Population vs Sample

• A population is the entire group that you want to draw conclusions about
• A sample is the specific group that you will collect data from
• The size of the sample is always less than the total size of the population

Population

• The population can be defined in terms of geographical location, age, gender, occupation, etc.
• The population is the entire group that you want to draw conclusions about
• Researchers rarely examine the entire population because of cost, time and accessibility
• Defining the population is the first step in any statistical study

Sample

• A sample is a subset of individuals from a larger population
• Researchers use sampling to make inferences about the larger population
• Sampling saves time and resources
• The sample should mirror the characteristics of the population
• Random sampling is the best way to achieve this

Parameters and Statistics

• A parameter is a characteristic describing an entire population
• A statistic is a characteristic describing a sample

Population Parameter

• Population parameters are the true values, but we can never know them for sure
• Parameters are often denoted using Greek letters
  • μ is the population mean
  • σ is the population standard deviation
  • p is the population proportion

Sample Statistic

• Sample statistics are estimates of population parameters
• Statistics are denoted using Roman letters
  • x̄ is the sample mean
  • s is the sample standard deviation
  • p̂ is the sample proportion

Inferences

• Statistical inference is the process of drawing conclusions about a population based on a sample
• We use statistics to estimate parameters
• A good sample is essential for making accurate inferences
• The sample must be representative of the population
• Random sampling helps ensure representativeness

Sampling Error

• Sampling error is the difference between a sample statistic and the corresponding population parameter
• Sampling error is unavoidable
• Sampling error can be reduced by increasing the sample size
• The larger the sample size, the more closely the sample statistic will estimate the population parameter

Types of Sampling

• Probability sampling involves random selection, allowing you to make statistical inferences about the whole group
• Non-probability sampling involves non-random selection based on convenience or other criteria, allowing you to easily collect data

Probability Sampling

• Simple random sampling: Every member of the population has an equal chance of being selected
• Systematic sampling: Selecting members of a population at regular intervals e.g. every 10th person on a list
• Stratified sampling: Divide the population into subgroups (strata) based on shared characteristics and then randomly sample from each group
• Cluster sampling: Divide the population into clusters and then randomly select entire clusters to sample

Non-Probability Sampling

• Convenience sampling: Select individuals who are easiest to reach
• Voluntary response sampling: Individuals volunteer to participate
• Purposive sampling: Researcher uses their judgment to select participants who are most likely to provide useful information
• Snowball sampling: Existing participants recruit future participants from among their acquaintances

Sample Size

• The sample size is the number of individuals included in your sample
• A larger sample size generally leads to more accurate inferences
• The required sample size depends on the variability of the population, the desired level of precision, and the confidence level

Sample Size and Variability

• Populations with more variability require larger samples
• If individuals in a population are very similar, a smaller sample size will be sufficient

Sample Size and Precision

• Precision refers to the margin of error around your estimate
• A smaller margin of error requires a larger sample size

Sample Size and Confidence Level

• Confidence level refers to the probability that the true population parameter falls within the margin of error
• A higher confidence level requires a larger sample size

Bias

• Bias is a systematic error that can distort your results
• Selection bias occurs when the sample is not representative of the population
• Non-response bias occurs when individuals selected for the sample do not participate
• Response bias occurs when participants provide inaccurate or dishonest answers

Minimizing Bias

• Use random sampling techniques to minimize selection bias
• Take steps to encourage participation and reduce non-response bias
• Use careful questionnaire design and data collection procedures to minimize response bias

Examples of Population and Sample

• If you want to know the average height of all students at a university
  • The population is all students at the university
  • The sample could be a random selection of students from that university
• If you want to know the proportion of voters in a country who support a particular candidate:
  • The population is all voters in the country
  • The sample could be a random selection of registered voters

Conclusion

• Understanding the difference between population and sample is a vital concept in statistics
• Researchers use samples to make inferences about populations
• A well-chosen sample can provide valuable insights into the characteristics of the population
• Being aware of potential sources of bias and error is essential for drawing accurate conclusions