Inquiry, Research, & Quantitative Methods: Comprehensive Study Notes

Nature of Inquiry and Research

Inquiry

  • Like investigating; it's focused on asking questions to understand something better.

  • Relies a lot on HOTS (Higher-Order Thinking Skills) such as analyzing, judging, and putting ideas together.

  • Mostly about exploring and might stop once a good understanding is reached.

Research

  • A structured, scientific, experimental, or logical way of thinking that starts with specific observations and builds up to bigger, more complex ideas.

  • Uses all kinds of thinking skills—from LOTS (Lower-Order Thinking Skills) like remembering and understanding to HOTS like analyzing, judging, and creating.

  • Follows organized, documented steps to discover or confirm truths about the world.

  • Usually produces results that are shared, can be repeated, or used by others.

Quantitative Research

Essence and Key Terms

  • Closely linked to numbers, measurement, and statistical reasoning.

  • Answers questions like “how many,” “how much,” “how long,” “to what extent,” etc.

  • Information is often shown with numbers like counts, percentages, fractions, or other number indicators.

General Characteristics

  • Objective – Tries to reduce personal opinions by using standard tools and methods.

  • Includes theorizing, predicting, analyzing, inferring, and sometimes creating models that guess future outcomes.

  • Mostly used in sciences like physics, chemistry, biology, and medicine, but can be used in many other fields too.

Major Classifications

  1. Experimental Research

  • Purpose: Change one thing (independent variable) to see how it affects another thing (dependent variable).

  • Examples: Like testing new drugs or trying out different teaching methods in a controlled way.

a. True Experimental

  • People are randomly put into groups; other outside factors are strictly controlled.

  • Example: Randomly assigning students to two teaching methods and comparing their exam scores.

b. Quasi-Experimental

  • Changes are made, but people aren't randomly assigned; instead, existing groups are used.

  • Sub-types:

    • Matched comparative group

    • Time-series design

    • Counterbalanced design

  • Example: Comparing academic results between two schools that already use different learning plans.

c. Single-Subject Designs

  • Studies one person in great detail over time, taking many measurements.

d. Pre-Experimental

  • Very little control; no random choosing; often just a first look or a test.

  • Example: A teacher tries a new method in one class and just casually observes if it helps.

  1. Non-Experimental Research

  • No changes are made; the researcher just observes, measures, or looks at things as they already are.

  • Common types: surveys, historical studies, observations, looking for connections (correlation), describing things, or comparing things.

Statistics: Foundations for Quantitative Research

Sampling Theory

Broad Categories

  • Probability (True/Random) Sampling – Everyone in the group has an equal chance to be chosen.

  • Non-Probability (Quasi/Bias) Sampling – Not everyone in the group has a chance to be chosen.

Probability Techniques

  1. Simple Random – Uses random number tools; each person has an equal chance P(i)= \frac{1}{N}.

  2. Systematic – Selects every k-th item after a random start.

  3. Stratified – Divides the group into layers (strata), then chooses samples from each layer based on their size to get more accurate results.

  4. Cluster – Randomly picks whole groups (clusters); sometimes you pick smaller groups within those clusters (multistage).

Non-Probability Techniques

  1. Convenience – Choose whoever is easiest to find; very likely to be biased.

  2. Purposive (Judgment) – Researcher specifically chooses people who fit certain requirements.

  3. Snowball – First participants find more people; good for groups that are hard to find.

  4. Quota – Fill a set number of people from each subgroup, but not randomly.

Measurement Scales

  1. Nominal – Categories with names (e.g., gender, blood type).

  2. Ordinal – Ranked order, but the steps between ranks aren't equal (e.g., satisfaction levels).

  3. Interval – Equal steps between values, but no true 'nothing' point (e.g., \text{°C} temperature).

  4. Ratio – Equal steps between values, and a true 'nothing' point (e.g., height, weight, Kelvin temperature).

Frequency Distribution

  • Puts information into groups or categories and shows how many items are in each.

  • Key Elements:

    1. Class Limits – The lowest and highest values for each group.

    2. Class Size (Width) – C= \frac{\text{Range}}{\text{desired C.I.}} . How wide each group is.

    3. Class Boundaries – Lines that completely separate groups without any gaps.

    4. Class Marks – Midpoints: x= \frac{\text{Lower limit}+ \text{Upper limit}}{2}. The middle value of each group.

  • Construction Steps:

    1. Figure out the range \text{Range}= \text{Highest}- \text{Lowest}.

    2. Decide how many groups you want and calculate their width.

    3. Set up the limits and boundaries for each group.

    4. Mark observations, then count how often they appear.

    5. Add up cumulative frequencies, percentages, etc.