Hypothesis Testing

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Questions and Answers

What is the primary goal of a researcher when analyzing a sample?

  • To eliminate all random variability
  • To prove a specific hypothesis
  • To compute the exact statistics for the sample
  • To generalize findings to a larger population (correct)

What term is used to describe the corresponding values of a population?

  • Means
  • Sample values
  • Parameters (correct)
  • Statistics

What does sampling error refer to?

  • A systematic issue in data collection
  • An error in the methodology used
  • The variation in statistics from one sample to another (correct)
  • The mistakes made during sample selection

What primarily causes Type II errors in research design?

<p>The sample size is too small. (B)</p> Signup and view all the answers

If a sample shows a statistical relationship, what can be concluded about the population?

<p>The relationship in the population is uncertain and may be due to sampling error (C)</p> Signup and view all the answers

How can the chance of a Type I error be reduced?

<p>By setting α to less than 0.05. (B)</p> Signup and view all the answers

What implication does the presence of random variability have on statistical conclusions?

<p>It introduces uncertainty in interpreting population parameters (A)</p> Signup and view all the answers

Why might the mean number of depressive symptoms differ across various samples?

<p>Because of random variability in sample statistics (D)</p> Signup and view all the answers

What is the implication of lowering αlpha to reduce Type I errors?

<p>Increases the chance of Type II errors. (D)</p> Signup and view all the answers

What is the relationship between sample statistics and population parameters?

<p>Sample statistics can be used to approximate population parameters (A)</p> Signup and view all the answers

Why do researchers consider replicating studies important?

<p>To check for Type I or Type II errors. (D)</p> Signup and view all the answers

What is the commonly accepted significance level among researchers to manage errors?

<p>0.05 (C)</p> Signup and view all the answers

What is the purpose of null hypothesis testing?

<p>To decide between two interpretations of a statistical relationship in a sample (A)</p> Signup and view all the answers

What does the null hypothesis (H0) represent?

<p>There is no relationship in the population (C)</p> Signup and view all the answers

What is the significance level often set to in null hypothesis testing?

<p>.05 (C)</p> Signup and view all the answers

What happens if the p value is lower than your alpha level?

<p>The null hypothesis is rejected (C)</p> Signup and view all the answers

What is a Type I error?

<p>Rejecting the null hypothesis when it is true (D)</p> Signup and view all the answers

When is a result considered statistically significant?

<p>When the p value is smaller than or equal to .05 (A)</p> Signup and view all the answers

What does a Type II error signify?

<p>Concluding there is no relationship when there is one (D)</p> Signup and view all the answers

What is the logical first step in null hypothesis testing?

<p>Assume the null hypothesis is true (B)</p> Signup and view all the answers

What questions did Mehl and his colleagues investigate regarding talkativeness? (refer to reading)

<p>Is there a sex difference in talkativeness? (A)</p> Signup and view all the answers

If a researcher states 'fail to reject the null hypothesis', what does it indicate?

<p>Insufficient evidence to reject the null hypothesis (B)</p> Signup and view all the answers

Flashcards

Sample Statistic

A numerical value calculated from a sample of data.

Population Parameter

A numerical value calculated using the entire population.

Sampling Error

Random variation in a statistic from sample to sample.

Statistical Relationship (Sample)

A relationship between variables that exists in a chosen sample.

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Statistical Relationship (Population)

A relationship between the same variables, considering the entire population.

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Inference

The process of drawing conclusions about a population based on sample data.

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Imperfect Estimate

Sample statistics aren't precise representations of population parameters, due to variability.

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Type II Error

Failing to reject a false null hypothesis. This means you miss a real effect or relationship that actually exists in the population.

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Statistical Power

The ability of a study to detect a real effect or relationship. Higher power means a lower chance of making a Type II error.

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Why is α = 0.05?

The conventional significance level (0.05) balances the chances of Type I and Type II errors. This means a 5% chance of rejecting a true null hypothesis, and a reasonable chance of detecting a real effect.

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Replication and Errors

Replicating studies helps to confirm the true nature of results. If multiple studies find the same effect, it strengthens confidence that the effect is real and not due to Type I or II errors.

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Interpreting Studies

Be cautious about interpreting single study results. The possibility of Type I or Type II error means results may not represent the true population reality.

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Null Hypothesis

The idea that there's no relationship between variables in the population, and any observed relationship in the sample is due to chance.

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Alternative Hypothesis

The idea that there is a relationship between variables in the population, and the observed relationship in the sample reflects this.

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P-value

The probability of getting a result as extreme as the observed sample result, assuming the null hypothesis is true.

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Alpha (α)

The threshold for rejecting the null hypothesis. Typically set to 0.05, meaning we reject the null if there's a 5% or less chance of observing the result due to chance.

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Statistical Significance

A result is statistically significant when the p-value is less than α, meaning the result is unlikely to have occurred by chance alone.

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Null Hypothesis Testing Logic

A process to decide between two interpretations of a statistical relationship: 'chance' or 'true relationship'. We assume the null is true, then see how likely the sample result is under this assumption. If it's unlikely, we reject the null.

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Study Notes

Null Hypothesis Testing

  • Researchers aim to draw conclusions about populations based on samples.
  • Sample statistics are estimates of population parameters.
  • Sampling error refers to random variability in a statistic from sample to sample.
  • Statistical relationships in a sample may or may not reflect population relationships.
  • The null hypothesis (H₀) posits no relationship in the population.
  • The alternative hypothesis (H₁) posits a relationship in the population.

Logic of Null Hypothesis Testing

  • Assume the null hypothesis is true.
  • Assess the likelihood of the sample relationship if H₀ were true.
  • Reject H₀ if the sample relationship is highly unlikely.
  • Retain H₀ if the sample relationship is not highly unlikely.
  • p-value represents the likelihood of the sample result under H₀.
  • A low p-value suggests the sample result is unlikely under H₀, leading to rejection.
  • α (alpha) is the criterion for rejecting H₀, usually set to 0.05.
  • A statistically significant result has a p-value ≤ α.

Type I and Type II Errors

  • Type I error: Rejecting H₀ when it's true. This means concluding there's a relationship when none exists.
    • Occurs due to sampling error.
    • Probability of Type I error is α.
  • Type II error: Retaining H₀ when it's false. This means concluding there's no relationship when one does exist.
    • Often due to low statistical power (insufficient sample size).
  • Researchers must balance the risk of both types of errors.
  • Lowering the risk of one type increases the risk of another.
  • α=0.05 is a common compromise.
  • Replication is crucial to increase confidence in results.

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