Data Analysis for Marketing Decisions
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What does a Type I error indicate in hypothesis testing?

  • Incorrectly rejecting a true null hypothesis (correct)
  • Failing to detect an effect that exists
  • Correctly accepting a true null hypothesis
  • Correctly rejecting a false null hypothesis

    • Which statement accurately describes a Type II error?

  • It indicates a failure to reject a false null hypothesis (correct)
  • It is synonymous with the significance level alpha
  • It occurs when an effect is incorrectly identified
  • It occurs when a true null hypothesis is rejected

    • What does the significance level (α) represent in hypothesis testing?

  • The likelihood of retaining a false null hypothesis
  • The probability of making a Type II error
  • The risk of incorrect sample selection
  • The probability of making a Type I error (correct)

    • What is indicated by the term 'power of a test'?

    <p>The probability of detecting an effect when one actually exists</p> Signup and view all the answers

    When considering the potential for errors in hypothesis testing, what might the significance level α be compared to in a legal context?

    <p>The risk of releasing an innocent individual</p> Signup and view all the answers

    What does the alternative hypothesis (H1) represent in hypothesis testing?

    <p>Our predictions of how things are in reality.</p> Signup and view all the answers

    In the statement 'H1: Heavy metal fans have above average IQ', what does H0 signify?

    <p>Heavy metal fans do not have above average IQ.</p> Signup and view all the answers

    Which statement correctly describes the relationship between H1 and H0?

    <p>Rejecting H0 does not provide evidence for H1.</p> Signup and view all the answers

    What is the main purpose of null hypothesis significance testing (NHST)?

    <p>To assess the likelihood of obtaining sample results if H0 is true.</p> Signup and view all the answers

    Which of the following statements is true regarding the rejection of H0?

    <p>Rejecting H0 provides support for H1.</p> Signup and view all the answers

    In hypothesis testing, what does failing to reject H0 suggest?

    <p>There is no evidence against H0.</p> Signup and view all the answers

    How do hypotheses H1 and H0 collectively function in testing?

    <p>They define a complete framework for all potential outcomes.</p> Signup and view all the answers

    Which of the following correctly describes the concept of perceived quality among brands?

    <p>The perceived quality of local brands is less than that of global brands.</p> Signup and view all the answers

    If a hypothesis test results in a Type I error, what has occurred?

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

    What is the probability of correctly rejecting a false null hypothesis called?

    <p>Power of the test</p> Signup and view all the answers

    When the sample's Confidence Interval does not contain the value stated in H0, what is the decision regarding H1?

    <p>H1 is accepted.</p> Signup and view all the answers

    Which of the following represents a Type II error?

    <p>Failing to reject a false null hypothesis</p> Signup and view all the answers

    What is the interpretation of a 95% Confidence Interval that includes the H0 value?

    <p>There is insufficient evidence to reject H0.</p> Signup and view all the answers

    What does a p-value less than or equal to the alpha level indicate?

    <p>Statistical significance is achieved</p> Signup and view all the answers

    What must be true for H1 to be accepted in hypothesis testing?

    <p>The sample mean is greater than H0 value and CI does not contain H0 value.</p> Signup and view all the answers

    What are common values used for the significance level (α)?

    <p>0.001, 0.01, 0.05</p> Signup and view all the answers

    What happens when the p-value is greater than the alpha level?

    <p>There seems to be no effect</p> Signup and view all the answers

    What does a p-value indicate in hypothesis testing?

    <p>How frequently results occur under the null hypothesis</p> Signup and view all the answers

    What does a p-value indicate in relation to H0?

    <p>The probability of observing the sample data if H0 is true.</p> Signup and view all the answers

    What is the relationship between the test statistic and critical value when p < α?

    <p>The absolute value of the test statistic is greater than the absolute value of the critical value</p> Signup and view all the answers

    When is a null hypothesis typically rejected?

    <p>When the p-value is less than or equal to the significance level</p> Signup and view all the answers

    In the provided examples, which sample resulted in rejecting H1?

    <p>Sample C.</p> Signup and view all the answers

    In hypothesis testing, what do critical values help determine?

    <p>Whether to accept or reject the null hypothesis</p> Signup and view all the answers

    What condition leads to rejecting H0 according to the inferential rules?

    <p>When the Confidence Interval does not include the H0 value.</p> Signup and view all the answers

    Which statement about Type I and Type II errors is correct?

    <p>Type I error is more serious than Type II error in all cases</p> Signup and view all the answers

    Which of the following alpha levels indicates a stricter criterion for significance?

    <p>0.01</p> Signup and view all the answers

    What is primarily tested in hypothesis testing following the null hypothesis significance testing (NHST) approach?

    <p>The presence of a significant effect</p> Signup and view all the answers

    What is the consequence of a moderate overlap (≤ 50%) in confidence intervals?

    <p>It may lead to failing to reject H1 in some cases.</p> Signup and view all the answers

    What does it mean when a test is one-tailed?

    <p>It checks for effects only in one direction</p> Signup and view all the answers

    What does it imply when the p-value is less than α?

    <p>The null hypothesis can be rejected.</p> Signup and view all the answers

    What does the null hypothesis typically state in the context of hypothesis testing?

    <p>Observed results are due to random chance</p> Signup and view all the answers

    What does it indicate when a confidence interval includes the H0 value?

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

    Which of the following statements correctly differentiates statistical significance from substantive significance?

    <p>Substantive significance considers the context of the effect.</p> Signup and view all the answers

    What is meant by 'effect size'?

    <p>It assesses the magnitude of an observed effect.</p> Signup and view all the answers

    Which of the following measures is NOT commonly used to determine effect size?

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

    What would be a possible consequence of having a huge sample size in hypothesis testing?

    <p>Statistical significance for trivial effects.</p> Signup and view all the answers

    What ranges define a small effect according to Cohen's d?

    <p>r = 0.1, d = 0.2</p> Signup and view all the answers

    Why may hypothesis testing not provide information about the magnitude of an effect?

    <p>It only provides a p-value to assess significance.</p> Signup and view all the answers

    When evaluating the size of an effect, why is context important?

    <p>Because the same effect size can mean different things in different fields.</p> Signup and view all the answers

    Study Notes

    Data Analysis for Marketing Decisions

    • The session is about statistical inference, specifically Null Hypothesis Significance Testing (NHST).
    • A hypothesis is a testable statement about the world. It must be falsifiable.
    • Hypotheses can be translated into relationships between variables that can be measured.
    • An example of a hypothesis: "Being in a bad mood makes people spend more money."

    Types of Hypotheses

    • Directional hypotheses predict the direction of a relationship (e.g., positive or negative).
      • Example: "Global brands evoke higher perception of quality than local brands."
    • Non-directional hypotheses don't predict the direction of a relationship.
      • Example: "Global and local brands evoke different perceptions of quality."

    Types of Hypotheses (Pairs)

    • Every alternative hypothesis has a corresponding null hypothesis.
      • The null hypothesis usually states that no effect exists.
    • Examples:
      • Alternative: Heavy metal fans have above average IQ
      • Null: Heavy metal fans do not have above average IQ.

    NHST (Null Hypothesis Significance Testing)

    • NHST considers the probability of observing sample data, assuming the null hypothesis is true.
    • Rejecting the null hypothesis does not prove the alternative hypothesis, it merely maintains it.
    • Failing to reject the null hypothesis also does not prove the null hypothesis, it merely maintains it.

    Test Statistic

    • A numerical summary of dataset that models the expected effect (hypothesis).
    • Determined by the formula/equation of the statistical test.
      • Examples:
        • z-test
        • t-test
        • ANOVA
        • Chi-square test

    Type I and Type II Error

    • Type I error: Rejecting a true null hypothesis (false positive).
    • Type II error: Failing to reject a false null hypothesis (false negative).
    • The likelihood of making these errors is represented by alpha (α) and beta (β), respectively.

    Significance Level (Alpha)

    • The maximum risk of rejecting a true null hypothesis (Type I error).
    • Alpha is a predetermined value (e.g., 0.05 or 0.01); represents the acceptable likelihood of a Type 1 error).

    Test Statistic, Critical Value, and P-value

    • The probability of obtaining a test statistic (or a more extreme one) if the null hypothesis is true. This is the p-value.
    • Statistical significance is determined by comparing the p-value to the significance level (alpha).

    Regions of Rejection

    • For a 1-tailed test, the rejection region is in one tail of the distribution.
    • For a 2-tailed test, the rejection region is in both tails of the distribution.

    Practical Example (Spending in Restaurants)

    • Research question: Is average customer spending in restaurants higher than €18?
    • Method: Use a z-test to compare sample mean spending against the value €18.

    Statistical Significance and Power

    • Statistical significance is not synonymous with substantive significance.
    • A high sample size could lead to a statistically significant result even if the effect is small.
    • Statistical power is the probability of detecting an effect if it truly exists.

    Statistical Significance and Confidence Intervals (CIs)

    • Confidence intervals are used to estimate the range within which the population mean probably lies.
    • If a confidence interval includes the predicted value, then the result is not statistically significant.
    • If there is substantial overlap in confidence intervals from two sample groups then statistical significance may not be present.

    Inferential rules

      • If the test statistic is greater than the critical value then reject the null hypothesis.
    • If the test statistic is less than the critical value then accept the null hypothesis.
      • If the p-value is less than the significance level (alpha) then reject the null hypothesis.
      • If the p-value is greater than the significance level (alpha) then accept the null hypothesis.

    Effect Size

    • Helps determine the actual importance or magnitude of observed effects.
      • Measures effect size like Cohen's d can help assess this.
      • Example: Pearson's r or Cohen's d (measures size of effect)
    • The effect size should be placed within the research context to understand its true impact.

    Statistical power

    • Power is the ability of a test to detect an effect of a particular size if the effect truly exists.

    • Statistical power is (1 - β). A power of 80% (β=.20) is typically considered desirable.

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    Data Analysis for Marketing Decisions - Lecture Notes PDF

    Description

    Explore statistical inference and Null Hypothesis Significance Testing (NHST) in marketing data analysis. This quiz covers types of hypotheses including directional and non-directional, and gives practical examples. Test your understanding of relationships between variables crucial for making informed marketing decisions.

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