Statistics Sampling Methods Quiz

SAMPLING

• Descriptive Statistics: Methods used to summarize and present data.
• Inferential Statistics: Methods using data from a small group to make conclusions about a larger group.
• Population: The entire group of interest. It can include individuals, events, or objects.
• Sample: A subset of the population, selected for a study.
• Census: A complete enumeration of an entire population's data or information.
• Survey: A tool providing data or information about the entire population.
• Sampling: Data is collected from a sample rather than the entire population; it's chosen to represent the entire population.
• Cost: Sampling reduces the cost compared to a census.
• Timeliness: Data is obtained quickly using sampling.
• Detailed Information: In-depth information can be gathered from the sample.

PROBABILITY SAMPLING

• Probability Sampling: Every member of a population has a known, non-zero chance of being chosen for the sample.
• Simple Random Sampling (SRS): Each member of the population has an equal chance of being chosen. This sampling requires that all the elements are listed, and elements can be chosen with or without replacement.
• Stratified Random Sampling: Similar to SRS, but the population is first divided into strata (groups) based on shared characteristics. For each stratum, a SRS is used to select the sample.
• Systematic Sampling: Members of a population are selected at a fixed interval (e.g., every 10th member). The first member is selected randomly.
• Cluster Sampling: The population is divided into clusters, and a random sample of clusters is selected. Then, either all members of the chosen clusters are included or further sampling within clusters occurs.

NON-PROBABILITY SAMPLING

• Haphazard Sampling: Elements are selected without a specific plan (e.g., whoever is available).
• Convenience Sampling: Elements are used because they are easily available (e.g., standing in a mall).
• Volunteer Sampling: Individuals choose themselves to participate in the sample.
• Quota Sampling: A sample is chosen in which subgroups are represented according to their proportion within the population.
• Purposive Sampling: Researchers select specific participants believed to possess specific features relevant to the study.
• Snowball Sampling: Initial participants are used to recruit other participants in the study.

TYPES OF ERRORS

• Coverage Error: Exists when certain groups are excluded from the sampling frame, thus not having a chance to be selected.
• Nonresponse Error: Bias in samples resulting from individuals who choose not to respond.
• Measurement Error: Bias resulting from measurement error, such as leading questions, poor design, or respondent errors (misunderstanding the question or intentionally omitting answers).
• Sampling Error: Variation in sample results from one sample to another.

ETHICAL ISSUES ABOUT SURVEYS

• Bias: Researchers can choose questions or conduct the survey in such a way that it causes bias.
• Nonresponse: Not reporting the margin of error for the results when conducting a survey.
• Measurement error: Includes using leading questions.

SAMPLING DISTRIBUTIONS

• The sampling distribution of all sample means: A distribution of sample means from a large number of random samples taken from a population.
• Central Limit Theorem: For sample sizes of 30 or greater, the sampling distribution of the sample mean approximates a normal distribution. The mean of the sampling distribution is equal to the population mean, and the standard error (standard deviation) is equal to the population standard deviation divided by the square root of sample size.
• Sampling Distribution Properties: The sampling distribution properties are: (i) Mean of the sampling distribution is equal to the population mean, (ii) The standard deviation of the sampling distribution is equal to population standard deviation divided by square root of sample size.

CONFIDENCE INTERVALS

• Confidence Interval: A range of values likely to contain the true population parameter.
• t distribution: Used when population standard deviation is unknown, and sample size is less than 30.
• Z distribution: Used when population standard deviation is known, and sample size is greater than or equal to 30.
• Confidence Level: Probability that a confidence interval will contain the true population parameter in a repeated sampling procedure.
• Margin of error: Half the width of the confidence interval.
• Assumptions for Confidence Intervals for μ (σ unknown): Population is normally distributed or has a sufficiently large sample size (n > 30).

HYPOTHESIS TESTING

• Null Hypothesis (H₀): Statement of no effect or difference between groups, often assumed true until proven false.
• Alternative Hypothesis (H₁): Statement that there is an effect or difference between groups.
• Significance Level (α): Probability of rejecting a true null hypothesis (typically 0.05 or 0.01).
• Test Statistic: A calculated value comparing the sample to the null hypothesis.
• p-value: Probability of obtaining the sample result or a more extreme one, assuming null hypothesis is correct; if p-value<α, reject null hypothesis
• Critical Value: A specific test statistic value that is used to determine if the sample results are significantly different from the null hypothesis.
• Rejection Region: Area or region defined by the critical values, outside which the null hypothesis must be rejected.

REGRESSION ANALYSIS

• Regression Analysis: Used to study the relationship between two or more variables.
• Dependent variable: The variable being predicted.
• Independent variable: The variable used to predict the dependent variable
• Simple Linear Regression: A regression model with one independent variable.
• Multiple Linear Regression: A regression model with more than one independent variable.
• Coefficient of determination: Measures the proportion of variance in the dependent variable explained by the independent variable(s).
• Correlation Coefficient: A measure of the direction and strength of the linear association between two variables.

TWO-SAMPLE TESTS

• Paired Samples: Data are from the same subjects measured twice (e.g., before and after).
• Independent Samples: Data are from different subjects (e.g., comparing two groups).
• Pooled Variance T-Test: Used for independent samples when population variances are assumed equal, and sample sizes are small (typically less than 30).
• Separate Variance T-Test: Used for independent samples when population variances are not assumed equal.
• Two Sample Z-Test & T-test: Used for the difference of two samples from two distinct populations.