Quantitative Research Methods and Sampling Techniques

What is the difference between a population and a sample in quantitative research?

A population is the entire group you want to study (e.g., all Grade $8$ students in the school), whereas a sample is a smaller group chosen from that population (e.g., $15$ selected Grade $8$ students).

What are the five common approaches used to determine sample size in quantitative research?

1. Heuristics; 2. Lunenburg and Irby Approach; 3. Literature Review Approach; 4. Slovin's Formula; 5. Power Analysis.

What is the Heuristics Approach for determining sample size, and when is it used?

The Heuristics Approach is a rule-of-thumb method based on expert recommendations and previous studies that does not use mathematical formulas. It is used during exploratory research, pilot studies, when time and budget are limited, when population size is unknown, or when no statistical formula is required.

What are the suggested sample sizes for various research types under the Heuristics Approach?

According to Heuristics sample size recommendations: Pilot Study requires $10\text{–}30$; Survey Research requires at least $100$; Experimental Research requires at least $30$ per group; and Correlational Research requires $30\text{–}100+$.

What is the purpose of the Lunenburg and Irby Approach in research?

It is a systematic, 10-step guide commonly used in educational research to help researchers complete studies step-by-step, ensuring organized and credible research.

What are the first five steps of the Lunenburg and Irby Approach?

1. Identify the Research Problem; 2. Review Related Literature; 3. Develop Research Questions or Hypotheses; 4. Select the Research Design; 5. Identify the Population and Sample.

What are steps 6 through 10 of the Lunenburg and Irby Approach?

6. Develop or Select Research Instruments; 7. Collect the Data; 8. Analyze the Data; 9. Interpret the Findings; 10. Draw Conclusions and Make Recommendations.

What is the Literature Review Approach to research design and sample size?

It is a method where existing studies related to a topic are analyzed and summarized without collecting new data first, focusing on what other researchers have already discovered.

What are the seven steps involved in the Literature Review Approach?

1. Identify the Research Topic; 2. Search for Related Literature; 3. Evaluate the Sources; 4. Organize the Information; 5. Analyze and Compare; 6. Identify the Research Gap; 7. Write the Literature Review.

What is Slovin's Formula and how is it expressed mathematically?

Slovin's Formula is a statistical formula used to calculate sample size when total population is known but little is known about its behavior or variability. The formula is $n = \frac{N}{1 + N e^2}$, where $n$ is sample size, $N$ is total population, and $e$ is margin of error.

How is sample size calculated using Slovin's Formula when total population $N = 500$ and margin of error $e = 0.05$?

Using $n = \frac{N}{1 + N e^2}$, substitute $N = 500$ and $e = 0.05$: $n = \frac{500}{1 + 500(0.05)^2} = \frac{500}{1 + 500(0.0025)} = \frac{500}{2.25} \approx 222.22$, resulting in a final sample size of $222$ respondents.

What is the function of Power Analysis in quantitative research?

Power Analysis helps researchers determine how many participants are needed to produce accurate, reliable, and statistically meaningful results by choosing a sample size large enough to detect a true effect if one exists.

What is probability sampling and what are its key characteristics?

Probability sampling is a sampling technique where every member of the population has a known and equal (or measurable) chance of selection. Key characteristics: selection is based on random methods, produces representative samples, reduces sampling bias, and allows researchers to generalize findings to the population.

What are the four types of probability sampling?

1. Simple Random Sampling (every individual has an equal chance); 2. Systematic Sampling (select every $k\text{th}$ member after a random starting point); 3. Stratified Random Sampling (divide population into strata and randomly select from each group); 4. Cluster Sampling (divide population into clusters and randomly select whole clusters).

How is the sampling interval $k$ calculated in systematic sampling?

The sampling interval formula is $k = \frac{N}{n}$, where $N$ is total population size and $n$ is target sample size. For example, given $N = 987$ and $n = 310$, $k = \frac{987}{310} = 3.18 \approx 3$, meaning every $3\text{rd}$ room or participant is systematically selected.

What are five common types of quantitative research instruments?

1. Questionnaire (written or online list of questions); 2. Survey (collecting information from many people); 3. Test (measuring knowledge or skills); 4. Checklist (checking if something is present or completed); 5. Rating Scale (rating answers on a scale, such as Strongly Agree to Strongly Disagree).

What are the main characteristics of a good research instrument?

Validity, Reliability, Objectivity, Practicality (Usability), Clarity, Relevance, Standardization, Accuracy, and Feasibility.

In research instrumentation, how do Validity and Reliability differ?

Validity means the instrument measures what it is intended to measure (e.g., a math test measures mathematical ability, not reading skills), whereas Reliability means the instrument produces consistent and stable results when used repeatedly under similar conditions.

What are the four measurement scales used in quantitative research?

1. Nominal Scale (classifies data into categories without order or ranking); 2. Ordinal Scale (classifies data into categories with a meaningful order, but unequal differences); 3. Interval Scale (ordered values with equal intervals, but no true zero point); 4. Ratio Scale