Intro to Descriptive Statistics

Course Aims

• Descriptive statistics are introduced to help understand how to present data and describe observations in data form.
• Course objectives include introducing data types, outlining the importance of data and statistics, comparing data groups in statistical language, and predicting statistical outcomes from observations.

Definition of Statistics

• Defined as numerical values or indicators computed through mathematical manipulation.
• Presented as percentages, index numbers, averages, and medians.
• A branch of mathematics dealing with analysis and interpretation of numerical data in terms of samples and populations
• Classified facts respecting condition of the people in a state, can be stated in numbers, tables, or classified arrangements
• Major steps are data collection, organizing/summarizing, analyzing/interpreting, and using results for rational decisions.

Purposes of Statistics

• To present large amounts of quantitative information.
• To provide meaningful interpretations of data.
• To predict the likelihood of events.
• To make inferences from observations.
• To condense large information into tables.
• To evaluate the quality of services.
• To analyze group behaviors in specific environments/situations.
• To determine the wants/needs of people via statistical sampling.

Role in Social Inquiry

• Social inquiry involves investigations to determine facts using statistical techniques.

Roles of Statistics

• Simplifies and presents complex data for comprehension.
• Presents data in comprehensive and definite numerical forms.
• Interprets conditions attractively using charts.
• Classifies numerical data.
• Facilitates data comparison.

Statistical Research Classification

• Includes data collection, organization, analysis, and interpretation of facts.

Determination of Statistical Unit

• Necessary for the interpretation and presentation of facts.

Basic Concepts

• Data represents qualitative or quantitative attributes.
• Variables have multiple values, either discrete or continuous.
• Quantitative variables vary in magnitude. Examples include weight, height, age, and test scores
• Qualitative variables differ in kind; e.g., gender, nationality, and marital status.
• Independent variables are manipulated, affecting dependent variables.
• Discrete variables are countable with fixed values.
• Continuous variables relate to a numerical scale like length or temperature.
• Distribution is the arrangement of numbers by attributes.
• Population includes all observations of a group.
• Sample is a subset of a population.
• Parameter is a numerical value describing a population characteristic.
• Statistic is a descriptive measure of a sample

Scope of Inquiry

• Space: A study's particular scope.
• Time: A study's specific time lag.

Functions of Statistics

• Compression: Reducing or condensing data.
• Evaluation: Using classification and tabulation to compare data.
• Forecasting: Predicting, estimating, or projecting into the future.
• Estimation: Drawing population inferences from sample analysis.

Intellectual Foundations in Social Inquiry

• Regularities: Generalizations of social behavior to explain and predict social phenomena.
• Verification: Knowledge based on observation and empirical investigation.
• Techniques: Using correct methods to acquire and interpret valid data.
• Quantification: Measuring and quantifying data for verifiable conclusions.

Limitations of Statistics

• Neglect qualitative phenomena since statistics deal with numerical data.
• Ignores the importance of individual items.
• Lacks exactitude, providing approximations instead.
• Misuse of records by inexperienced individuals can lead to incorrect conclusions.

Types of Statistics

• Descriptive describes events without conclusions, using measures like mean, median, mode, standard deviation, range, percentile, kurtosis, correlation coefficient, and proportions.
• Experimental relates to experiment design for cause and effect. Includes experimental and quasi-experimental designs.
• Inferential builds on descriptive statistics (chi-square, t-test, f-test) to interpret a population for decision-making.

Methods Used in Social Statistics

• Quantitative and Qualitative methods.

Presentation of Data Techniques

• Data presented in tables, graphs, or charts.

Tables

• Tables are orderly data arrangements, effectively organizing statistical information.
• Tables present data logically, identify features, and facilitate comparisons.
• Tables show relationships among variables and enable quick decision-making.
• Essential characteristics include simplicity, understandability, numbering (if multiple), a title, stated subheadings, source citation for secondary data, indicated units of counting, and alphabetical or chronological arrangement.

Technique of Data Collection

• Literature reviews involve examining scholarly works and secondary sources.
• Surveys use interviews/questionnaires and are known as primary sources.

Sources of Data Collection

• Two main types of sources, selection depends on the purpose, time, funds, accuracy needed, and researcher status.

Primary Data

• Statistical data generated by the researcher for their study.

Secondary Data

• Data collected from printed materials published by others.

Types of Variables

• Independent variables influence other variables, representing inputs or causes; it is assigned a value whose variation does not depend on other variables and they can be manipulated in a study.
• Dependent variables are measured in research with values determined by independent variables/factors.

Measurement of Variables

• Instruments for measuring variables are measurement scales/levels using nominal, ordinal, interval, and ratio.

Nominal Scale

• Lowest and simplest scale, sorts objects into categories with numbers as identifiers.

Ordinal Scale

• Sorts variables into mutually exclusive categories, ranking them with an order for each class

Interval Scale

• Contains all ordinal scale properties; addition of distance between categories is known to calculate the difference between variables.

Ratio Scale

• Highest scale with all properties and an absolute zero point (e.g., traffic density).

Diagrammatic Presentation of Data

• Pictograms use pictures to explain statistical data.
• Bar Charts use bars to represent information where the bar length corresponds to the value, and width of each bar is equal.
• Pie Charts explain data using diagrams.
• Histograms mark class boundaries/intervals on the horizontal axis and class frequency on the vertical axis.

Range

• Specifies the distance between the highest and lowest values in a distribution; calculated as H (highest value) minus L (lowest value).

Class Interval

• Classes used to define raw data or group size.

Class Limit

• End numbers of a class interval; the lower value is the lower class limit, and the upper value is the upper class limit.

Class Boundaries

• Obtained by subtracting 0.5 from the lower class limit and adding 0.5 to the upper class limit.

Class Mark

• Midpoint of the class interval, derived by averaging the lower and upper class limits or boundaries.

Frequency Distribution

• Used with large forms of quantitative data.
• Ungrouped Frequency Distribution is a type where data are not compressed.
• Grouped Frequency Distribution may have equal or unequal intervals, each given as a class interval.
• Class Limit comprises the High and Low number in the range.
• Class Boundaries are determined by +/- deviations.
• Class Mark is the midpoint value of the class interval.
• Class Width is the overall Class Size, subtracting High and Low boundaries.

Nature of Measurement

• Observations be measured to some degree of accuracy,
• Errors can occur from inaccuracy, changing circumstances, or human judgment.

Scales of Measurement

• Involve assigning numbers to objects and events according to logical rules.

Measures of Central Tendency

• Arithmetic Mean (average).
• The median with “n” members arranged in order of magnitude.
• The mode with the most frequent value in the distribution.

Standard Deviation

• The range is the difference between the largest and smallest values.
• Mean Deviation uses the mean of deviations from the mean, median, or mode.
• The standard deviation is an improvement of mean deviation and are desirable to calculate dispersion.
• Assumed mean calculation guess of an assumed mean is made.