Research Methodology - Hypothesis Testing
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Questions and Answers

Which statistical tests rely on assumptions about the population distribution?

  • Permutation tests
  • Non-parametric tests
  • Bootstrap tests
  • Parametric tests (correct)

What is a key characteristic of non-parametric tests?

  • They are always more powerful than parametric tests
  • They can only test for means
  • They do not assume a specific distribution (correct)
  • They require a large sample size

Which factor is not considered when selecting a probability distribution for hypothesis testing?

  • The population size (correct)
  • The purpose of the test
  • The type of test (one or two-tailed)
  • The level of significance

What is the purpose of comparing the test statistic to the critical value?

<p>To accept or reject the null hypothesis (C)</p> Signup and view all the answers

Which of the following is a primary source of hypotheses according to the provided information?

<p>Cultural traditions (D)</p> Signup and view all the answers

Which type of hypothesis test assumes that the data comes from a normally distributed population?

<p>Parametric tests (B)</p> Signup and view all the answers

What is a primary characteristic of a non-parametric test?

<p>Used when sample sizes are small and non-normal (C)</p> Signup and view all the answers

Which of the following is NOT considered a parametric test?

<p>Mann-Whitney test (B)</p> Signup and view all the answers

Which test is specifically used to compare two independent samples?

<p>Two-group T-test (D)</p> Signup and view all the answers

What condition must be met to use a Z-test effectively?

<p>Population variance is known (B)</p> Signup and view all the answers

Which non-parametric test is used for comparing paired samples?

<p>Wilcoxon signed-rank test (C)</p> Signup and view all the answers

What is the main difference between parametric and non-parametric tests?

<p>Non-parametric tests do not assume a specific population distribution (C)</p> Signup and view all the answers

Which of the following tests is appropriate for analyzing differences across multiple independent samples?

<p>ANOVA (A)</p> Signup and view all the answers

When should a t-distribution be used instead of a normal distribution in hypothesis testing?

<p>When the sample size is small and population variance is unknown (B)</p> Signup and view all the answers

What is the consequence of rejecting the null hypothesis when it is actually true?

<p>Type I error (D)</p> Signup and view all the answers

Which step is NOT part of the hypothesis testing process described?

<p>Collecting qualitative data (A)</p> Signup and view all the answers

In a two-tailed hypothesis test, the value for α when comparing calculated probability must be:

<p>Half of α (D)</p> Signup and view all the answers

What does it mean if the calculated probability is greater than the level of significance (α)?

<p>Accept the null hypothesis (C)</p> Signup and view all the answers

What risk is associated with accepting the null hypothesis?

<p>Committing a Type II error (D)</p> Signup and view all the answers

Which is a correct sequence of steps in hypothesis testing?

<p>Set significance level, decide distribution, random sampling, calculate probability (C)</p> Signup and view all the answers

Why is random sampling important in hypothesis testing?

<p>It ensures the sample reflects the population (C)</p> Signup and view all the answers

What statement accurately describes the significance level (α)?

<p>It is a threshold to determine Type I error probability (D)</p> Signup and view all the answers

What is the overall goal of hypothesis testing?

<p>To determine if there is enough evidence to reject the null hypothesis (A)</p> Signup and view all the answers

Which test is appropriate for judging the significance of means in small samples when the population variance is unknown?

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

What does the chi-square test primarily compare?

<p>Sample variance to a theoretical population variance (D)</p> Signup and view all the answers

In what scenario is the paired T-test used?

<p>When judging the mean of differences between two related samples (C)</p> Signup and view all the answers

Which test would you use to assess the significance of the correlation coefficient?

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

What is the primary distribution associated with the F-test?

<p>Chi-square distribution (B)</p> Signup and view all the answers

When should the Z-test be used over the T-test?

<p>When the sample size is large and population variance is known (A)</p> Signup and view all the answers

Which test can be used for analysis of variance (ANOVA)?

<p>F-test (D)</p> Signup and view all the answers

Which of the following is a characteristic of parametric tests?

<p>They require certain assumptions about the population parameters (C)</p> Signup and view all the answers

Which statistical method primarily focuses on comparing the variance of two independent samples?

<p>F-test (C)</p> Signup and view all the answers

When is a Z-test typically used?

<p>When testing the significance of proportions in large samples (A)</p> Signup and view all the answers

Which non-parametric test is specifically designed for analyzing matched pairs?

<p>Wilcoxon matched pairs test (C)</p> Signup and view all the answers

Which of the following tests can be utilized to compare two independent samples?

<p>Wilcoxon Mann-Whitney test (B)</p> Signup and view all the answers

Which of the following statements about the Kruskal-Wallis H-test is true?

<p>It is an analysis of variance for non-parametric data. (A)</p> Signup and view all the answers

Which method is primarily used to determine the degree of association among multiple sets of ranked data?

<p>Kendall's coefficient of concordance (A)</p> Signup and view all the answers

What is a critical requirement for conducting a sign test?

<p>The data must contain ordinal or nominal scales. (B)</p> Signup and view all the answers

In which scenario would the McNemar test be most appropriately applied?

<p>Evaluating the change in opinions in two related samples. (D)</p> Signup and view all the answers

Which non-parametric test would be the most appropriate for assessing the correlation between variables?

<p>Rank correlation method (D)</p> Signup and view all the answers

What distinguishes the Wilcoxon Mann-Whitney test from the Sign test?

<p>The Wilcoxon test considers both direction and magnitude of differences. (C)</p> Signup and view all the answers

Which of the following is NOT a characteristic of non-parametric tests?

<p>They are always less powerful than parametric tests. (D)</p> Signup and view all the answers

Flashcards

Parametric Test

A statistical test that assumes specific characteristics (like normality) of the population being studied.

Non-Parametric Test

A statistical test that doesn't require assumptions about the population distribution.

Z-test

A parametric test used to assess the significance of a mean, often for large samples or known population variances.

T-test

A parametric test used for comparing means of two groups or a sample mean to a hypothesized population mean.

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Chi-Square Test

A statistical test used for analyzing categorical data, often to assess independence of variables.

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One-sample Z-test

A hypothesis test comparing a sample mean to a population mean (when population variance is known).

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Two-sample t-test

A test comparing the means of two independent groups.

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Paired t-test

Compares means of two related groups or measurements (e.g., before and after).

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Hypothesis Testing

A statistical method for testing a claim about a population using sample data.

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Null Hypothesis (H0)

A statement about the population that we want to disprove. It usually represents the 'no effect' or 'no difference' scenario.

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Alternative Hypothesis (Ha)

The statement we try to find evidence for. It contradicts the null hypothesis and usually represents the desired outcome.

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Significance Level (α)

The probability of rejecting a true null hypothesis. Often set at 0.05 (5%), controlling the risk of making a wrong decision.

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Sampling Distribution

The distribution of sample statistics (like means) that we would expect to see if the null hypothesis were true.

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Type I Error

Rejecting a true null hypothesis. We conclude there's an effect when there's actually none.

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Type II Error

Failing to reject a false null hypothesis. We fail to detect an effect that is actually present.

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One-Tailed Test

A test focused on checking whether the sample result is significantly higher or lower than the null hypothesis value.

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Two-Tailed Test

A test checking for significant differences in both directions (higher or lower) from the null hypothesis value.

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P-value (Probability Value)

The probability of obtaining a result as extreme as the observed data if the null hypothesis were true. A small p-value suggests evidence against the null hypothesis.

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What is Z-test used for?

Z-test is employed to assess the significance of the difference between means of two independent samples when the sample size is large, or when the population variance is known. It's also used to compare a sample proportion against a theoretical population proportion, or to analyze the difference in proportions of two independent samples with large sample sizes.

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What is the difference between Z-test and T-test?

While Z-test is used for large samples or known population variance, T-test is used for small samples with unknown population variance. It analyzes the significance of a sample mean or the difference between means of two small samples.

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What is a paired T-test?

A paired T-test is specifically used for analyzing the mean difference between two related samples. It's essentially comparing two measurements taken from the same subject or group, like before and after a treatment.

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What are the applications of T-test?

T-test can be used to analyze the significance of a sample mean, evaluate the difference between means of two samples (either independent or related), and assess the significance of the coefficient of simple and partial correlations.

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What is Chi-square test used for?

Chi-square test is a parametric test designed to compare a sample variance with a theoretical population variance. It's used for analyzing categorical data.

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What is F-test used for?

F-test compares the variances of two independent samples. It's also employed in analysis of variance (ANOVA) for judging the significance of more than two sample means simultaneously and for analyzing the significance of multiple correlation coefficients.

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What is the key difference between F-test and Chi-square test?

Both tests are parametric, but F-test compares the variances of two independent samples, while Chi-square test compares a sample variance to the theoretical population variance.

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What is the relationship between the F-test & ANOVA?

F-test is a core part of ANOVA. In ANOVA, F-test is used to analyze the significance of more than two sample means simultaneously, determining if there's a significant difference between the groups beyond random chance.

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When is the F-test used in relation to correlation coefficients?

F-test is employed to determine the significance of multiple correlation coefficients. It assesses whether the observed correlations are strong enough to be considered statistically significant, or likely due to chance.

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What are the common characteristics of statistical tests?

Many statistical tests involve calculating a test statistic, comparing it to a critical value, and determining whether to accept or reject the null hypothesis. This process helps to determine if there's enough evidence to support a claim about the population based on the sample data.

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Null Hypothesis

A statement about a population parameter that we assume to be true until proven otherwise. It's often a statement of 'no difference' or 'no effect'.

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Alternative Hypothesis

A statement that contradicts the null hypothesis, proposing a specific effect or difference. It's the hypothesis we aim to support.

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Critical Value

A threshold value that determines whether we reject or accept the null hypothesis. It's calculated based on significance level, degrees of freedom, and the type of test.

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Test Statistic

A value calculated from sample data that summarizes the evidence for or against the null hypothesis.

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What does a hypothesis test help us decide?

A hypothesis test helps us make a decision about whether our sample data provides enough evidence to reject or accept the null hypothesis. This allows us to draw conclusions about the population based on the sample.

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Sign Test

A non-parametric test used to compare a sample mean to a hypothesized population mean by analyzing the direction of differences.

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Wilcoxon Matched Pairs Test

A non-parametric test comparing paired data (e.g., before/after measurements). It considers both direction and magnitude of differences.

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Wilcoxon Mann-Whitney (U) Test

A non-parametric test comparing the distributions of two independent groups.

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Kruskal-Wallis H-Test

A non-parametric analysis of variance used to compare more than two independent groups.

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Rank Correlation

A non-parametric measure that describes the relationship between two variables, without assumptions about their distributions.

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Kendall’s Coefficient of Concordance

A non-parametric statistic used to measure the agreement between multiple sets of ranked data.

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McNemar Test

A non-parametric test used to analyze changes in paired categorical data, often related to before-and-after scenarios.

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One-Sample Run Test

A non-parametric test used to assess the randomness of data. It checks if a sequence of observations is random or exhibits a pattern.

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Advantages of Non-Parametric Tests

These tests are robust to violations of assumptions, applicable to various data scales, and easier to calculate (sometimes).

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Study Notes

Research Methodology - Hypothesis Testing

  • Hypothesis is a key instrument in research, suggesting experiments and observations. Many experiments are deliberately designed to test hypotheses.
  • Decision-makers often use hypothesis testing based on available data, before making a decision in social sciences.
  • Hypothesis testing is a strategy for deciding if sample data supports generalization about population parameters.
  • A hypothesis may not be definitively proven but is accepted if it withstands critical testing.

What is a Hypothesis?

  • A hypothesis is a tentative assumption or supposition that's tested or disproved.
  • It's a formal question to be resolved, explaining the occurrence of phenomenon, or an explanation supported by existing evidence.
  • A research hypothesis is a predictive statement about an independent variable and a dependent variable.

Types of Hypotheses

  • Null Hypothesis (H₀): Represents the assumption that no significant difference or relationship exists between factors.
    • Often used as a starting point, assuming no effect is present.
  • Alternative Hypothesis (Hₐ): Represents the assumption that a significant difference or relationship does exist between factors.
  • In a comparison (e.g., method A vs method B), the null hypothesis suggests both are equally effective.
  • The alternative hypothesis posits that one method is more effective than another.
    • Symbolically, H₀: μ = μ₀, and Hₐ: μ ≠ μ₀, with μ being a population mean.

Alternative Hypothesis Interpretations

  • Hₐ: μ ≠ μ₀: The population mean is not equal to the hypothesized mean.
  • Hₐ: μ > μ₀: The population mean is greater than the hypothesized mean.
  • Hₐ: μ < μ₀: The population mean is less than the hypothesized mean.

Considerations for Choosing a Null Hypothesis

  • Risk avoidance: If rejecting a true null hypothesis carries high risk, it should be the null hypothesis.
  • Specific statements: The null hypothesis should make specific statements about a value, not general or close approximations.

Significance Level

  • The significance level (often 5%, or 1%) is the risk a researcher is willing to take of incorrectly rejecting a null hypothesis when it's true.
  • It's the percentile for making decisions in hypothesis testing.

Decision Rules and Hypothesis Tests

  • A decision rule, crucial for hypothesis testing, dictates when to accept or reject a null hypothesis.
  • Example: Given a lot of items, to accept Ho it must contain low number of defective items.

Type 1 and Type 2 Errors

  • Type 1 error: Rejecting a true null hypothesis.
  • Type 2 error: Accepting a false null hypothesis.
  • Type 1 error (α) known as significance level.
  • Type 2 error (β) is less specific and hard to determine.

Probability of Errors

  • Probability of type 1 error is typically set in advance.
  • It's a trade-off: reducing one error typically increases the other.

Hypothesis Testing Steps

  • Formulating hypotheses: Define the null and alternative hypotheses.
  • Choosing the significance level: Set the acceptable risk of error.
  • Selecting a distribution: Choose the appropriate probability distribution.
  • Sampling randomly: Collect a sample and calculate necessary statistics.
  • Calculating probability: Compute the probability of obtaining the sample results if the null hypothesis is true.
  • Comparing probabilities: Compare the calculated probability to the significance level.
  • Final decision: Reject or accept the null hypothesis.
  • Test of Hypothesis Classification: Parametric versus Non-Parametric testing.

Sources of Hypothesis

  • Culture: Traditions and contexts.
  • Scientific theories: Existing theory, usually affects culture.
  • Analogies: Other fields or ideas, providing possible theories.

Parametric Tests

  • Based on assumptions about the distribution of the population.
    • These tests require a normal distribution.
  • Common examples include Z-test, T-test, Chi-square test, and F-test.

Non-Parametric Tests

  • Often used when assumptions of normality cannot be made.
  • Common examples include sign test, Wilcoxon matched-pairs test, Wilcoxon-Mann-Whitney test, Kruskal-Wallis test, rank correlation, Kendall's coefficient of concordance, McNemar test.

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Hypothesis Testing PDF

Description

Explore the critical concepts of hypothesis testing in research methodology. This quiz covers definitions, types of hypotheses, and their applications in decision-making processes. Improve your understanding of how hypotheses influence research outcomes.

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