Quantitative Methods: Basic Concepts

• Quantitative Methods including Modeling & Simulation is covered within this text

Learning Module 1: Basic Concepts of Quantitative Methods

• Quantitative methods play a central role in the discipline, especially in the United States

• The method focuses on gathering numerical data and generalizing across groups to explain phenomena

• Mathematical and statistical methods are used for managerial and decision-making problems

• Quantitative methods support decision-making in transportation, logistics, and supply chain management

• Quantitative methods are compact representations, where a single equation may describe system performance

• Quantitative refers to something that can be measured

• Quantitative data is expressed as numbers

• Quantitative analysis involves numerical methods to ascertain size, magnitude, and amount

• Discrete and continuous data ae the two types of quantitative data, also referred to as numeric data

• Counts are discrete, while measurements are continuous

• Discrete data is a count that can't be made more precise, typically involving integers

• Continuous data can be divided and reduced to finer levels, taking on any value

• Several methods or tools are available for collecting quantitative data

• Experiments

• Controlled observations

• Surveys on paper, kiosk, or mobile (close-ended)

• Longitudinal studies

• Polls

• Telephone interviews

• Face-to-face interviews

• Quantitative observation examples include age, weight, height, length, population, and size

• Quantitative data collection methods are often based on mathematical calculations

• Data obtained is usually seen as more objective and reliable

Scales of Measurement

• The nominal scale describes differences between things by assigning them to categories

• Subjects are classified into qualitative cases, such as sex, nationality, or religion

• Numbers or symbols classify objects, persons, or characteristics

• Socio-economic status, race, occupation, or religious affiliation are other examples

• The ordinal scale ranks classes like social class, profession, or nutritional status

• Variables differ in amount or degree

• Items or individuals from highest to lowest are ranked

• Ordinal measures lack absolute values, and differences between adjacent ranks may not be equal

• The interval scale shows an exact distance between two categories, but the zero point is arbitrary

• Ratios between differences are known, like in temperature scales

• The lack of a true zero is the primary limitation

• Psychological tests and inventories are interval scales with limitations, yet they can be added, subtracted, multiplied, and divided

• Ratio scales are similar to interval scales, but the zero point is fixed

• The ratio between any two values is considered (ages, heights, or weights)

• A true zero indicates the complete absence of a property

• Numerals have qualities of real numbers and can be added, subtracted, multiplied, and divided

• Ratio scales are the same as interval scales, but the zero means "does not exist"

• Weight or age of zero doesn't exist, temperature is not a ratio scale, because zero exists

• Examples include age, weight, height, scales, and income

• Data is classified as univariate (single variable), bivariate (two variables), or multivariate (multiple variables)

• Single variable data is a list, while bivariate or multivariate data can be expressed with rows and columns

Learning Module 2: Variables

• Variables can represent numeric values, characters, character strings, or memory addresses

• Variables play a role in computer programming because of their flexible programs and use

• Observations are the raw materials with which research workers deal

• Variables can be quantitative or qualitative

• A quantitative variable is one where observations can be measured with a natural order or ranking (heights, weights)

• Observations are further classified as continuous or discrete

• Continuous variables allow of all values in some range (height, weight)

• Discrete variables do not allow possible values to be observed on a continuous scale, having of gaps between possible values (petals of a flower, households in a block)

• Qualitative variables are not numerically measurable

• Individuals are assigned to mutually exclusive categories, only classified and then enumerated

• Independent (IV) and dependent (DV) are the two most common variables

• Independent variables are manipulated, while dependent variables are affected by the changes

• Independent variables are the "cause," and dependent variables are the "effect" in cause and effect

• The independent variable is manipulated, and the outcome is measured in the dependent variable

• Independent and dependent variables are always placed on the same parts of a graph

• The independent variable goes on the x-axis, and the dependent variable goes on the y-axis

Learning Module 3: Statistical Methods

• Statistical methods consist of mathematical formulas, models, and techniques for statistical analysis of research data

• Statistical research methods extract information from research data and assess the robustness of research outputs

• Descriptive and inferential statistics are the two methods used in statistics

• Descriptive statistics summarize and organize data

• Inferential statistics make inferences and predictions about data

• Descriptive statistics collects and describes a set of data to yield meaningful information

• Information only covers the collected data, refraining from inferences or conclusions concerning a larger set of data

• It describes relationships with variables, objectives, among people, and situations

• The descriptive tools are:

• Percentage and frequency distribution

• Ratios and ranking

• Measures of Central Tendency

• Measures of variability

• Statistics of association

• Tables and graphs

• Statistical inference analyzes a subset of data, leading to predictions or inferences about the entire data set

• It takes data from a sample and makes inferences about the larger population

• Random sampling mirrors the population, avoiding overly-high or low statistics

• Standard analysis tools of inferential statistics:

• Hypothesis tests,

• Confidence intervals, and

• Regression analysis.

Learning Module 4: Descriptive Methods

• The mean, median and mode are the known measures of centrality which aim in identifying the midpoint in a data set through statistical means

• The mode, median, and mean are measures of central location

• There measures convey a great deal of information in a small amount of space and time

• It reduced a large quantity of data to a single value that is represents the entire mass data

• Known popularly as averages -The mode is simple in both concept and computation -The median is defined in a distribution that divides an ordered set of scores into two equal parts -The arithmetic mean is the average most think

-The concept of the mean is importatbt to adavanced discussions of measurement and sampling -Each of these sample averages we are referring to here has a unique meaning that is different from that of the other averages; each represents a different aspect of the data. -Since the mean depends on the value of each and every score in a distribution; it is strongly influenced by extreme scores.

-there are many instances in which a comparison of the same average over two distributions may be misleading. -In statistics, a frequency distribution is a list, table or graph that displays the frequency of various outcomes in a sample. Each entry in the table contains the frequency or count of the occurrences of values within a particular group or interval

Learning Module 5: Measures of Dispersion

• Dispersion (variability, scatter, or spread) is the extent to which a distribution is stretched or squeezed

• Examples of measures of statistical dispersion are the range, variance, standard deviation, and interquartile range

• The measure of dispersion shows the scatterings of the data

• It informs the variation of the data from one another and gives a clear idea about the distribution of the data

• The measure of dispersion shows the homogeneity or the heterogeneity of the observations

• Range is the common and easily understandable measures of dispersion

• Difference between two extreme observations of the data set

• In statistics, the range of a set of data is the difference between the lowest and highest values.

• Variance calculates the extent to which a set of data is spread out

• A zero variance demotes that all the value are similar. Variance is the squared value of the standard deviation, so it can never be negative

• Standard Deviation provdies a concept of the closeness of the whole set of data to the mean or the average value

Learning Module 6: Basic Terms in Inferential Statistics

• Experiments and research have, for convenience, chosen several arbitrary standards, called levels of significance, usually designated by the Greek letter alpha a. The 0.05 and the 0.01 level of significance are the ones most often used.
• traditionally framed as a declarative sentence, this operational distillation of a study's purpose is what we call the hypothesis. A formally written hypothesis has a number of merits. Among these is its ability

Learning Module 7: Analysis Tools in Inferential Methods

• correlation coefficient is a numerical measure of some type of correlation, meaning a statistical relationship between two variables. The variables may be two columns of a given data set of observations, often called a sample, or two Pearson product-moment correlation coefficient measures linear correlation between two variables X and Y. It has a value between +1 and 1. A value of +1 is total

Learning Module 8: Tools in Inferential Methods

• Regression Analysis (LR) deals with the simplest type of prediction: that of predicting one variable (y) with the knowledge of another variable (x). Researchers on the field of behavioural science are mostly concerned with problems on prediction