Inferential Statistics: Chi-Square Test
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Questions and Answers

What is the primary purpose of inferential statistics?

  • To calculate basic measurements like mean and median
  • To describe a phenomena using visual data
  • To prove or disprove theories using sample data (correct)
  • To summarize data through graph or table

Which statement correctly differentiates between null and alternative hypothesis?

  • The null hypothesis is used for descriptive analysis, while the alternative is used during significance testing.
  • The null hypothesis claims there is a significant effect, while the alternative claims no effect.
  • The null hypothesis typically posits that any observed effect is due to chance, while the alternative proposes a real effect. (correct)
  • The alternative hypothesis is always proven true if the null is rejected.

What does a chi-square test fundamentally evaluate?

  • The correlation between two continuous variables
  • The prediction accuracy of a regression model
  • The average of a numerical dataset
  • The association between categorical variables (correct)

Which of the following best describes the concept of 'level of significance' in hypothesis testing?

<p>The probability of rejecting a true null hypothesis (D)</p> Signup and view all the answers

Which type of analysis is described as summarizing data through frequencies and percentages?

<p>Descriptive Statistics (D)</p> Signup and view all the answers

In hypothesis testing, the alternative hypothesis is accepted when:

<p>The chi-square test returns a p-value less than the level of significance. (D)</p> Signup and view all the answers

Which of the following is NOT a characteristic of inferential statistics?

<p>It involves calculating frequencies and basic measurements. (A)</p> Signup and view all the answers

In a chi-square test, a significant result typically indicates:

<p>The observed frequencies are significantly different from the expected frequencies. (B)</p> Signup and view all the answers

What type of data is necessary for the use of parametric tests?

<p>Continuous data (D)</p> Signup and view all the answers

What is the purpose of hypothesis testing in inferential statistics?

<p>To draw conclusions about a population based on sample data (B)</p> Signup and view all the answers

Which statistical test would be used to analyze the relationship between two categorical variables?

<p>Chi-square test for independence (C)</p> Signup and view all the answers

Which condition must be met for a Chi-Square Test to be valid?

<p>Each cell must contain a count of 5 or more (B)</p> Signup and view all the answers

Which hypothesis states that there is no association between variables?

<p>Null hypothesis (H0) (B)</p> Signup and view all the answers

What does a p-value of less than or equal to 0.05 indicate in hypothesis testing?

<p>Reject the null hypothesis (B)</p> Signup and view all the answers

How are expected frequencies calculated in a Chi-Square Test?

<p>Using the formula e = (row marginal)(column marginal)/total cases (B)</p> Signup and view all the answers

What does the term 'significance level' refer to in hypothesis testing?

<p>The minimum probability for a type I error (A)</p> Signup and view all the answers

What type of variables does the Chi-square test for independence examine?

<p>Categorical variables (B)</p> Signup and view all the answers

What is the formula to determine the degrees of freedom for a Chi-Square Test?

<p>df = (r – 1)(c – 1) (D)</p> Signup and view all the answers

Which of the following is an example of a parametric test?

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

In the null hypothesis (H0) of a Chi-Square Test, what does it state regarding the variables?

<p>The variables are independent of each other (C)</p> Signup and view all the answers

Which of the following is a limitation of the Chi-Square Test?

<p>It gives no information about the strength of the relationship (B)</p> Signup and view all the answers

What does a test result of Χ2(2) >= 3.171, p = 0.205 indicate in terms of association?

<p>No association was found (A)</p> Signup and view all the answers

When can the Chi-Square Test reject the null hypothesis?

<p>If the test statistic is greater than the critical value (C)</p> Signup and view all the answers

Flashcards

Inferential Statistics

Methods used to make inferences and draw conclusions about a population based on a sample.

Descriptive Statistics

Methods used to summarize and describe data.

Hypothesis Testing

A process to determine if there's enough evidence to support a claim or theory.

"Chi-square" Test

A statistical test used to determine if there's a significant association between categorical variables.

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Null Hypothesis

A statement of no effect or no relationship between variables, usually what's being tested against.

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Alternative Hypothesis

A statement of an effect or relationship between variables.

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Level of Significance

The probability of rejecting the null hypothesis when it's actually true.

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Categorical Data

Data that represents categories or groups (e.g., 'yes'/'no', 'male'/'female').

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Parametric Tests

Statistical tests used for continuous data that is normally distributed, such as height, weight, or test scores.

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Nonparametric Tests

Statistical tests used for categorical or ordinal data, or for continuous data that doesn't follow a normal distribution.

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T-tests

Parametric test used to compare the means of two groups.

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ANOVA

Parametric test used to compare the means of more than two groups.

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Correlation

Parametric test used to measure the strength and direction of the relationship between two continuous variables.

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Contingency Table

A table that displays the frequency counts of observations for two categorical variables.

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Random Selection

A sampling method where every individual in the population has an equal chance of being selected for the sample.

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Chi-Square Test Requirement: Categorical Data

The Chi-Square test requires data to be in categories, such as 'yes' or 'no', 'male' or 'female'.

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Chi-Square Test Requirement: Independent Observations

Each observation in the data must be independent, meaning the outcome of one observation doesn't influence others.

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Chi-Square Test Requirement: Sample Size

The Chi-Square test needs a minimum of 30 observations (people) in the table.

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Chi-Square Test Requirement: Random Sampling

The data should be collected using a random sampling method, ensuring a representative sample.

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Chi-Square Test Requirement: Minimum Cell Counts

Each cell in the table must have a count of at least 5 observations.

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Null Hypothesis (H0) for Chi-Square

States that there's no association or no relationship between the variables being tested.

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Alternative Hypothesis (H1) for Chi-Square

States that there is a relationship or association between the variables being tested.

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P-value for Chi-Square

A measure of probability that the observed result is due to chance, not a real relationship.

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Study Notes

Inferential Statistics (Chi-Square Test)

  • Inferential statistics are used to draw conclusions about a population by examining a sample
  • The accuracy of inferences depends on the representativeness of the sample from the population
  • Researchers set a significance level for statistical tests to assess the likelihood that a difference is real or due to chance

Objectives

  • Differentiate between descriptive and inferential statistics
  • Identify types of inferential statistical tests
  • Define null and alternative hypotheses
  • Describe "hypothesis testing"
  • Define chi-square
  • Explain the uses and applications of the chi-square test
  • Outline the principles of chi-square
  • Interpret the significance of a chi-square test (χ2 test)

Hypothesis Testing

  • Null Hypothesis (H0): There is no association between the exposure and the disease of interest
  • Alternative Hypothesis (H1): There is an association between the exposure and the disease of interest

Chi-Square Test of Independence

  • A technique to determine if there is a relationship between two categorical variables
  • Data is organized in a contingency table/cross tabulation
  • Counts (frequency data) of observations in each category are used
  • Example uses: smoking and lung cancer, obesity and diabetes

Chi-Square Requirements

  • One or more categories
  • Independent observations
  • Sample size of at least 30 observations in the table
  • Each cell must contain a count of 5 or more
  • Random sampling

Calculating Degrees of Freedom (df)

  • df = (r-1)(c-1)
    • where
      • r = number of rows
      • c = number of columns

P-value

  • A measure of the probability that a result is due to chance
  • If the p-value is less than or equal to 0.05, it suggests that the null hypothesis should be rejected, and the alternative hypothesis is accepted or supported

Calculating Expected Frequencies

  • Multiply row totals by column totals for each cell, then divide the result by the total number of cases in the table. This provides the expected frequency.

Limitations of the Chi-Square Test

  • Doesn't measure the strength of the relationship or its substantive significance in the population.
  • Sensitive to sample size; larger samples give larger chi-square values
  • Sensitive to small expected frequencies in cells of the table.

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Inferential Statistics (Chi-Square Test) PDF

Description

Test your knowledge on inferential statistics and the chi-square test. This quiz covers hypothesis testing, the differences between descriptive and inferential statistics, and the significance of the chi-square test. Dive deep into concepts like null and alternative hypotheses to enhance your statistical skills.

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