What is the primary difference between a population and a sample?

A population is the entire group of interest, while a sample is a smaller subset of that group used for data collection. We use samples because measuring an entire population is often too expensive or time-consuming.

How does Stratified Sampling differ from Cluster Sampling?

In Stratified Sampling, the population is divided into groups and a random sample is taken from *every* group. In Cluster Sampling, the population is divided into groups, and *entire* groups are randomly selected to be surveyed.

Why is Convenience Sampling considered a non-probability method?

It is a non-probability method because individuals are selected based on ease of access rather than a random process. This means not every member of the population has a known or equal chance of being selected, leading to high bias.

What is 'Non-Response Bias' and why is it a problem?

Non-response bias occurs when people who choose not to participate in a survey have different characteristics or opinions than those who do. This makes the resulting data unrepresentative of the actual population.

What is the formula for the sampling interval in Systematic Sampling?

The interval $k$ is calculated as $k = \frac{N}{n}$, where $N$ is the total population size and $n$ is the desired sample size. You then pick a random starting point between 1 and $k$ and select every $k^{th}$ item.

What is the difference between Sampling Error and Bias?

Sampling error is the natural, random variation that occurs because we are looking at a sample instead of the whole population. Bias is a systematic error caused by a flawed collection method that consistently over- or under-represents certain groups.

How can 'Leading Questions' cause Response Bias?

Leading questions are phrased in a way that suggests a 'correct' or preferred answer, influencing the respondent's choice. This results in data that reflects the researcher's bias rather than the participant's true opinion.

When is a Census more appropriate than a Sample?

A census is appropriate when the population is small, when absolute accuracy is required (like a national population count), or when the cost of missing even one individual is extremely high.

What is a 'Sampling Frame'?

A sampling frame is the actual list or set of directions used to identify the members of the population. If the list is missing names or includes people who aren't in the target population, the sample will be flawed.

Why does increasing sample size not fix Selection Bias?

Selection bias is a structural flaw in the sampling method (e.g., only surveying people at a gym). If the method is fundamentally excluding certain groups, simply collecting more data from the same biased source will not make the sample representative.

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The Collection of Data

Collecting Data

Summary

Data collection is the systematic process of gathering information from a target population to answer research questions or test hypotheses. The validity of any statistical analysis depends entirely on the quality of the data collected, which is determined by the sampling method used and the minimization of various forms of bias.

1. Definition & Core Concepts

Population: The entire group of individuals or objects that a researcher is interested in studying. It is the 'target' for which conclusions are drawn, though it is often too large to measure directly.
Sample: A subset of the population selected for actual measurement. A representative sample must accurately reflect the characteristics of the entire population to ensure that findings can be generalized.
Census: A data collection process where every single member of the population is measured. While providing complete accuracy, a census is often impractical due to high costs, significant time requirements, and the potential for data to become obsolete before processing is finished.
Sampling Frame: A list or database of all individuals in the population from which the sample is drawn. If the sampling frame is incomplete or inaccurate, it introduces immediate bias into the study.

2. Probability Sampling Methods

Diagram comparing Stratified Sampling (taking some individuals from every group) versus Cluster Sampling (taking all individuals from randomly selected groups).

3. Non-Probability Sampling

Convenience Sampling: Selecting individuals who are easiest to reach or most available. While fast and inexpensive, this method is highly prone to bias because the sample is unlikely to represent the broader population.
Quota Sampling: A non-random version of stratified sampling where researchers are assigned a 'quota' of specific types of people to find (e.g., 50 men and 50 women). Once the quota is met, no further individuals from that group are included, regardless of their potential contribution.
Self-Selection (Volunteer) Bias: Occurs when individuals choose to participate in a study themselves. This often results in a sample of people with strong opinions or specific interests, which does not reflect the average population view.

4. Key Distinctions

5. Sources of Bias and Error

6. Exam Strategy & Tips