Introduction to Statistics

Introduction to Statistics

• Statistics refers to recorded data such as the number of enrollees, common class sizes, number of patients, and average scores.
• It also denotes characteristics of a group, like mean, median, standard deviation, and coefficient of correlation.
• Statistics is defined as a science dealing with the collection, presentation, analysis, and interpretation of data.
• Statistics is concerned with understanding data structures and involves methods for describing and summarizing data which enable a way of thinking that helps to describe or characterize objects, situations, and phenomena reliably.
• Statistics also helps to make objective statements and comparisons and to make evidence-based decisions.

Steps in Statistical Investigation

• Identification of the problem.
• Collection of data involves different methods and techniques for gathering data.
• Presentation of data refers to the tabulation and organization of data into tables, graphs, and charts.
• Analysis of data is the process of deriving relevant information using various statistical tools.
• Interpretation of data is the task of drawing conclusions or inferences from the analyzed data.

Population and Sample

• Population is the complete collection or totality of all possible values of a variable.
• Examples of population include the total number of enrollees from a university, collections of books in a library, and the total number of registered nurses.
• A sample is a subset or sub-collection of elements drawn from a population which refers to a portion of the population.
• Examples include a television survey using a sample of 1,500 newly graduated nurses, a doctor interviewing 10 dengue victims from a local barangay with 100 dengue cases, and researchers considering two years' mortality rates to analyze the infant mortality rate in the Philippines for five years.
• Identifying whether a group or set is a population or sample requires analyzing if the group relates to a larger set. If it does, it's a sample, otherwise, it's a population.

Divisions of Statistics

• Descriptive Statistics summarizes or describes the important characteristics of a given set of data.
• Examples include the average body temperature of 100 people being 36.78°C, the deviation of scores of all examinees being 5, and the monthly income of a nurse being P15,000.00.
• Descriptive Statistics is applied when the data refers to a population or a sample.
• In contrast to descriptive statistics, Inferential Statistics goes beyond description and it is using a sample to make a conclusion about a population.
• Inferential Statistics provides information about the population by studying the characteristics of a sample.

The Nature of Data

• Data include any information concerning a population or sample.

Types of Data According to Source

• Primary Data is information gathered directly from the original source.
• Example: Information gathered by an interviewer from an interviewee, biographical data written by an applicant, and news from a field reporter.
• Secondary Data is information taken from a secondary source such as a newspaper, published or unpublished book, thesis, or dissertation.

Types of Data According to Functional Relationship

• Independent Data refers to any controlling data.
• Dependent Data is any data affected by the controlling data.

Variable

• Variable is the attribute of interest observable of each entity in the universe.
• Parameter are numerical measures that describe the population of interest.

Categories of Data

• Qualitative Data are uses categories or attributes that are distinguished by nonnumeric characteristics, such as sex, religion, race, "Yes" or "No" responses, and color of the skin.
• Quantitative Data consist of numbers representing counts or measurements.
• Examples of quantitative data include weights, heights, temperature, scores, number of enrollees, and length of a table.

Types of Quantitative Data

• Discrete Data is quantitative data capable of assuming a finite or countable number of values, which cannot be represented by fractions or decimal numbers but any whole number only.
• Examples include number of enrollees, scores, number of tables, number of body temperatures recorded, and number of schools.
• Continuous Data is quantitative data that can assume an infinite number of possible values corresponding to points on a line interval using fractions.
• Examples include temperature, heights, weights, length of tables, size of classrooms, and blood pressure.
• Both qualitative and quantitative data can be represented by numerical values, but for qualitative data, numerical values represent different categories.

Measurements of Data

• There are four levels of measurements used in preparing data for analysis

Nominal data

• Nominal data consists of names, labels, or categories and uses numbers to categorize data.
• For example, gender (Male, Female), religion (Catholic, INC, Islam, Protestant), and responses (Yes, No).

Ordinal data

• Ordinal deals with order or rank, providing relative comparison but not the degree of difference.
• Examples include computer ratings (Good, Better, Best), programmer rankings, and grading systems (A-Excellent, B-Very Good, etc.).

Interval data

• Interval is similar to ordinal but shows likeness or differences between data and gives meaningful amounts of differences and does not have a "true-zero" starting point (arbitrarily assigned).
• Examples include temperature scales and age brackets.

Ratio data

• Ratio is a modified interval level includes the starting point "zero." indicating the quality of ratio/proportion.
• Examples include time, rate of change, height, weight, volume, density, and velocity.

Methods of Data Collection

• Direct or Interview Method involves person-to-person interaction where ideas are exchanged between the interviewer and interviewee.

Indirect or Questionnaire Method

• Indirect or Questionnaire Method, also known as paper and pencil method, uses a questionnaire to elicit answers to a problem.

Registration Method

• Registration Method is a documentary analysis that gathers data from files, such as births, deaths, licenses, land titles, and company registrations.

Observation Method

• Observation Method a scientific approach that uses of all senses to collect data.

Experiment Method

• Experiment Method controls factors affecting the variable in question to examine cause and effect.

Methods of Sampling

• Sampling is a technique to draw samples from a population.
• Sampling is applied when the entire population is unavailable or too large.
• Populations are commonly studied through samples to draw conclusions through inference and the taken sample is reliable enough to be determined by the characteristics of the population it represents.

Determination of the Sample Size

• One way to determine the sample size is by percentage which is arbitrary and based on the researcher's notion.
• It's suggested to consider 10% of a large population, and at least 20% if small.
• Another way is by using the Slovin's Formula
• N = N / (1 + Ne^2)
• n = sample size, N = population size, e = margin of error (range from 1% to 10%).

Generation of the Elements of the Sample

• There are two basic sampling procedures which are probability and non-probability sampling.
• Probability sampling is unbiased or random.
• Non-probability sampling is biased or non-random.

Probability Sampling

• Each population element has an equal chance to be included

Simple Random Sampling

• Elements are selected through lottery after writing names/numbers of population members on pieces of paper.

Systematic Sampling

• Elements are selected by taking every element in the population.

Stratified Sampling

• The population is divided into strata/subpopulations sharing characteristics.

Multi-Stage Sampling

• Multi-Stage Sampling selects samples in several stages.

Cluster Sampling

• A technique used to dividing the population into sections and randomly selects some of these clusters as the member of the sample size.

Non-Probability Sampling

• The sample has no random selection from the population.

Purposive Sampling

• It is a Judgmental Sampling.
• Elements are selected according to criteria/rules.

Quota Sampling

• The sample sizes are limited to the required number of subjects.

Convenience Sampling

• Elements from a particular place at a specific time are selected by the researcher.

Methods of Presenting Data

• Textual Form: Data is presented in paragraph form
• Example: Consumer spending, businessmen are reluctant to spend this year.
• Tabular Form: Data is presented in rows and columns.
• Graphical Form: Data is visualized using methods of pictures to present data.
• Frequency Distribution: Data is presented in terms of list categories or classes.

The Frequency Distribution - Definition of Terms

• Class Interval is a grouping or category, and a symbol defining class like 60-62 is a class interval.
• Class Boundaries are more precise expressions of class limits at least 0.5 of their value.
• Class Frequency refers to the number of observations belonging to a class interval.
• Class Mark (x) is also known as the Class Midpoint; It is obtained by adding the upper and lower limits.
• Class Size (i) is the difference between the upper class boundary and the lower class boundary of an interval.
• Cumulative Frequency It is known as ogives, and both the "less than" and " greater than" ogives.
• Tabulation classifies/groups data into different class intervals in a frequency distribution.
• Array arranges data in ascending or descending order of ungrouped data.

Steps in Constructing Frequency Distribution

• Step 1: Determine the highest and lowest score and compute for the range.
• Step 2: Determine the number of class intervals.
• Step 3: Determine the class size by dividing the range.
• Step 4: Set up the class interval using the lowest score as the starting point.
• Step 5: Determine the class frequency for each class interval by referring to the tally column.

Graphical Presentation of Frequency Distribution

• Frequency Histogram consists of a set of rectangles, where frequency (on y-axis) is plotted against the class boundaries (on x-axis).
• Frequency Polygon is the line graph of the class frequency plotted against the class mark.
• Cumulative Frequency use "less than" and "Greater Than" ogives.