Basic Statistics - Hypothesis Testing

A set of 40 flashcards covering key concepts from the lecture on hypothesis testing and statistics.

Inferential Statistics

Statistical methods that draw conclusions about a population based on sample data.

Sampling Error

The error that occurs when a sample statistic differs from the population parameter it is supposed to represent.

Parametric Statistics

Statistical procedures that assume a certain distribution for the population, typically a normal distribution.

Nonparametric Procedures

Statistical methods that do not assume a specific distribution for the population.

Robust Procedures

Parametric procedures that remain relatively valid even when precise assumptions are violated.

Hypothesis

A testable prediction about the relationship between two or more variables.

Null Hypothesis (H0)

The hypothesis that there is no effect or no difference; assumes the default state.

Alternative Hypothesis (Ha)

The hypothesis that there is an effect or a difference; contradicts the null hypothesis.

One-Tailed Test

A hypothesis test that determines if a sample mean is either greater than or less than a known population mean.

Two-Tailed Test

A hypothesis test that determines if a sample mean is significantly different from a known population mean in either direction.

Alpha (α)

The probability threshold set for rejecting the null hypothesis, commonly set at 0.05.

Critical Value (z-crit)

The threshold in a statistical test that defines the boundaries for rejecting the null hypothesis.

Type I Error

The error of rejecting a true null hypothesis; also known as a false positive.

Type II Error

The error of failing to reject a false null hypothesis; also known as a false negative.

Significant Results

Results that are unlikely to have occurred under the null hypothesis, indicating a statistical effect.

Sampling Distribution

The probability distribution of a statistic obtained by selecting random samples from a population.

Z-Score

A measurement of how many standard deviations a data point is from the mean of a group.

Standard Error

An estimate of the variability of a sample statistic from the population parameter.

Rejecting H0

The conclusion drawn when the test statistic is beyond the critical value, suggesting a significant effect.

Falsely Rejecting H0

Incorrectly concluding that a relationship exists when it does not, usually due to sampling error.

Failing to Reject H0

The conclusion drawn when the test statistic does not exceed the critical value, suggesting no significant effect.

Power of a Test

The probability that a test will correctly reject a false null hypothesis.

One-Sample Experiment

An experimental design where one group is tested against known population parameters.

Smart Pill Experiment

An illustrative example involving testing the effects of a hypothetical smart pill on IQ.

Critical Value Region

The area in a distribution where, if a test statistic falls, the null hypothesis is rejected.

Two-Tailed Hypothesis Testing

Testing where the direction of the relationship is not specified.

Probability of Type I Error

The theoretical likelihood of committing a Type I error, represented by alpha (α).

Probability of Type II Error

The theoretical likelihood of committing a Type II error, represented by beta (β).

Constructing a Hypothesis

The process of defining H0 and Ha in a clear, testable manner.

Sample Mean (x̄)

The average value from a sample used to estimate the population mean.

Null Hypothesis Example

H0: μ = 100; indicates no effect from the treatment.

Alternative Hypothesis Example

Ha: μ ≠ 100; indicates an effect from the treatment.

Two-Tailed Example

Testing whether a new treatment has any effect, without predicting the direction.

One-Tailed Direction Increase

Hypothesis indicating the independent variable causes an increase in dependent variable scores.

One-Tailed Direction Decrease

Hypothesis indicating the independent variable causes a decrease in dependent variable scores.

Significant vs. Non-Significant

Significant means results are unlikely due to chance; non-significant suggests results may simply be due to chance.

z-Test

A statistical test used to determine if the means of a sample and population are significantly different.

Constructing a z-Test

Calculating z-scores to analyze sample means in relation to population means.

Research Design Importance

The framework for how an experiment will be conducted, influencing the reliability of results.

Experimental Hypotheses Definitions

The prediction stating whether a relationship will be found or not.

Data Interpretation

The process of making sense of statistical results and deciding implications.

Balancing Errors in Research

The challenge of minimizing false positives (Type I) while not overlooking significant relationships (Type II).