Module 1.2 - Levels of Measurement (1).pdf

Introduction to Statistics LESSON 1 – PART 2 Outline: Level of Measurement Sample Sampling Techniques  Level of Measurement  When we observe and record a variable, it has characteristics that influence the type of statistical analysis that we can perform on it  These character...

Introduction to Statistics LESSON 1 – PART 2 Outline: Level of Measurement Sample Sampling Techniques  Level of Measurement  When we observe and record a variable, it has characteristics that influence the type of statistical analysis that we can perform on it  These characteristics are referred to as the level/scale of measurement of the variable  The first step in any statistical analysis is to determine the level of measurement; it tells us what statistical tests can and cannot be performed  Four widely recognized levels of measurement 1. Nominal 2. Ordinal 3. Interval 4. Ratio Nominal level of measurement Is mutually exclusive and exhaustive meaning it is used to differentiate classes or categories for purely classification or identification purposes. Nominal data are discrete variables. Exhaustive is a property of a set of categories such that each individual or object must appear in a category. For example: Qualitative Variable Categories Gender Male, Female Automobile Ownership Yes, No  Ordinal level of measurement Is used in ranking. Ordinal data are discrete variables. Qualitative Variable Categories Student Class Designation Freshman, Sophomore, Junior, Senior Movie Classification G, PG, PG-13, R-18, X Student Grades 1.00, 1.25, 1.50, 1.75, … Ratings ☆☆☆☆☆ ★☆☆☆☆ ★★☆☆☆ ★★★☆☆ ★★★★☆ ★★★★★  Interval level of measurement Is used to classify order and differentiate between classes or categories in terms of degrees of differences. Interval data are either discrete or continuous variables. Qualitative Variable Temperature (in degree °C or °F) Calendar Time (Gregorian, Hebrew, Roman, etc.)  Ratio level of measurement Differs from interval measurement only in one aspect; it has a true zero point. Ratio variables, on the other hand, never fall below zero. Ratio data are either discrete or continuous variables. Qualitative Variable Weight (pounds or kilograms) Age (in years or days) Salary (dollar or peso)  Classification of Numerical Data Numerical Data Qualitative Quantitative Nominal Ordinal Interval Ratio  Sample Is a group in a research study on which information is obtained. A population is a group to which the results of the study are intended to apply. In most all researches, the sample is smaller than the population, since researchers rarely have access to all the members of the population. One of the most important steps in the research is to select the sample of individuals who will participate as a part of the study. Sampling refers to the process of selecting these individuals.  Sample Number of Samples: One-Sample – procedures used to test statistics for only one sample. Ex: a group of internet users Two-Sample – two samples or group of subjects. Ex: male users, female users K-Sample – refers to statistical tools used for more than two samples. Ex: providers; businessmen; clients  Sample Types of Samples: Independent Samples – groups are unrelated to one another (mutually exclusive), that is, measurement of subjects has nothing to do with measurements of subjects in the other group. Correlated Samples – two or more samples in which members of the separate samples share characteristics or relationship with one another.  Sampling Techniques Sample is a group in a research study on which information is obtained. -a subset of the population from which observations are actually obtained, and from which conclusions about the population will be drawn. A population is a group to which the results of the study are intended to apply. In most all researches, the sample is smaller than the population, since researchers rarely have access to all the members of the population. One of the most important steps in the research is to select the sample of individuals who will participate as a part of the study. Sampling refers to the process of selecting these individuals. – a pattern, arrangements or methods used for selecting a sample of sampling units from the target population.  Sampling Techniques Division of Sampling Techniques: Sampling Techniques Random Non-random Simple Systematic Stratified Cluster Convenience Purposive Quota Snowball  Random Sampling Is a process whose members had an equal chance of being selected from the population; it is called probability sampling. 1. Simple Random Sampling is a process of selecting n sample size in the population via random numbers or through lottery. 2. Systematic Sampling is a process of selecting a nth element in the population until the desired number of subjects or respondents is attained. Example: For instance we have the data shown below; say we want to consider every 5th on the list. 23 34 12 14 13 23 24 39 27 23 12 15 16 23 26 28 23 22 19 34 25 22 18 30 23 24 17 18 15 12 Therefore, the samples from every 5th from left to right are: 13, 26, 23, 23, 34, and 12  Random Sampling 3. Stratified Sampling Is a process of subdividing the population into subgroups or strata and drawing members at random from each subgroup or stratum. A stratum (plural strata) refers to a subset (part) of the population which is being sampled. Example: Given the population of a certain university and a target sample population of 5,455 determine the sample size of each subgroup or courses. Field of Specialization Population Nursing 6,000 Accountancy 500 Management 2,000 Marketing 1,000 Education 2,500 Total 12,000  Random Sampling To determine the sample size in each subgroup, we will simply multiply the sample population with respect to each subgroup percentage in reference to the population. The computation is shown in the last column of the table below. Field of Population Percentage Computation Sample Size Specialization Nursing 6,000 50 0.5000 x 5,455 2,728 Accountancy 500 4.16 0.0416 x 5,455 227 Management 2,000 16.66 0.1666 x 5,455 909 Marketing 1,000 8.33 0.0833 x 5,455 455 Education 2,500 20.83 0.2083 x 5,455 1,136 Total 12,000 100 5,455  Random Sampling 4. Cluster Sampling Is a process of selecting clusters from a population which is very large or widely spread out over a wide geographical area. Example: If we want to know the opinion of residents of Manila regarding the improvement of living in the city. We may use the cluster sampling by subdividing the city into district then select at random the number of district to be used as sample.  Non-random Sampling Is a sampling procedure where samples selected in a deliberate manner with no attention to randomization; it is also called non-probability sampling. 1. Convenience Sampling is a process of selecting a group of individuals who (conveniently) are available for study. Example: A researcher may only include close friends and clients to be included in the sample population. 2. Purposive Sampling is a process of selecting based from judgement to select a sample which the researcher believed, based on prior information, will provide the data they need. The disadvantage of purposive sampling is that the researchers judgment may be in error. It is also called judgment sampling. Example: A human resource director interviews the qualified applicants. Note: Qualified applicants are selected by the director based from his own judgment.  Non-random Sampling 3. Quota Sampling is applied when an investigator survey collects information from an assigned number, or quota of individual from one of several sample units fulfilling certain prescribed criteria or belonging to one stratum. Their advantage is that they are cheaper to administer. Example: When the respondents are composed of men aged over 30 or 20 people who have bought cellular phones in the last week. 4. Snowball Sampling is a technique in which one or more members of a population are located and used to lead the researchers to other members of the population. Example: Attempting to obtain the frame that includes all homeless people in Metro Manila. To obtain a sample of homeless individuals the researcher will interview individuals on the street or a homeless shelter.  Representing Variables By convention, in statistical formulae variables are represented by a capitalized letter, usually X or Y E.g., X might represent how introverted the people in your sample are Representing Individual Values When a variable is subscripted (Xi), the subscript implies that you should deal with a particular observation E.g. X3 might represent how introverted the third person in your sample is  The Summation Operator (∑) Most statistical procedures involve the summation of the values of variables i Xi Rather than to write all the values out 1 4 (X1 + X2 + X3 + X4 + …) a short hand notation is used: 2 2 ∑X 3 -1 N represents the number of observations 4 7 ΣX = 12 N=4 END