positively associated, negatively associated, and non-associated variables:

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TRANSER GROUP NAME

Associated variables:

associated variables:

COMPONENT BAR DIAGRAM

A simple bar diagram is used to present only one variable.

But when a breakdown of total or a series of totals is to be represented, we have to use what is called sub-divided or component bar diagrams.

This is preferable to the pie chart in situations where comparisons has to be done between 2 or more groups

HISTOGRAM

graphical representation of the frequency distribution of a continuous quantitative variable including age.

Used to depict counts , absolute or relative of each class groupings.The horizontal axis is a continuous scale showing units of measurements of the variables under consideration .The vertical scale shows absolute and relative frequencies

The area of a rectangle is proportional to both the frequency and width of the class under consideration ( comparisons between groupings are based on the area of the rectangle and not on the heights).

The limits of the ends of the base of the rectangles are the true class boundaries.

Histogram : Points in the construction:

1. The limits of the ends of the bases of the rectangles are the true class limits or boundaries . There should be no gaps between the rectangles of a histogram since the distribution of a continuous variable is being depicted

2. The area of a rectangle is proportional to both the frequency and width of the class being depicted, any distortion regarding the data could be secondary to this point not being heeded.

Double Bar Graphs

Double bar graphs can be found from time to time.

They are used for when each data group contains two different sets of frequency data. A double bar graph is used to compare both between and within data groups.

Quarterly Reports of Income and Expenses for Dry Cleaning Associates and Co.

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