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Questions and Answers
Which measure of central tendency is used when there are extreme outliers in the data?
What does the standard deviation measure in a dataset?
In a normally distributed dataset, what can be said about the mean, median, and mode?
Which of the following is a step in hypothesis testing?
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What does a negative skew in data indicate?
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When examining data, what is the significance of the critical value?
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What does the variance of a dataset measure?
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Which statistical test would you use when comparing one mean and the standard deviation is unknown?
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What is a p-value in hypothesis testing?
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What happens to the confidence interval as the sample size increases?
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What is the consequence of rejecting H0 when it is actually true?
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Which assumption is NOT required for conducting a z-test?
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How is the z-score calculated for a sample score?
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What does an effect size measure in statistics?
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What does a smaller alpha level (a) indicate in hypothesis testing?
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Which formula represents the calculation for z-statistics for a sample mean?
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What is the main difference between descriptive and inferential statistics?
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Which statement accurately describes a dependent variable?
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In which type of research design is the independent variable manipulated by the researcher?
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What characterizes categorical variables?
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What is a key feature of a within-subjects design?
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Which of the following statements about continuous variables is true?
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What is a primary characteristic of the mean as a measure of central tendency?
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How does a confounding variable affect research conclusions?
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What does it mean if the Q value is greater than or equal to the critical value (Qcrit)?
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How should F statistics be reported in APA style?
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What represents the minimum absolute difference necessary to consider two means significantly different?
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What does a significant result in the Kolmogorov-Smirnov test indicate?
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What can be inferred if the median is less than the mean in a dataset?
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What should be considered when determining whether to reject H0 based on assumptions?
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In a study, what is typically reported to represent the pattern of mean differences among groups?
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Which test is more powerful for assessing normality, especially for unspecified means and variances?
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What does the residual variance (MSr) represent in a one-way ANOVA?
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Under what condition do we reject the null hypothesis (H0) in an ANOVA test?
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What is the formula for calculating the F-statistic in ANOVA?
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What does the symbol dfM represent in ANOVA calculations?
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Which statement is true regarding the F-distribution used in ANOVA?
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What does SSm in ANOVA stand for?
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What does a significant post-hoc test indicate in the context of ANOVA?
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In one-way ANOVA, what does the value of F = MSm / MSr indicate?
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Study Notes
What are statistics?
- Statistics are used to describe data and draw conclusions about the population.
- Population: All entities or individuals of interest.
- Parameter: A value that describes the population.
- Sample: A subset of individuals from the population.
- Estimate: A value that describes the sample.
Types of Statistics
- Descriptive Statistics: Summarize and describe sample or population properties.
- Inferential Statistics: Draw conclusions about population properties based on sample data.
Variables
- Variable: A characteristic that varies across observations.
- Independent Variable: Predicts outcome/response; manipulated by researcher (Experimental) or measured by researcher (Correlational).
- Dependent Variable: Outcome/response; predicted.
Types of Research
- Correlational Research: Measures independent variable; good for ecological validity; bad for inferring causality.
- Experimental Research: Manipulates independent variable; good for inferring causality; lab settings may feel detached from the real world.
- Between-Subjects Design: Each participant is only in one experimental condition.
- Within-Subjects Design: Each participant is in more than one experimental condition; DV is measured multiple times.
Categorical Variables
- Nominal: Classifies objects; not quantitative.
- Ordinal: Rank data based on attribute.
Continuous Variables
- Interval: Rating data in equal distances; assigned numbers have meaningful units with constant sizes.
- Ratio: Interval with an absolute zero point (lack of the attribute).
Measures of Central Tendency
- Mean: Average of all values.
- Median: Middle value.
- Mode: Value occurring most frequently.
Measures of Variation
- Range: Difference between largest and smallest observation.
- Variance: Average of squared deviations of values from the mean.
- Standard Deviation: Shows variation about the mean; same units as original data.
Shape of Distribution
- Left Skew: Mean < Median.
- Symmetric: Mean = Median.
- Right Skew: Median < Mean.
Normal Distribution
- Mean = Median = Mode.
- Density: Height of curve at different values of X.
- Mean + SD contains 68% of values.
- Mean + 2*SD contains 95% of values.
- Mean + 3*SD contains 99.7% of values.
Hypothesis Testing
- Theories: Systems of ideas used to describe a phenomenon.
- Hypothesis: Empirically testable statement derived from a theory.
- Null Hypothesis (H0): No effect.
- Alternative Hypothesis (H1): Research hypothesis.
- Non-Directional H1: Some effect.
- Directional H1: Specifies the effect's direction.
- Alpha Level (a): The proportion of times we are willing to accidentally reject H0, even if it's true.
Steps of Hypothesis Testing
- Setting up an hypothesis.
- Choosing an alpha level (a).
- Examining data and computing the appropriate test statistic:
- Chi-Square for frequency distributions comparisons.
- Z for comparing one mean if SD is known.
- T for comparing one mean if SD is unknown or comparing two means.
- F for comparing more than two means or ANOVA.
- Making a decision whether to reject or accept H0:
- Compare calculated value of test statistic to critical value.
- If calculated value is greater or equal to critical value, reject H0.
- Alternatively, look at p-value for test statistic value.
- If p < a, reject H0.
Confidence Interval
- Gives us information about the precision of our estimate.
- Usually formed as [(1 - a) * 100%] CI.
- As sample size increases, the estimate gets more precise.
- As a decreases, CI intervals become larger/wider.
Effect Sizes
- Standardized measure of treatment effect's magnitude.
- Effect sizes measures include:
- Pearson's r or correlation ratio squared.
- Cohen's d.
- Omega or omega squared.
- Eta squared.
Errors of Hypothesis Testing
- Type 1 Error: Reject H0 when it's true.
- Type 2 Error: Accept H0 when it's false.
- Power: Reject H0 when it's false (1 - B).
- Trade-off: Higher a results in lower B (+ power).
Z-Test
- Based on sample mean, we test if the population mean is equal to a hypothesized value.
- Assumptions needed for z-test:
- Variable X in the population is normally distributed.
- Population standard deviation must be known.
- Sample must be independent.
ANOVA
- ANOVA (ANalysis Of VAriance) has three steps:
- Divides variance observed in data into different parts resulting from different sources.
- Assesses the relative magnitude of the different parts of variance.
- Examines if a particular part of the variance is greater than expectation under H0.
- Variance explained by the model (MSm): Variance between groups due to the IV or its different levels/treatments.
- Residual variance (MSr): Variance within groups.
Calculating F Value
- F = MSm / MSr.
- If the F statistic is greater than the critical F value, we reject H0 that group means are equal in the population.
- The F-distribution is a right-skewed distribution used in ANOVA.
Assumptions of ANOVA
- H0 and assumptions determine the shape of the sampling distribution.
- Assessing normality:
- Kolmogorov-Smirnov test.
- Shapiro-Wilk test.
APA Style Guidelines
- 1-2 sentence overview of analyses, including IV and DV.
- Description of the F test overall results.
- Description of the pattern of means differences among groups.
- A conceptual conclusion.
- Everything written in the active past tense.
- Concise, no extra stuff necessary.
Assumptions of ANOVA
- The H0 and assumptions determine the shape of the sampling distribution.
- Assumptions about normality/equal variances are about the population.
- If assumptions don’t hold, we may not know the shape of the sampling distribution, leading to incorrect p-value/critical F value and low power or type 1 error rates.
Assessing Normality
- Kolmogorov-Smirnov test: Compares sample scores to a set of scores generated from a normal distribution with sample mean and SD. Less powerful than the Shapiro-Wilk test.
- Shapiro-Wilk test: Looks at normality in general, unspecified mean and variance; more powerful but only for normal distributions.
- If the test is significant, reject H0 that the distribution of the variable is normal.
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Description
This quiz covers the basics of statistics, including definitions and types. It explores key concepts such as population, samples, descriptive versus inferential statistics, and types of variables used in research. Perfect for beginners looking to understand statistical foundations.
