Statistical Concepts: Descriptive and Inferential

Basic Statistical Concepts

• Statistics is a science that involves collecting, organizing, summarizing, analyzing, and interpreting data.
• Statistics as an academic field focuses on data analysis to aid decision-making, analyzing surveys, and making decisions in scientific studies/controlled experiments.

Types of Statistics

• Descriptive Statistics is a method to gather, organize, and use numerical data from the empirical world.
• Descriptive Statistics aims to analyze a data group without conclusions or inferences.
• National Statistics Office uses descriptive statistics to determine the average age, income, and other characteristics of the Filipino population.
• Inferential Statistics utilizes sample data to make inferences about a population by generalizing from samples to populations.
• Inferential Statistics also performs hypothesis testing, determining relationships among variables, and predictions, using probability.
• Inferential statistics also tests for variable associations, identifying the form of relationships, refining into causal relationships, and generalizing/predicting.

Variables and Data

• Data are the values that the variables can assume.
• Random variables have values determined by chance, with data used in different ways.
• A variable is a characteristic that changes/varies over time and/or for different individuals or objects.
• Example of variables are the number of customers entering an internet café and t-shirt sizes

Types of Variables

• Qualitative variables are words or codes that represent a class or category.
• Examples of qualitative variables are rainbow colors and t-shirt sizes.
• Quantitative variables measure numerical quantities/amounts on individuals/objects, often represented as discrete or continuous.
• Examples of qualitative variables are the number of cellphones sold by a company and the height of Grade 11 students enrolled in Western Institute of Technology.
• Discrete variables can assume finite or countable values.
• Examples of discrete variables are the number of cars parked at Western Institute of Technology's parking and the number of ball pens sold by JAG School Supply.
• Continuous variables assume infinitely many values corresponding to a point on a line interval.
• Examples of continuous variables are the height of PBA players and the weight of grade 12 Fayol students.

Population and Sample

• Population is the complete and entire collection of elements that are studied.
• Sample is a subset of a population
• A parameter is a numerical measurement describing some characteristics of a population.
• A statistic is a numerical measurement describing some characteristics of a sample.

Summation Notation

• Summation notation is used to denote the sum of values where the uppercase Greek letter ∑ is used.
• By definition the summation of values is ∑xi = x1 + x2 + … + xn

Levels of Measurement, Data Collection and Sampling Techniques

• The learner is able to identify and differentiate the different levels of measurement, methods of data collection and sampling techniques.

Levels of Measurement

• Nominal Level is defined by data consisting of only names, labels, or categories.
• Data cannot be arranged in an ordering scheme and there is no criterion as to which values can be identified as greater than or less than other values.
• Examples are classifying instructors in a university by gender and classifying residents by area codes.
• Ordinal Level involves data in some order where differences between data values either cannot be determined or are meaningless.
• An example of this is temperature.
• Ratio Level includes the inherent zero starting point. The difference and ratios of data are meaningful, so the Ratio Level is considered the level of measurement.
• The difference and ratios of data are meaningful.
  • Height, weight, and area are examples of Ratio Level
• Interval Level is the same as the ordinal level, where meaningful amounts of differences between the data may lack an inherent zero starting point.
• An example of this is temperature.
• The levels of measurement depend on the measurement method, not the property measured.
• Categorizing the weight of primary school students measured into overweight, normal, and underweight will measure the weight in an ordinal level.
• Many levels are only interval because their zero point is arbitrarily chosen.

Data Collection

• Data collection methods of variables are observed or measured using any of the three methods of data collection: objective, subjective, and existing records.
• Objective and subjective methods obtain data directly from the source.
• Objective method uses the senses of sight, touch, hearing, taste, and smell to measure a variable.
• The subjective method obtains data by getting responses through a questionnaire.
• The resulting data from objective and subjective methods is referred to as primary data.
• Existing records are data collected by other entities for certain purposes where secondary data are obtained.
• Using data gathered by the Philippine Statistics Authority is secondary data and the method used to gather is the records.

Basic Methods of Sampling

• Random Sampling is done using chance methods or random numbers.
• Number each subject, place in container, select as many card numbers as needed. The subjects are the sample.
• Systematic Sampling is done by numbering each subject of the population. Then, every kth number is selected.
• For example, in a city of 5000 families, 50 families are needed for the experiment. Fifty families divided by 5000 is 100, representing that every 100th subject would be selected.
• Stratified Sampling divides the populations into distinct groups, drawing SRSs's from each of the groups. Strata are groups within the samples.
• Members in each strata are more homogenous that is very similar to each other. The results are then grouped together to form the sample, which is useful in populations stratified by groups categorized by gender, race, or geography.
• Cluster Sampling uses intact groups called clusters.
• A medical researcher wanting to study patients in Metro Manila would use cluster sampling because obtaining random sampling is very costly, so hospitals could be selected at random to study patients in a cluster.

Stratified vs Cluster Sampling

• Groups are divided by specific traits for stratified sampling then randomly selected for groups in cluster.
• Stratified sampling gives the researcher more control by allowing particular group.
• Stratified sampling includes an equal representation of the diverse group.
• Cluster sampling includes members who area not represented from the entire group.
• Stratified is used to improve precision while cluster is used to improve cost-effectiveness and efficiency.

Explore basic statistical concepts including data collection, organization, and interpretation. Learn about descriptive statistics for numerical data analysis and inferential statistics for making predictions and hypothesis testing. Examples include determining population characteristics and variable relationships.