Introduction to Statistics
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Questions and Answers

Which measure of central tendency is used when there are extreme outliers in the data?

  • Range
  • Mode
  • Median (correct)
  • Mean

    • What does the standard deviation measure in a dataset?

  • The average of the values
  • The difference between the largest and smallest values
  • The variation about the mean (correct)
  • The most frequent value

    • In a normally distributed dataset, what can be said about the mean, median, and mode?

  • Mean = Median = Mode (correct)
  • Mean < Median < Mode
  • Median < Mean < Mode
  • Mode < Median < Mean

    • Which of the following is a step in hypothesis testing?

    <p>Setting up a hypothesis</p> Signup and view all the answers

    What does a negative skew in data indicate?

    <p>Median is greater than mean</p> Signup and view all the answers

    When examining data, what is the significance of the critical value?

    <p>It is the cutoff for deciding to reject H0</p> Signup and view all the answers

    What does the variance of a dataset measure?

    <p>The average of squared deviations from the mean</p> Signup and view all the answers

    Which statistical test would you use when comparing one mean and the standard deviation is unknown?

    <p>T-test</p> Signup and view all the answers

    What is a p-value in hypothesis testing?

    <p>The proportion of data sets yielding a result as extreme as observed, assuming H0 is true</p> Signup and view all the answers

    What happens to the confidence interval as the sample size increases?

    <p>The confidence interval becomes more precise</p> Signup and view all the answers

    What is the consequence of rejecting H0 when it is actually true?

    <p>Type 1 error</p> Signup and view all the answers

    Which assumption is NOT required for conducting a z-test?

    <p>Population standard deviation must be unknown</p> Signup and view all the answers

    How is the z-score calculated for a sample score?

    <p>Z = (sample score - mean) / population SD</p> Signup and view all the answers

    What does an effect size measure in statistics?

    <p>The magnitude of the treatment effect</p> Signup and view all the answers

    What does a smaller alpha level (a) indicate in hypothesis testing?

    <p>Higher probability of Type 2 error</p> Signup and view all the answers

    Which formula represents the calculation for z-statistics for a sample mean?

    <p>Z = (sample mean - hypothesized mean) / Standard error</p> Signup and view all the answers

    What is the main difference between descriptive and inferential statistics?

    <p>Descriptive statistics summarize sample properties, while inferential statistics infer population properties from sample data.</p> Signup and view all the answers

    Which statement accurately describes a dependent variable?

    <p>It is the outcome or response being measured.</p> Signup and view all the answers

    In which type of research design is the independent variable manipulated by the researcher?

    <p>Experimental research.</p> Signup and view all the answers

    What characterizes categorical variables?

    <p>They represent attributes that cannot be quantitatively assessed.</p> Signup and view all the answers

    What is a key feature of a within-subjects design?

    <p>Participants are measured multiple times under different conditions.</p> Signup and view all the answers

    Which of the following statements about continuous variables is true?

    <p>Ratio variables can represent measurements like weight or price.</p> Signup and view all the answers

    What is a primary characteristic of the mean as a measure of central tendency?

    <p>It is the most commonly used measure unless outliers are present.</p> Signup and view all the answers

    How does a confounding variable affect research conclusions?

    <p>It can create a false impression of a relationship between the independent and dependent variables.</p> Signup and view all the answers

    What does it mean if the Q value is greater than or equal to the critical value (Qcrit)?

    <p>Reject H0</p> Signup and view all the answers

    How should F statistics be reported in APA style?

    <p>F(2, 21) = 5.9, p = 0.01, w2 = 0.29</p> Signup and view all the answers

    What represents the minimum absolute difference necessary to consider two means significantly different?

    <p>HSD</p> Signup and view all the answers

    What does a significant result in the Kolmogorov-Smirnov test indicate?

    <p>The null hypothesis of normality is rejected</p> Signup and view all the answers

    What can be inferred if the median is less than the mean in a dataset?

    <p>The data is positively skewed</p> Signup and view all the answers

    What should be considered when determining whether to reject H0 based on assumptions?

    <p>The shape of the sampling distribution under H0</p> Signup and view all the answers

    In a study, what is typically reported to represent the pattern of mean differences among groups?

    <p>Means and standard deviations along with significant differences</p> Signup and view all the answers

    Which test is more powerful for assessing normality, especially for unspecified means and variances?

    <p>Shapiro-Wilk test</p> Signup and view all the answers

    What does the residual variance (MSr) represent in a one-way ANOVA?

    <p>Variance within groups due to random variation</p> Signup and view all the answers

    Under what condition do we reject the null hypothesis (H0) in an ANOVA test?

    <p>The F value is greater than or equal to the critical value</p> Signup and view all the answers

    What is the formula for calculating the F-statistic in ANOVA?

    <p>F = MSm / MSr</p> Signup and view all the answers

    What does the symbol dfM represent in ANOVA calculations?

    <p>Degrees of freedom for between groups</p> Signup and view all the answers

    Which statement is true regarding the F-distribution used in ANOVA?

    <p>It is a right-skewed distribution</p> Signup and view all the answers

    What does SSm in ANOVA stand for?

    <p>Sum of squares due to the model</p> Signup and view all the answers

    What does a significant post-hoc test indicate in the context of ANOVA?

    <p>At least one group mean is different from others</p> Signup and view all the answers

    In one-way ANOVA, what does the value of F = MSm / MSr indicate?

    <p>Group means differ from each other</p> Signup and view all the answers

    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.

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