Quantitative Research Methods

• Janine Crystal C. Sayo, RPM, JD, is the presenter of the material on quantitative research.

Quantitative Method

• Quantitative methods quantify "how much", "how many", and "how often".
• Aims to be objective and scientific in its approach.
• Literature, data, analysis, and interpretation are the basis.
• There is no place in quantitative methods for personal comments.

Assessing The World

• A primary aim to measure and understand the world well enough to predict and control it through identifying cause-and-effect relationships.
• Correlation does not equal causation.
• Systematic empirical investigation of observable phenomena is done via statistical, mathematical, or computational techniques (Aliaga & Gunderson, 2000).
• Involves quantifiable variables.

Methods and Tools

• Descriptive and Inferential.
• Inferential includes correlational, non-parametric, and Analysis of Variance.
• Tools involve frequencies/graphs, Pearson’s, Spearman, Kendall, Chi-Square, and T-test/ANOVA.

Basic Statistics Overview

• The overview starts with a short introduction, variety of variables, discussions about sample, getting to know stat tools, and includes an activity.

Terms

• Data: Observations and/or measurements collected.
• Statistic: Description of a sample.
• Population: All subjects to be studied.
• Sample: Selected members of the population.

Methods (cont.)

• Descriptive and Inferential.
• Inferential: Includes correlational, quasi-experimental, experimental, surveys, and interviews.
  • Experimental Example: Reaction time, Frequencies
  • Survey: Likert Scale, Frequency Count
  • Interview: Frequency

Two Types of Statistics

• Descriptive
• Inferential
• Data set: 1, 1, 2, 3, 5, 5, 5
  • Mean: 3.14
  • Range: 1-5
  • Sample Size(n) 7
  • Mode: 5
• The solutions to data set 20, 25, 25, 25, 30, 35, 40 are:
  • Mean: 28.57
  • n: 7
  • Range: 20-40
  • Mode: 25

Statistical Tools

• Tools: T-test, ANOVA, Correlation, Regression, and Chi-Square.

Probability

• Probability helps to understand if research findings matter, using p-values.
  • P-value of 0.05: 5 out of 100 happened by chance.
  • P-value of 0.01: 1 out of 100 happened by chance.

Variables

• Types of variables: Independent, Dependent, Moderating, Mediating, Extraneous, Subject, Quantitative (Continuous), and Qualitative (Categorical or Discrete).

IV vs DV

• Independent Variable (IV) or Predictor Variable: Manipulated by the researcher.
• Dependent Variable (DV) or Criterion Variable: Measured. It is presumed to change through the manipulation of the IV.
• E.g. In a color and memory experiment the Independent Variable is color, yellow and red, and the Dependent Variable is digit span.

Mod vs Med

• Moderating variables are generally qualitative like sex, race or class.
• Moderating variables affect the direction and/or strength of the relation between an IV and a DV.
• Mediating variables account for the relation between the variables and explains why the effect occurs.

Extraneous/Confounding Variables

• Any variable not intentionally studied but plays a vital role and threatens validity.
  • Control the variable, Eliminate, Add the variable, Blinding

Subject Variables

• Variables that are innate to a person: age, sex, gender, belief, religion, IQ, etc.
• These cannot be manipulated but can still be used as an IV.
  • Experimental -> Quasi-experimental

Quali vs Quanti

• Qualitative variable: Categorical
• Quantitative variable: Continuous or Discrete, is also referred to as levels of measurement.

Levels of measurement

• Nominal and Ordinal are categorical.
• Interval and Ratio are continuous.
• Nominal: Gender, Disease Outcome uses numbers as labels.
• Ordinal: Position 1, 2 or 3.
• Interval: Thermometer.
• Ratio: Currencies.

Summary of variables

• Nominal: Counts, aka "Frequency of Distribution".
• Ordinal: Counts, mode, median and data in a known order.
• Interval : Counts, mode, median, known order, can quantify each difference, can add and subtract values.
• Ratio: Counts, mode, median, known order, can quantify each difference, can add, multiple and divide values and has a true zero

Samples

• In general, the more respondents, the higher the chance of significant findings, but not for experimental design, focus group discussions and in-depth interviews.
• Before we calculate the sample size, the following items are needed; Population Size, Confidence Interval, Confidence level, and SD.
• Learning Style of Grade 10 Students
  • The total number of Grade 10 students in Bulacan = 250,000.
  • Sampling Frame = 100,000.
• Confidence Interval aka Margin of Error
  • Z-Scores: 90% - 1.645, 95% - 1.96, 99% - 2.576
  • Standard Deviation- Researcher's discression with values of 0.5 and 1 usually used.
• Sample size calculation uses the following formula:
  • n = (X² * N * P * (1-P)) / (ME² * (N-1)) + (X² * P * (1-P))
    • n = sample size
    • X² = Chi-square for the specified confidence level at 1 degree of freedom
    • N = Population Size
    • P = population proportion (.50 in this table)
    • ME = desired Margin of Error (expressed as a proportion)

Sample Methods

• Sampling methods guarantee that the sample chosen is representative of the population.
• Sampling methods: random, systematic, stratified, cluster, multistage, convenience.

Statistical Tools

• Tools consist of T-tests, ANOVA, Correlation, Regression, and Chi-Square.

T-Tests

• IV: Categorical and DV: Continuous
• The test of comparison between two means of two sets of scores.
• It is the simplest Inferential Stat.
• The statistical significance uses the mean accorded to the condition.
• Equal and un-equal variance (t-test independent).
  • Dependent: 2 sets of scores; 1 set of respondents. (ex spelling competency, verbal vs visual)
  • Independent: 2 sets of scores; 2 sets of respondents. (ex EQ scores, male vs femal)

ANOVA

• Analysis of Variance.
• Compares three or more means.
  • One way : Extension of t-test Independent, 1 IV (Categorical) & 1 DV (Continuous), 3 or more groups of respondents, F- Ratio: Between/Within.
  • Two way : Two IV (Categorical), One DV (Continuous), Individual and Interaction Effect, and a sample experiment.

Correlation

• Relationship between variables measured by direction and strength.
• Continuous Variables are usually tested.
• Does not mean causation.
• Correlation Coefficient: ±1
• Levels of Relationship: Directly proportional(+), Inversely Related (-), No Correlation, Weak, Moderate, Strong, Perfect
• Number of Novels Read, Reading Comprehension Score, No IV and DV

Regression

• Only after significant Correlation
• Simple
• Multiple Linear Both variables are at Continuous Level

Practice Analysis

The data set:

1. Researcher Purple wants to examine if consumption of calcium is related to large foot size. Calcium is measured in milligrams and foot size is measured in centimeters . Researcher Purple hypothesizes that calcium affects foot size.

• Dependent is Foot Size Interval
• Independent is Calcium Ratio

2. Researcher Orange wants to know if a man's consumption of orange juice is related to an increase in male pattern baldness. Consumption of orange juice is measured in millilitres, and male pattern baldness is measured on a scale of 1-3 (1=totally bald, 2=some balding, 3=no balding). Researcher Orange hypothesizes that orange juice affects male pattern baldness.

• Dependent is Male Patter Baldness
• Independent is Orange Juice Ratio

3. Researcher Blue wants to know if pet type is associated with happiness. Pet type is classified on a coding scheme of 1-5 (1-cat, 2-dog, 3-bird, 4-fish, 5-other). Happiness is measured on a scale of 1-3 (1=not happy, 2=somewhat happy, 3=very happy). Researcher Blue hypothesizes that pet type will affect level of happiness.

• Dependent is Happiness Ordinal
• Independent is Pet Type Nominal

Data Set Examples

• What is your gender? M = Male and F = Female. (Nominal)
• What is your hair color? 1 = Brown, 2 = Black, 3 = Blonde, 4 = Gray, 5 = Other.(Nominal)
• Where do you live? A = North of the equator, B = South of the equator, C = Neither: In the international space station.(Nominal)
• How do you feel today? 1 = Very Unhappy, 2 = Unhappy, 3 = OK, 4 = Happy, 5 = Very Happy.(Ordinal)
• How satisfied are you with our service? 1 = Very Unsatisfied, 2 = Somewhat Unsatisfied, 3 = Neutral, 4 = Somewhat Satisfied, 5 = Very Satisfied.(Ordinal)
• GPA, Height, Weight and Time are all ratio variables.