Statistics Lecture 1.5: Sampling Techniques. How to Develop a Random Sample

Introduction and Vocabulary Review

In this section, the instructor briefly reviews the vocabulary words discussed in the previous session, such as qualitative and quantitative data. The focus is on preparing for the upcoming topics in section 1.5.

Vocabulary Review

• Qualitative and quantitative data types are reviewed.

• Section 1.4 is recommended for further reading.

Overview of Section 1.5

The instructor introduces section 1.5, which will cover design of experiments and the concept of randomness in data collection.

• Design of experiments will be discussed.

• The concept of randomness will be defined.

• Collecting data randomly will be explained.

• If time permits, chapter 2 on frequency distributions may also be covered.

Difference Between Experiments and Observations

This section focuses on understanding the difference between experiments and observations based on how subjects are treated.

• Observations involve measuring specific traits without modifying subjects.

• Examples of observational studies include polling to gather opinions.

• Experiments involve applying treatments to subjects and observing their effects.

• Control groups and test groups are common in experiments.

Examples of Observations and Experiments

Additional examples are provided to illustrate observations and experiments.

• Polling is an example of observation where attitudes or opinions are observed without modifying subjects.

• Drug treatments with control groups and test groups demonstrate experiments where subjects are modified by applying a treatment.

Understanding Randomness in Data Collection

The concept of randomness in data collection is explained.

• Randomness refers to collecting data without any bias or predetermined pattern.

• The importance of randomness in data collection is emphasized.

No specific timestamp was provided for the explanation of randomness.

Random Sampling and Simple Random Sample

In this section, the speaker discusses the concept of random sampling and simple random sample. They explain that in a random sample, no single person can be predicted to be included, and each member of the population has an equal chance of being selected. A simple random sample means that any group of the same size has an equal likelihood of being selected.

Definition of Random Sampling

• Random sampling refers to selecting a sample where no single person can be predicted to be included.

• Each member of the population has an equal chance of being selected.

Simple Random Sample

• In a simple random sample, any group of the same size has an equal likelihood of being selected.

• No single group can be singled out as having a special case or being more likely to be selected.

• The speaker gives an example using names in a hat, where every name has an equal chance of being picked.

Making it Happen: Four Common Ways

• There are four common techniques for achieving random sampling:

• Technique 1: Asking friends or people you already know their opinions (not truly random).

• Technique 2: Asking strangers on the street (not truly random).

• Technique 3: Using a table or computer-generated random numbers.

• Technique 4: Using a physical method like drawing names from a hat.

Simple Random Sample Defined

The speaker further explains the concept of simple random sample and its definition. They clarify that each group of the same size should have an equal chance of being selected.

Definition of Simple Random Sample

• A simple random sample means that any group of the same size has an equal likelihood of being selected.

• No single group should have a higher probability than others.

• It ensures that every individual within each group has an equal chance of being selected.

Making it Happen: Four Common Ways (Continued)

• The speaker continues discussing the four common techniques for achieving random sampling:

• Technique 1: Asking friends or people you already know their opinions (not truly random).

• Technique 2: Asking strangers on the street (not truly random).

• Technique 3: Using a table or computer-generated random numbers.

• Technique 4: Using a physical method like drawing names from a hat.

Techniques for Achieving Simple Random Sample

The speaker discusses the four common techniques for achieving a simple random sample in more detail.

Technique 1: Asking Friends or People You Already Know

• This technique is not truly random as it involves asking people you already know.

• It may introduce bias and does not ensure an equal chance of selection for everyone.

Technique 2: Asking Strangers on the Street

• Similar to technique 1, this method is also not truly random as it involves selecting individuals based on proximity.

• It may introduce bias and does not ensure an equal chance of selection for everyone.

Technique 3: Using Table or Computer-Generated Random Numbers

• This technique involves using a table or computer-generated random numbers to select individuals randomly.

• It ensures an equal chance of selection for each individual but requires access to such tools.

Technique 4: Using Physical Methods like Drawing Names from a Hat

• This technique involves physically drawing names from a hat or similar methods.

• It ensures an equal chance of selection for each individual and can be easily implemented without advanced tools.

Conclusion

The speaker concludes by summarizing the four common techniques discussed earlier and emphasizes the importance of ensuring every group has an equal likelihood of being selected in order to achieve a simple random sample.

Recap of Four Common Techniques

• Technique 1: Asking friends or people you already know.

• Technique 2: Asking strangers on the street.

• Technique 3: Using a table or computer-generated random numbers.

• Technique 4: Using physical methods like drawing names from a hat.

Importance of Equal Likelihood

• To achieve a simple random sample, it is crucial to ensure that every group of the same size has an equal likelihood of being selected.

• This ensures fairness and avoids bias in the sampling process.

Sampling Methods in Statistics

In this section, the speaker discusses different sampling methods used in statistics.

Convenience Sampling

• Convenience sampling is a non-random method where easy-to-access results are used.

• It is not considered a realistic statistical basis and is rarely used.

Systematic Sampling

• Systematic sampling involves selecting every kth element from a population list.

• The starting point on the list is chosen randomly to ensure randomness in the selection process.

Stratified Sampling

• Stratified sampling aims to include representatives from each subgroup or layer of a population.

• It ensures that all groups are represented, especially when studying specific characteristics like race or religion.

Sampling Methods: Stratified and Cluster Sampling

In this section, the speaker discusses two sampling methods: stratified sampling and cluster sampling. The speaker explains how these methods are used to ensure representation in a sample.

Stratified Sampling

• Stratified sampling involves breaking the population into subgroups based on characteristics.

• A random sample is then taken from each subgroup.

• This method ensures that every subgroup is represented in the sample.

Cluster Sampling

• Cluster sampling involves breaking up the population into groups or clusters, regardless of any characteristic.

• Random numbers of clusters are selected, and data is collected from everyone within those clusters.

• This method does not involve grouping by characteristics but randomly selecting clusters.

Differences between Stratified and Cluster Sampling

• Stratified sampling involves grouping by characteristics and taking a random sample within each subgroup.

• Cluster sampling does not involve grouping by characteristics but randomly selecting clusters and collecting data from everyone within those clusters.

Convenience sampling and systematic sampling were mentioned as other methods but were not recommended for use.

Types of Errors in Sampling

In this section, the speaker discusses the two types of errors that can occur when sampling a population.

Types of Errors

• Non-sampling error: This type of error occurs when there are mistakes or inaccuracies made during the sampling process, such as recording incorrect information or making mathematical errors.

• Sampling error: This type of error is inherent in the process of sampling a population. It refers to the differences in characteristics between the sample and the entire population. Since the sample cannot perfectly represent every individual in the population, there will be some variation in their characteristics.