Introduction to Statistics

Statistics

• Statistics is the science dealing with the collection, analysis, interpretation, presentation, and dissemination of data.

Biostatistics

• Biostatistics applies statistical methods to biological sciences, medicine, and public health.

Vital Statistics

• Vital Statistics focuses on vital events such as births, deaths, marriages, and fertility rates.

Uses of Statistics

• Statistics are useful for planning national health services.
• Statistics are essentail for conducting medical and epidemiological research.
• Statistics assist in determining the casuality of disease.
• Statistical reasoning is important for clinical judgment.

Data

• Data represents a set of values or observations recorded on one or more studied units.

Types of Data

• Constants do not vary among individuals, making them not applicable for statistics.
• Variables vary among individuals or over time, the main focus of statistics.

Quantitative Variables

• Quantitative variables are expressed as quantities or numbers.

Quantitative Variable Subtypes

• Continuous variables are obtained from measurement, which can take integral or frational amounts.
• Discrete variables are obtained through enumeration, which can only take integral values.

Qualitative Variables

• Qualitative variables cannot be expressed as quantities or numbers and take the form of qualities or names.
• Qualitative variables can be categorized, but no enumerated.

Qualitative Variable Subtypes

• Ordinal variables have categories that can be arranged in definite order.
• Nominal variables have categories that cannot be arranged in a definite order.

Variable Transformation

• Quantitative variables can be transformed into qualitative ordinal variables.

Other Variable Classifications

• Independent variables are input/cause variables.
• Dependent variables are outcome/effect variables.
• Confounding variables are intervening variables.
• Background variables include age, sex, and occupation.

Sources of Data

• Historical and ongoing recording systems include census, vital statistics, hospital records and international publications.
• Surveys: Used to collection of data
• Experiments: Used to collection of data

Tools for Data Collection

• Observation
• Questionnaires
• Interviews
• Record analysis

Presentation of Statistical Data

• Tabular: Data presented in tables
• Diagrammatic: Data presented in diagrams
• Numerical: Data presented numerically

Tabular Presentation

• A table is a data set arranged in rows and columns.

Types of Tables

• Simple frequency distribution table: for one variable
• Contingency table: Used for two or three variables.
• Comparing frequency distribution table
• Two way table: Two way classification

Characteristics of a Good Table

• Self-explanatory
• Titles should be clear, concise, and answer what, when, and where.
• Titles are separated from the table's body.
• Rows and columns are labeled clearly.
• Specific units of measure are provided.
• Totals should be given.
• Abbreviations/symbols are explained in footnotes.
• Simple as possible; small are preferable to single larger ones.
• The source is given in a footnote for non-original data.

Simple Frequency Distribution Table (Qualitative)

• Qualitative variables
• Table consists of 2 columns
• Left column shows the variable, then categories, then total
• Right column shows the frequency of observations for each category.
• Percentage of each included

Simple Frequency Distribution Table (Quantitative)

• Quantitative variables
• The range of values are detemrined by difference between the smallest and largest
• Select a reasonable amount of class intervals [5-20] based on magnitude and table requirements
• Determine the width of the class interval
• Range of values / class interval = width of each class

Contingency Tables

• Contingency tables, also known as cross-tabulations, are used to show the relationship between two or more categorical variables.
• Data is presented as totals.

Two-by-Two Table

• Used to show a relationship between two variables, such as exposure and disease.

C x R Table

• More than 2 columns by 2 or more rows.
• Illustrate different types of treatments for a disease and their outcomes.

Comparing Frequency Distribution Tables

• Compare two different groups based on one variable.

Two Way Table

• Classifies one group according to two variables.

Diagrammatic Presentation

• Methods that show quantitative data using coordinate systems.
• X-axis: horizontal and displays the independent variable.
• Y-axis: vertical and displays the dependent variable/frequency.
• Charts: Use only one coordinate

Types of Graphs

• Arithmetic scale line graph
• Histogram
• Frequency polygon
• Scatter diagram

Arithmetic Scale Line Graph

• Best for representing data with a time variable.

Histogram

• Suitable for simple frequency distributions type.
• No spaces between columns signify continuous quantitative data.

Frequency Polygon

• Connects midpoints of class intervals with a straight line.
• Best when the variable is a continuous quantitative type.

Scatter Diagram

• Shows the relationship or association between two variables.

Types of Charts

• Simple bar chart
• Component bar chart
• Grouped bar chart
• Pie chart
• Maps (geographic coordinate chart)
• Dot plots and box plots

Simple Bar Chart

• Columns have the same width.
• Categories are shown on the X-axis and frequency on the Y-axis.
• Best for qualitative data (2 types) and qualitative discrete type.

Grouped Bar Chart

• A simple bar chart showing more than one variable.

Component Bar Chart

• Bars are divided into portions.
• Portions are colored or shaded to denote classification.

Pie Chart

• Values should have a constant sum.
• Suitable for variables with 3-10 categories.
• Segments are arranged in order of magnitude, starting at 12 O'clock.

Maps (Geographic Coordinate Chart)

• Used to show the location of events.

Spot Maps

• Use dots/symbols to show where an event or disease occurs.
• Show the geographical distribution of an event.
• May use plot or symbols to indicate more than 1 case

Area Maps

• Show whether an event is occurring over a geographic area.

Dot Plots

• Similar to a scatter diagram, plotting one variable against another.
• The x-axis represents discrete categories.

Box Plots

• Used to compare distributions of non-continuous variables.
• Illustrate data distributions as box and whiskers diagrams.
• The box: represents the middle 50% of the data.
• Whiskers: They extend from minimum to maximum values.
• A line: Shows the median across the box.
• The central location (median) and dispersion (inter-quartile range) can be shown

Numerical Presentation

• Summarizes data into an easily understandable number.

Measures of Central Values

• Arithmetic mean ± SD
• Median
• Mode
• Midrange
• Geometric mean

Measures of Dispersion

• Range
• Standard deviation
• Variance
• Average deviation
• Co-efficient of variation

Arithmetic Mean (Average)

• The sum of all observations divided by the number of observations.
• Computed by summing values and dividing by the count.

Arithmetic Mean Advantages

• All observations are taken into consideration.
• Best average for quantitative data to be used in statistical analysis.

Arithmetic Mean Disadvantages

• Not suitable for qualitative data.
• Affected by extreme observations.

Median

• The value that divides a series of observations into two equal halves when they are listed from lowest to highest.
• If the number is odd: median = (n+1)/2
• If the number is even: median = (n+1)/2, median = average between 3rd and 4th number = 7+8/2 = 7.5

Mode

• The observation which has the highest frequency.
• If there are 2 modes, choose smaller

Mode Advantages

• Usable for all types of variables.
• Not affected by extremes.

Mode Disadvantages

• Cannot be determined if all observations have the same frequency.
• 2 or more mode are sometimes obtained

Range

• The difference between the highest and lowest values.
• It takes the same unit of the original.

Range Disadvantages

• Provides not information about data scatter.
• Greatly affected by extreme values.

Standard Deviation

• Definition: Squared root of the sum of the squared deviations of the values from the mean divided by the number of values minus one.

Standard Deviation Importance

• Shows the dispersion around the mean.
• Used to test the difference of 2 values.
• In normal distribution curve
• 68.3 % of the observation fall in the area between 1 SD.
• 95.5 % of the observation fall in the area between 2 SD.
• 99.7 % of the observation fall in the area between 3 SD.

Normal Curve

• Symmetrical unimodal continuous distribution of infinite range.
• It is described by its mean & SD of the population
• Heights determined by the value of SD.
• More concentration of observations at middle
• It approaches infinity in either directions

Characteristics of Normal Curve

• Bell shaped and Symmetrical
• In a normally distributed population, mean = median = mode.

Uses of Normal Curve

• Solves certain questions
• If mean is known median and mode can be know
• Estimates the population mean from the sample mean.