. Differentiating Between Population and Sample
1.1 Population
A population refers to the entire group of individuals, objects, or events that a researcher is interested in studying. It includes all possible subjects that meet the criteria for inclusion in the study. The population can be finite or infinite, depending on the research context.
Example: In a study on the reading habits of high school students in a particular city, the population would include all high school students in that city.
1.2 Sample
A sample is a subset of the population that is selected for the actual study. Researchers collect data from the sample and use the results to make inferences about the entire population. Sampling is necessary when it is impractical or impossible to study the whole population.
Example: From the population of all high school students in a city, a researcher might select a sample of 200 students to survey about their reading habits.
. Deciding About Sample Size
2.1 Research Objectives
The research objectives play a crucial role in determining the sample size. If the goal is to achieve high accuracy and detailed insights, a larger sample size may be necessary. For exploratory studies, smaller samples might suffice.
2.2 Population Size
The size of the population impacts the sample size. For large populations, the sample size does not need to increase proportionally to maintain accuracy. However, for small populations, the sample size may need to be a significant proportion of the population.
2.3 Desired Confidence Level
The confidence level indicates the probability that the sample accurately reflects the population. Common confidence levels are 90%, 95%, and 99%. Higher confidence levels require larger sample sizes to ensure the results are reliable.
2.4 Margin of Error
The margin of error represents the range within which the true population parameter is expected to lie. A smaller margin of error requires a larger sample size to provide more precise estimates.
2.5 Variability in the Population
The more variability or diversity in the population, the larger the sample size needed to capture that variability accurately. Homogeneous populations can be represented with smaller samples.
2.6 Sampling Method
The sampling method affects the required sample size. For example, stratified sampling, which divides the population into subgroups and samples each subgroup, may require a different sample size compared to simple random sampling.
2.7 Practical Considerations
Researchers must consider practical factors such as time, budget, and resources available for data collection. While larger samples provide more accuracy, they also require more resources.
Example of Determining Sample Size
In a study to determine the average reading time of high school students in a city, the researcher might follow these steps:
1. Define the research objectives: Estimate the average reading time with a 95% confidence level and a margin of error of 5 minutes.
2. Estimate population size: There are 10,000 high school students in the city.
3. Consider variability: Based on previous studies, the standard deviation of reading time is estimated to be 30 minutes.
4. Use a sample size formula or calculator: Using a sample size formula considering the confidence level, margin of error, and standard deviation, the researcher might determine that a sample size of 384 students is required.
By considering these factors, researchers can decide on an appropriate sample size that balances accuracy and practicality in their study.
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