Omitted Variable Bias in Statistics
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Questions and Answers

What is the consequence of leaving out an independent variable in the analysis?

  • A biased estimation of the relation between the explanatory and outcome variable
  • A more accurate estimation of the relation between the variables of interest
  • An over- or underestimation of the relation between the variables of interest (correct)
  • No effect on the estimation of the relation between the variables of interest

    • What is the purpose of controlling for other variables in the analysis?

  • To increase the precision of the estimates
  • To reduce the complexity of the model
  • To make unbiased claims about the relation between the explanatory and outcome variable (correct)
  • To reduce the number of observations

    • What is the exogeneity assumption in the context of controlling for a variable Z?

  • E(e|x, z) = 0
  • E(e|x) = 0
  • E(e|x) = 1
  • E(e|x, z = 0) (correct)

    • What is the purpose of multiple linear regression?

    <p>To control for the effect of multiple variables on the outcome variable</p> Signup and view all the answers

    What happens when we violate the exogeneity assumption?

    <p>We make incorrect claims about the direction and strength of the relation between the variables of interest</p> Signup and view all the answers

    What is the primary difference between correlation and regression?

    <p>Correlation quantifies the strength and direction of a linear relationship, whereas regression estimates the effect of one variable on another.</p> Signup and view all the answers

    What do we do when we have a categorical variable with multiple categories?

    <p>We create a binary variable for all but one of the categories</p> Signup and view all the answers

    What is the term for the process of estimating a linear relationship between two variables using a straight line?

    <p>Line-fitting</p> Signup and view all the answers

    What is the term for the variable that is omitted from the model and may cause bias?

    <p>Omitted variable</p> Signup and view all the answers

    In the context of simple linear regression, what does the intercept parameter (b0) represent?

    <p>The value of the dependent variable when the independent variable is equal to zero.</p> Signup and view all the answers

    What is the term for the situation where an independent variable is correlated with the error term in a regression model?

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

    What is the purpose of simple linear regression?

    <p>To estimate the effect of a single variable on the outcome variable</p> Signup and view all the answers

    What is the assumption of OLS that is most problematic in practice?

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

    What occurs when a determinant of the dependent variable is correlated with one or more of the included independent variables?

    <p>Omitted Variable Bias</p> Signup and view all the answers

    What is the purpose of controlling for variables in a regression model?

    <p>To isolate the effect of one independent variable on the dependent variable.</p> Signup and view all the answers

    What is the term for the type of regression that involves more than one independent variable?

    <p>Multiple Linear Regression</p> Signup and view all the answers

    What is the primary issue with obtaining data from the full population of interest?

    <p>It is impractical to obtain data from the full population.</p> Signup and view all the answers

    What is the term for the selection of data for analysis in a way that proper randomization is not achieved?

    <p>Sample selection bias</p> Signup and view all the answers

    What is the primary goal of drawing an independent and identically distributed sample from the population?

    <p>To avoid selection bias and ensure a representative sample</p> Signup and view all the answers

    What is the term for the degree to which a measure produces stable and consistent results?

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

    What is the primary difference between reliability and validity?

    <p>Reliability measures precision, while validity measures accuracy</p> Signup and view all the answers

    What is the term for the extent to which two variables vary together in a consistent way?

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

    What is the primary difference between linear regression and correlation?

    <p>Linear regression measures the relationship between two variables, while correlation measures the strength of the relationship</p> Signup and view all the answers

    What is the purpose of calculating the conditional mean?

    <p>To examine the relationship between two variables</p> Signup and view all the answers

    What is the purpose of creating dummy variables in regression analysis?

    <p>To reduce the impact of omitted variable bias</p> Signup and view all the answers

    What is the primary difference between linear regression and logistic regression?

    <p>The type of dependent variable used</p> Signup and view all the answers

    What is the purpose of hypothesis testing in regression analysis?

    <p>To determine the likelihood of the null hypothesis being true</p> Signup and view all the answers

    What is the relationship between the p-value and the significance level in hypothesis testing?

    <p>If the p-value is less than the significance level, the result is significant</p> Signup and view all the answers

    What is the primary difference between statistical significance and meaningfulness?

    <p>Statistical significance is a measure of the likelihood of the null hypothesis being true, while meaningfulness is a measure of the practical importance of the effect</p> Signup and view all the answers

    What is the purpose of calculating the standard error of the slope in regression analysis?

    <p>To calculate the t-value and p-value for hypothesis testing</p> Signup and view all the answers

    What is the assumption of exogeneity in regression analysis?

    <p>The assumption that the independent variable is not correlated with the error term</p> Signup and view all the answers

    What is the purpose of controlling for variables in multiple linear regression?

    <p>To isolate the effect of a particular independent variable</p> Signup and view all the answers

    What is the primary goal of quantitative research?

    <p>To answer a research question by collecting numerical data</p> Signup and view all the answers

    Which of the following is a threat to validity in research design?

    <p>Both a and b</p> Signup and view all the answers

    What is the purpose of controlling for variables in a research study?

    <p>To reduce omitted variable bias</p> Signup and view all the answers

    What is the assumption that underlies multiple linear regression?

    <p>All of the above</p> Signup and view all the answers

    What occurs when the direction of the arrow in a theoretical model is reversed?

    <p>Reverse causality</p> Signup and view all the answers

    What is the term for a measure that accurately represents what it is intended to measure?

    <p>Construct validity</p> Signup and view all the answers

    What is the primary objective of a research design?

    <p>To optimize the validity and reliability of the study</p> Signup and view all the answers

    What is the term for a variable that is not included in a model but affects the outcome?

    <p>Omitted variable</p> Signup and view all the answers

    What is the primary purpose of descriptive quantitative research?

    <p>To collect and analyze numerical data</p> Signup and view all the answers

    What does internal validity refer to in research design?

    <p>The degree to which correct conclusions about causal relationships can be drawn</p> Signup and view all the answers

    What is the purpose of Cronbach’s alpha in research?

    <p>To assess the internal consistency of a scale</p> Signup and view all the answers

    What is the primary goal of quantitative research?

    <p>To collect and analyze numerical data using mathematical methods</p> Signup and view all the answers

    What type of research involves counting the number of students enrolled in a premaster program?

    <p>Descriptive quantitative research</p> Signup and view all the answers

    What is the term for the extent to which a measure produces stable and consistent results?

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

    What is the primary objective of a research design?

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

    What is the term for a measure that accurately represents what it is intended to measure?

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

    What does a correlation coefficient close to 1 indicate?

    <p>A strong positive linear relationship</p> Signup and view all the answers

    What is the primary purpose of regression analysis?

    <p>To estimate how one variable affects another</p> Signup and view all the answers

    What does high external validity imply?

    <p>The findings can be generalized to a broader population</p> Signup and view all the answers

    What is the result of omitting an important variable that affects the dependent variable?

    <p>A biased estimate of the effect of the included variables</p> Signup and view all the answers

    Which type of variable can be used as a moderator in a moderation analysis?

    <p>Any type of variable (binary, categorical, continuous)</p> Signup and view all the answers

    What does a p-value less than 0.05 indicate in hypothesis testing?

    <p>The null hypothesis is likely to be false</p> Signup and view all the answers

    What is construct validity?

    <p>The degree to which a measure represents what it is supposed to measure</p> Signup and view all the answers

    What is the primary difference between correlation and regression?

    <p>Correlation measures the strength and direction of a linear relationship, while regression estimates how one variable affects another</p> Signup and view all the answers

    What is omitted variable bias?

    <p>Bias that results from not including an important variable that affects the dependent variable</p> Signup and view all the answers

    What is the primary goal of inferential quantitative research?

    <p>Establishing cause-and-effect relationships between variables</p> Signup and view all the answers

    What is the primary goal of hypothesis testing in quantitative research?

    <p>To assess the strength of the evidence against the null hypothesis</p> Signup and view all the answers

    What is the primary purpose of controlling for variables in a regression analysis?

    <p>To account for potential confounding factors</p> Signup and view all the answers

    What does the term correlation imply?

    <p>A linear relationship between two variables</p> Signup and view all the answers

    What is the term for the selection of a sample that is not representative of the population?

    <p>Sample selection bias</p> Signup and view all the answers

    What is the significance level commonly used in hypothesis testing?

    <p>All of the above</p> Signup and view all the answers

    What does a p-value represent in hypothesis testing?

    <p>The probability of obtaining the observed results if the null hypothesis is true</p> Signup and view all the answers

    What is a Type I error in hypothesis testing?

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

    What is a theory in the context of quantitative research?

    <p>An explanation of relationships among concepts or events within a set of boundary conditions</p> Signup and view all the answers

    What is an example of a good research question?

    <p>What is the relationship between students' self-esteem and their academic performance?</p> Signup and view all the answers

    What is the primary goal of quantitative research?

    <p>To explain and predict phenomena using numerical data</p> Signup and view all the answers

    What is the assumption of homoscedasticity in regression analysis?

    <p>The variance of the error terms is constant across all levels of the independent variable</p> Signup and view all the answers

    What is the purpose of a t-test in quantitative research?

    <p>To compare the means of two groups</p> Signup and view all the answers

    What is endogeneity in the context of regression analysis?

    <p>The error term is correlated with the independent variables</p> Signup and view all the answers

    What is an assumption of the Ordinary Least Squares (OLS) regression?

    <p>The error terms have a constant variance</p> Signup and view all the answers

    What is multicollinearity in regression analysis?

    <p>The presence of a strong linear relationship between two or more independent variables</p> Signup and view all the answers

    What is the standard error in the context of regression analysis?

    <p>The standard deviation of the sampling distribution of a statistic</p> Signup and view all the answers

    What is Cronbach's alpha?

    <p>A measure of reliability</p> Signup and view all the answers

    What is the difference between a dependent variable and an independent variable?

    <p>The independent variable is manipulated, while the dependent variable is measured</p> Signup and view all the answers

    What is the purpose of a control group in an experiment?

    <p>To provide a baseline for comparison</p> Signup and view all the answers

    What is the term for the situation where an independent variable is correlated with the error term in a regression model?

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

    Which type of study involves collecting data from different subjects at a single point in time?

    <p>Cross-sectional study</p> Signup and view all the answers

    What is the purpose of random sampling in research?

    <p>To ensure that every member of the population has an equal chance of being included in the sample</p> Signup and view all the answers

    What is a common threat to internal validity?

    <p>Sample selection bias</p> Signup and view all the answers

    What does the null hypothesis refer to in hypothesis testing?

    <p>The hypothesis that there is no significant effect or relationship</p> Signup and view all the answers

    What is the main purpose of using a scatterplot in data analysis?

    <p>To visualize the relationship between two continuous variables</p> Signup and view all the answers

    What does the term 'exogeneity' mean in the context of regression analysis?

    <p>The error term is not correlated with the independent variables</p> Signup and view all the answers

    What is a key component of a good theory?

    <p>It simplifies and explains complex real-world phenomena</p> Signup and view all the answers

    What is the purpose of a regression coefficient?

    <p>To predict the value of the dependent variable based on the independent variable</p> Signup and view all the answers

    What does the term 'heteroscedasticity' refer to in regression analysis?

    <p>The variance of the error terms is not constant across all levels of the independent variable</p> Signup and view all the answers

    What is the purpose of using a scatterplot in regression analysis?

    <p>To visualize the relationship between the dependent and independent variables</p> Signup and view all the answers

    What is the main advantage of using a longitudinal study design?

    <p>It enables the study of long-term effects and patterns</p> Signup and view all the answers

    Which of the following is a characteristic of a Likert scale?

    <p>It is an ordinal scale with a range of responses</p> Signup and view all the answers

    What is the purpose of using mediation analysis in regression?

    <p>To examine the indirect effect of an independent variable</p> Signup and view all the answers

    What does a high R-squared value indicate in a regression model?

    <p>The independent variables explain a large proportion of the variance</p> Signup and view all the answers

    What is the key feature of a randomized controlled trial (RCT)?

    <p>The independent variable is manipulated by the researcher</p> Signup and view all the answers

    What is the purpose of controlling for confounding variables in regression analysis?

    <p>To reduce the impact of extraneous variables</p> Signup and view all the answers

    What is the term for a variable that affects the dependent variable but is not related to the independent variable?

    <p>Extraneous variable</p> Signup and view all the answers

    What is the purpose of using dummy variables in regression analysis?

    <p>To include categorical variables in the model</p> Signup and view all the answers

    What is the term for the situation where the direction of the arrow in a theoretical model is reversed?

    <p>Reverse causality</p> Signup and view all the answers

    In the scenario where training leads to higher employee performance, but only when employees have high motivation levels, what is the role of motivation levels?

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

    If the relationship between exercise and weight loss is influenced by dietary habits, what is the role of dietary habits?

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

    In the scenario where stress leads to health problems through its impact on sleep quality, what is the role of sleep quality?

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

    If social support impacts job satisfaction by reducing job stress, what is the role of job stress?

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

    In the scenario where the effect of educational attainment on income is stronger for men than for women, what is the role of gender?

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

    If parental involvement influences children's academic performance through its effect on children's attitudes towards school, what is the role of attitudes towards school?

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

    In the scenario where the effectiveness of a new drug on reducing symptoms is higher in younger patients compared to older patients, what is the role of patient age?

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

    If work-life balance affects employee productivity by increasing job satisfaction, what is the role of job satisfaction?

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

    At a significance level of 0.05, should the null hypothesis be rejected if the p-value is 0.03?

    <p>Yes, because the p-value is less than the significance level</p> Signup and view all the answers

    What does a p-value of 0.12 indicate at a significance level of 0.05?

    <p>The null hypothesis should not be rejected</p> Signup and view all the answers

    What is the decision when the p-value is 0.007 at a significance level of 0.01?

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

    At a significance level of 0.10, what is the decision when the p-value is 0.15?

    <p>Fail to reject the null hypothesis</p> Signup and view all the answers

    What is the conclusion when the p-value is 0.02 at a significance level of 0.05?

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

    What does a p-value of 0.05 indicate at a significance level of 0.05?

    <p>It is a marginal case</p> Signup and view all the answers

    In a study, a researcher obtains a p-value of 0.02 when testing the null hypothesis that a new exercise program has no effect on heart rate. Should the null hypothesis be rejected at a 0.05 significance level?

    <p>Yes, because the p-value is less than the significance level</p> Signup and view all the answers

    A researcher is testing the null hypothesis that a new medication has no effect on blood pressure. The p-value obtained is 0.08. Should the null hypothesis be rejected at a 0.01 significance level?

    <p>No, because the p-value is greater than the significance level</p> Signup and view all the answers

    A company is testing whether a new marketing strategy has increased sales. The null hypothesis states that there is no increase in sales. The p-value obtained is 0.04. Should the null hypothesis be rejected at a 0.05 significance level?

    <p>Yes, because the p-value is less than the significance level</p> Signup and view all the answers

    In a study, a researcher is testing the null hypothesis that a new teaching method has no effect on student performance. The p-value obtained is 0.12. Should the null hypothesis be rejected at a 0.05 significance level?

    <p>No, because the p-value is greater than the significance level</p> Signup and view all the answers

    A researcher is testing the null hypothesis that a new diet has no effect on weight loss. The p-value obtained is 0.035. Should the null hypothesis be rejected at a 0.05 significance level?

    <p>Yes, because the p-value is less than the significance level</p> Signup and view all the answers

    A company is testing whether a new product has increased customer satisfaction. The null hypothesis states that there is no increase in customer satisfaction. The p-value obtained is 0.06. Should the null hypothesis be rejected at a 0.05 significance level?

    <p>No, because the p-value is greater than the significance level</p> Signup and view all the answers

    A researcher is testing the null hypothesis that a new exercise program has no effect on mental health. The p-value obtained is 0.01. Should the null hypothesis be rejected at a 0.05 significance level?

    <p>Yes, because the p-value is less than the significance level</p> Signup and view all the answers

    A researcher is testing the null hypothesis that a new technique has no effect on the accuracy of a measurement. The p-value obtained is 0.09. Should the null hypothesis be rejected at a 0.05 significance level?

    <p>No, because the p-value is greater than the significance level</p> Signup and view all the answers

    Study Notes

    Omitted Variable Bias and the DGP

    • Omitted variable bias occurs when a variable is left out of a model, leading to an over- or underestimation of the relationship between variables of interest.
    • Omitted variables are part of alternative explanations that violate the exogeneity assumption, leading to incorrect claims about the direction and strength of the relationship between X and Y.
    • To make unbiased claims, we need to reduce concerns of omitted variable bias by controlling for other variables.

    Controlling for Variables

    • When we believe a variable Z may cause omitted variable bias, we need to "control" or "adjust" for it by integrating it into our model.
    • The exogeneity assumption becomes: E(e|x, z) = 0.
    • Controlling for a variable Z involves adjusting for its effect on the relationship between X and Y.

    Simple Linear Regression

    • Simple linear regression involves predicting the outcome variable using a single explanatory variable.
    • The equation for simple linear regression is: Y = b0 + b1X + e.

    Multiple Linear Regression

    • Multiple linear regression involves predicting the outcome variable using multiple explanatory variables.
    • The equation for multiple linear regression is: Y = b0 + b1X + b2Z + e.

    Conditional Means

    • Conditional means involve calculating the mean of the outcome variable for specific values of the explanatory variable.
    • Conditional means are useful for understanding the relationship between variables.

    Correlation and Regression

    • Correlation measures the strength and direction of a linear relationship between two variables.
    • Regression estimates how one variable affects another and predicts values based on this relationship.
    • The correlation coefficient is computationally similar to the linear regression coefficient.

    Types of Variables

    • Variables can be categorized into different types, including continuous, categorical, binary, and ordinal.
    • Understanding the type of variable is important for choosing the correct statistical method.

    Hypothesis Testing

    • Hypothesis testing involves testing a null hypothesis against an alternative hypothesis.
    • The p-value is the probability of observing the test statistic under the null hypothesis.
    • If the p-value is below a certain significance level (e.g., 0.05), we reject the null hypothesis.

    Regression Inference

    • Regression inference involves making inferences about the population based on a sample of data.
    • The steps for regression inference are:
      1. Get the slope (b1)
      2. Get the standard error of the slope (SE)
      3. Calculate the test statistic (t-value)
      4. Calculate the p-value

    Quantitative Research

    • Quantitative research involves answering a research question by collecting numerical data and analyzing it using statistical methods.
    • Types of quantitative research include surveys, experiments, and observational studies.
    • Quantitative research is useful for understanding the relationship between variables and testing hypotheses.

    Theory and Research Design

    • A theory is a set of assumptions and hypotheses that explain a phenomenon.
    • A good theory should have clear concepts, associations, and predictions.
    • Research design is critical for testing hypotheses and achieving validity and reliability.
    • Threats to validity include omitted variable bias, reverse causality, and measurement error.

    Exam Preparation

    • The School of Business and Economics, Department of Management and Organization has a dedicated section for exam prep.
    • The exam prep section consists of 12 pages (from 279 to 290) focusing on preparing students for the exam.
    • A 10-minute course evaluation is included in the exam prep section.
    • There is an additional section for extra prep, which consists of 7 pages (from 292 to 298).
    • The extra prep section is also part of the School of Business and Economics, Department of Management and Organization.

    Quantitative Research Methods

    • Primary purpose of quantitative research: To collect numerical data and analyze it using mathematical methods.
    • Types of quantitative research: Descriptive, inferential, and correlational research.

    Descriptive Research

    • Example of descriptive research: Counting the number of students enrolled in a premaster program.
    • Goal of descriptive research: To describe the characteristics of a population or phenomenon.

    Validity

    • Internal validity: The degree to which correct conclusions about causal relationships can be drawn.
    • Construct validity: The degree to which a measure represents what it is supposed to measure.
    • External validity: The extent to which research findings can be generalized to a broader population.

    Measurement

    • Cronbach's alpha: Measures the internal consistency of a scale.
    • Reliability: The consistency of a measure across different instances.

    Correlation and Regression

    • Correlation: Measures the strength and direction of a linear relationship between two variables.
    • Regression: Estimates how one variable affects another.
    • Correlation coefficient: Ranges from -1 to 1, with 1 indicating a strong positive linear relationship.
    • R-squared: Measures the proportion of variance in the dependent variable explained by the independent variables.

    Hypothesis Testing

    • Null hypothesis: The hypothesis that there is no significant effect or relationship.
    • Alternative hypothesis: The hypothesis that there is a significant effect or relationship.
    • P-value: The probability of obtaining the observed results if the null hypothesis is true.
    • Significance level: The maximum probability of rejecting the null hypothesis when it is true (e.g. 0.05).

    Errors

    • Type I error: Rejecting the null hypothesis when it is true.
    • Type II error: Failing to reject the null hypothesis when it is false.
    • Sample selection bias: The selection of a sample that is not representative of the population.
    • Omitted variable bias: The failure to include an important variable that affects the dependent variable.

    Regression Analysis

    • Assumptions of Ordinary Least Squares (OLS) regression: Linearity, independence, homoscedasticity, normality, and no multicollinearity.
    • Homoscedasticity: The variance of the error terms is constant across all levels of the independent variable.
    • Multicollinearity: The presence of a strong linear relationship between two or more independent variables.
    • Endogeneity: The error term is correlated with the independent variables.
    • Exogeneity: The error term is not correlated with the independent variables.

    Study Design

    • Experimental design: A study in which the independent variable is manipulated by the researcher.
    • Control group: A group that does not receive the experimental treatment.
    • Cross-sectional study: A study that collects data from different subjects at a single point in time.
    • Longitudinal study: A study that collects data from the same subjects at multiple points in time.

    Measurement Scales

    • Binary variable: A variable that can take on only two values (e.g. male/female).
    • Likert scale: A scale used to measure the intensity of respondents' attitudes or feelings.

    Mediation and Moderation

    • Mediation: A variable that explains the relationship between an independent and dependent variable.
    • Moderation: A variable that affects the strength or direction of the relationship between an independent and dependent variable.

    Mediators vs. Moderators

    Scenarios to Illustrate the Difference

    • Training leads to higher employee performance, but only when employees have high motivation levels, making motivation levels a moderator.
    • The relationship between exercise and weight loss is influenced by dietary habits, with healthier diets strengthening the impact of exercise, making dietary habits a moderator.
    • Stress leads to health problems through its impact on sleep quality, with poor sleep quality mediating the link between stress and health problems.
    • Social support impacts job satisfaction by reducing job stress, with reduced job stress mediating the relationship between social support and job satisfaction.
    • The effect of educational attainment on income is stronger for men than for women, making gender a moderator.
    • Parental involvement influences children's academic performance through its effect on children's attitudes towards school, making attitudes towards school a mediator.
    • The effectiveness of a new drug on reducing symptoms is higher in younger patients compared to older patients, making age a moderator.
    • Work-life balance affects employee productivity by increasing job satisfaction, with increased job satisfaction mediating the link between work-life balance and productivity.
    • The relationship between job training and employee performance is stronger in high-tech industries compared to low-tech industries, making industry type a moderator.
    • The impact of physical activity on mental health is explained by the reduction in stress levels that comes from regular exercise, making stress levels a mediator.

    Hypothesis Testing and Null Hypothesis Rejection

    Understanding P-Values and Significance Levels

    • A p-value of 0.03 is less than a significance level of 0.05, indicating a statistically significant result, and the null hypothesis (H0) should be rejected.
    • A p-value of 0.07 is greater than a significance level of 0.05, indicating a non-statistically significant result, and the null hypothesis (H0) should not be rejected.
    • A p-value of 0.01 is less than a significance level of 0.05, indicating a statistically significant result, and the null hypothesis (H0) should be rejected.
    • A p-value of 0.04 is greater than a significance level of 0.01, indicating a non-statistically significant result, and the null hypothesis (H0) should not be rejected.
    • A p-value of 0.045 is less than a significance level of 0.05, indicating a statistically significant result, and the null hypothesis (H0) should be rejected.
    • A p-value of 0.15 is greater than a significance level of 0.10, indicating a non-statistically significant result, and the null hypothesis (H0) should not be rejected.
    • A p-value of 0.08 is greater than a significance level of 0.05, indicating a non-statistically significant result, and the null hypothesis (H0) should not be rejected.
    • A p-value of 0.025 is less than a significance level of 0.05, indicating a statistically significant result, and the null hypothesis (H0) should be rejected.
    • A p-value of 0.005 is less than a significance level of 0.01, indicating a statistically significant result, and the null hypothesis (H0) should be rejected.
    • A p-value of 0.12 is greater than a significance level of 0.05, indicating a non-statistically significant result, and the null hypothesis (H0) should not be rejected.

    Key Takeaways

    • If the p-value is less than the significance level, the null hypothesis (H0) should be rejected.
    • If the p-value is greater than or equal to the significance level, the null hypothesis (H0) should not be rejected.

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