Sampling Techniques and Statistical Significance Tests

Quora Sampling

Selects individuals based on specific traits.

Convenience Sampling

Selects individuals based on easy accessibility.

Selection Bias

Error when certain population segments are excluded.

Non-responsive Bias

Error from selected individuals not participating.

Sample Mean

Average value calculated from sample data.

Standard Error (SE)

Measures the accuracy of sample mean estimates.

Chance Error

Difference between sample mean and population mean.

Unbiasedness

Sample mean equals population mean on average.

Population Standard Deviation

SD calculated from entire population data.

Bootstrap

Resampling technique to estimate sampling distribution.

Confidence Interval (CI)

Range of values likely containing true population parameter.

Critical Value

Value used to calculate confidence intervals.

68-95-99.7 Rule

Probability distribution of data in standard deviations.

Current Population Survey (CPS)

Monthly survey collecting employment data in U.S.

Unemployment Rate

Percentage of labor force that is unemployed.

Stratified Sampling

Sampling method that divides population into subgroups.

Primary Sampling Units (PSU)

Initial units selected in a sampling design.

Cluster Sampling

Sampling method using clusters as sampling units.

Measurement Error

Difference between observed and true values.

Gaussian Box Model

Probabilistic model for understanding measurement errors.

Bayes' Theorem

Formula for calculating conditional probabilities.

Random Variables

Values dependent on random events.

Hypothesis Test

Procedure for comparing data against a claim.

Observed Value

Value obtained from a measurement instrument.

True Value

Actual value of the quantity being measured.

Sample Weight

Adjustment factor to correct sample biases.

Chance Models

Models used to predict outcomes and risks.

Sampling Distribution

Distribution of sample statistics over many samples.

Sampling Error

Error due to observing a sample instead of whole population.

Proportions

Relative frequencies of specific events in population.

Null Hypothesis (H0)

Assumes no significant difference or effect exists.

Alternative Hypothesis (H1)

Suggests a significant difference or effect exists.

One-tailed Test

Tests for effect in one specific direction.

Two-tailed Test

Tests for effects in both directions.

Test Statistic

Quantifies difference between observed and expected data.

Significance Level (α)

Threshold for rejecting the null hypothesis.

P-value

Probability of observing data as extreme as test statistic.

Type I Error

Rejecting true null hypothesis (false positive).

Type II Error

Failing to reject false null hypothesis.

Degrees of Freedom (DF)

Sample size minus one for t-tests.

T-test

Tests means of two groups; assumes normal distribution.

Independent Samples

Samples from different populations, unpaired.

Dependent Samples

Samples from the same population, paired.

Chi-square Test

Tests association between two categorical variables.

Chi-square Distribution

Probability distribution for chi-square tests.

Goodness of Fit

Tests if observed data matches expected distribution.

Kolmogorov-Smirnov Test

Non-parametric test for distribution comparison.

Data Snooping

Exploring data multiple times for significant results.

Bonferroni Correction

Adjusts significance level for multiple comparisons.

Sample Size

Number of observations in a study.

Cumulative Distribution Function (CDF)

Probability that a random variable is less than or equal.

Expected Frequency

Frequency expected under the null hypothesis.

Observed Frequency

Actual frequency counted in the data.

Statistical Significance

Indicates likelihood that result is not due to chance.

Right-tailed Test

Tests if a parameter is greater than a value.

Left-tailed Test

Tests if a parameter is less than a value.

Asymptotic Distribution

Probability distribution as sample size approaches infinity.