13 Lesson 1: Sampling, Sampling Error, and the Distribution of the Sample Mean

Define Probability Sampling

In this type of sampling, each member of the population has an equal probability of being selected for the sample. It generates more accurate and reliable results.

What is the objective of Probability Sampling?

This method aims to create a sample that accurately represents the entire population.

Define Non-Probability Sampling

In this type of sampling, the selection depends on factors other than probability such as judgment or data accessibility.

What are the risks and limitations of Non-Probability Sampling

The main risk is creating a non-representative sample which results in less reliable estimates of population parameters.

How can we estimate parameters?

Parameter estimation involves using sample data to make inferences about population parameters.

What is the relationship between probability and Simple Random Sampling?

Every individual or element in the population has the same probability or likelihood of being chosen for the sample.

What are some Random Sampling Techniques?

* Random number tables.
* Computer random-number generators.
* Systematic sampling, where every kth member in the population is selected.

When is useful to use Random Sampling?

Is particularly useful when the data in the population is similar or homogeneous. It helps ensure that the sample accurately represents the entire population.

What are Sampling Errors?

Is the error caused by observing a sample instead of the entire population to draw conclusion relation to population parameters.

What is a Sampling Distribution?

Is the probability distribution of a specific sample statistic when you repeatedly draw samples from a population.

What factor is essential for constructing Sampling Distributions?

All samples must be random and of the same size.

What is the process of Stratification?

Stratification is a process of dividing the population into relatively homogeneous subgroups or strata before drawing samples. Random sampling is then applied within each stratum

What is the goal of Stratification?

The goal is to create mutually exclusive and collectively exhaustive strata, meaning that each population element belongs to only one stratum, and no one is left out.

Why is Stratification useful?

Stratification helps improve the representativeness of the sample and reduces sampling error.

What is Cluster Sampling?

Cluster sampling is a sampling technique that divides the population into clusters or groups, where each cluster is a mini-representation of the entire population.

How are Cluster selected?

In cluster sampling, clusters are selected randomly from the population. This is typically done in two stages.

What are the different stage-methods for selection of Clusters?

* **One-Stage Cluster Sampling**: In one-stage cluster sampling, all members within each selected cluster are included in the sample. This approach simplifies the sampling process.
* **Two-Stage Cluster Sampling**: In two-stage cluster sampling, after selecting clusters in the first stage, a random subsample of individual elements is selected from each chosen cluster. This allows for a more detailed analysis.

Compare Clustering and Stratified sampling

Cluster sampling differs from stratified random sampling, where the entire population is divided into strata (homogeneous subgroups), and a random sample is drawn from each stratum. In cluster sampling, entire clusters are selected, while in stratified sampling, specific data points within each stratum are chosen.

When is Clustering sample adequate?

Cluster sampling can be more time-efficient and cost-effective when dealing with large and diverse populations.

What are the two types of Non-Probability Sampling

* Convenience Sampling
* Judgmental Sampling

Explain convenience sampling

Convenience sampling involves selecting elements for the sample based on ease of access or convenience. While it is quick and low-cost, it may limit sampling accuracy. Convenience sampling is often used in small-scale pilot studies or situations where time and resources are limited.

Explain judgmental sampling

Judgmental sampling involves handpicking elements from the population based on the researcher's knowledge and professional judgment. This method allows researchers to focus directly on the target population of interest. However, judgmental sampling can be susceptible to biases and may lead to skewed results. It is typically used when there are time constraints or when the expertise of the researcher is critical for selecting a more representative sample than other sampling methods.

What is the relationship between the Central Limit Theorem and the Sampling distribution of statistics?

The CLT states that, regardless of the distribution of the population, the sampling distribution of the sample mean (when the sample size is adequate, typically n ≥ 30) will be approximately normal with a mean equal to the population mean (μ) and a variance equal to the population variance (σ²) divided by the sample size (n).

In other words, for sufficiently large sample sizes, the sample mean follows a normal distribution.

Explain the standard error of the mean

The standard error of the mean (SE) is a measure of the variability of sample means that we would obtain if we took multiple random samples from the same population. It quantifies how much the sample mean is expected to vary from sample to sample.

How can we calculate the standard error of the mean when the population standard deviation is known?

How can we calculate the standard error of the mean when the population standard deviation is unknown?

We use the sample standard deviation

What is the relationship between sample size (n) and standard errors

The larger the sample size (n), the smaller the standard error, which means that larger samples tend to provide more precise estimates of the population mean.