Biostats Exam 4

• Correlation analysis


  Analyses the relationship between two variables
• Regression analysis


  Analyses the relationship between a dependent variable and one or more independent variables
• Correlation and regression analyses

  Differentiate between the two
• Correlation coefficient


  Measures the strength and direction of the linear relationship between two variables
• Types of correlation coefficients

  • Pearson's correlation coefficient
  • Spearman's rank correlation coefficient
  • Kendall's tau
• Interpretation of correlation coefficients

  • Positive, negative, or no correlation
  • Strength of correlation (weak, moderate, strong)
• Scatterplots


  Visualize the relationship between variables
• Correlation analysis has limitations and assumptions
• Regression model


  Consists of predictor variables (independent variables), outcome variable (dependent variable), and a regression equation
• Types of regression models

  • Simple linear regression
  • Multiple linear regression
  • Logistic regression
• Slope


  Indicates the change in the dependent variable for a one-unit change in the independent variable
• Intercept


  The value of the dependent variable when the independent variable is zero
• Residuals


  The difference between the observed and predicted values of the dependent variable
• Regression analysis has assumptions: linearity, independence of errors, homoscedasticity, normality of residuals
• Model fit and goodness of fit measures

  1. squared, adjusted R-squared, AIC, BIC
• Statistical software is used to conduct correlation and regression analyses
• Statistical software output should be interpreted to understand the results of correlation and regression analyses
• • Parametric tests make assumptions about the underlying data distribution and are suitable for interval or ratio data.
  • Nonparametric tests do not make distributional assumptions and are suitable for ordinal, nominal, or non-normally distributed data.
  • Parametric tests are more powerful and efficient when the assumptions are met, while nonparametric tests are more flexible and robust but may have lower power in certain situations.
• When assumptions of normality are violated, the underlying data does not follow a normal distribution
• Violations of normality can lead to inaccurate results and reduced statistical power in parametric tests
• Presence of outliers can greatly influence the results of statistical analyses
• Outliers


  Data points that are significantly different from the rest of the data
• Outliers can skew the distribution and impact the estimates of central tendency and variability
• Outliers may distort the results of both parametric and nonparametric tests, leading to biased estimates and inaccurate conclusions
• Small sample size


  Having a limited number of observations in the dataset
• With small sample sizes, statistical tests may lack power to detect true effects or differences between groups
• Small sample sizes can also increase the risk of Type I and Type II errors, making it challenging to draw reliable conclusions from the data
• Data measurement inaccuracy


  Errors or inaccuracies in the measurement process
• Measurement inaccuracy can introduce noise and bias into the data, affecting the validity and reliability of statistical analyses
• Alpha (α)


  The significance level chosen by the researcher before conducting a hypothesis test
• Type I error


  The rejection of a true null hypothesis
• Commonly used significance levels

  • 0.05 (5%)
  • 0.01 (1%)
• Alpha


  Serves as the threshold for determining whether the observed results are statistically significant
• Smaller alpha value


  Indicates a more stringent criterion for rejecting the null hypothesis
• 1. value


  The probability of observing the test statistic (or more extreme) under the assumption that the null hypothesis is true
• Smaller p-value


  Suggests stronger evidence against the null hypothesis and greater support for the alternative hypothesis
• If p-value is less than or equal to alpha (p ≤ α)


  The null hypothesis is rejected in favor of the alternative hypothesis
• If p-value is greater than alpha (p > α)


  The null hypothesis is not rejected
• Statistical significance decision rule


  A guideline for making decisions based on the comparison of the p-value to the chosen significance level (alpha)
• If p-value is less than or equal to alpha (p ≤ α)


  The results are considered statistically significant, and the null hypothesis is rejected