Biostatistics Lecture

• Statistical Inference:

  • Is the procedure through which inferences about a population are made based on a certain characteristics calculated from a sample of data drawn from that population
  • Make statements not merely about the particular subjects observed in a study but also, more importantly, about the larger population of subjects from which the study participants are drawn
• Deductive Reasoning:

  • Proceeds from general assumptions or propositions to specific thoughts
• Inductive Reasoning:

  • Seek valid generalization from data
• Type of data interpretation in statistical hypothesis testing:

  • Quantitative aid to inductive reasoning
  • From the specific data to the general formula or conclusion about the data
• Hypothesis Testing:

  • Is the process used to evaluate the strength of evidence from the sample and provides a framework for making determinations related to the population
  • Provides a method for understanding how reliably one can extrapolate observed findings in a sample under study to the larger population
• False Positive and False Negative Errors:

  • False Positive Error (Alpha Error or Type 1):
  • The data support a hypothesis when in fact the hypothesis is false
  • Occurs when you incorrectly reject the null hypothesis
  • False Negative Error (Beta Error or Type II):
  • The data do not support a hypothesis when in fact the hypothesis is true
  • When you erroneously receive a negative result and do not reject the null hypothesis
• • P Value is the probability of obtaining results more extreme than the observed results of a statistical test, assuming the null hypothesis is correct

  4. Compare p value obtained with Alpha Level

  5. Reject or Fail the Null Hypothesis:

  • If P value > alpha level, it fails to reject the null hypothesis
  • If P value < alpha level, the investigator rejects the null hypothesis in favor of the alternative hypothesis
• Process of Testing a Null Hypothesis for Statistical Significance:

  1. Develop Null and Alternative Hypothesis:

  • Null Hypothesis (Ho) states that there is no association between variables in the data set
  • Alternative Hypothesis states that there must be a true association between the variables

  2. Establish Alpha Level:

  • Threshold value used to judge whether a test statistic is statistically significant

  3. Perform Test of Statistical Significance:
• Variations in Individual Observation in Multiple Samples:

  • Importance of assessing the differences in individual observation compared with multiple samples
  • Standard Deviation Error of the Mean (SEM) helps estimate the probable error of the sample mean's estimate of the true population mean
  • Confidence Intervals refer to the probability that a population parameter will fall between a set of values for a certain proportion of times
• Testing Hypothesis:

  T-Test: To test difference between means

  Z-Test:To test differences between proportions

  • Critical Ratio:
  • The ratio of an estimate of a parameter divided by the standard error (SE) of the parameter
  • Critical Region:
  • The range of standard deviations away from the mean the critical ratio has to be in order to be significant
  • Two-tailed test for significance
• Degrees of Freedom:

  • Refers to the number of observations that are free to vary
  • T-Test: Degrees of freedom are equal to the total sample size minus 1 degree of freedom for each mean that is calculated
  • Two sample t-test: 2 degrees of freedom are lost because 2 means are calculated
• Testing two proportions:

  • Involves two samples and two groups
  • Requires independence between samples and populations
  • Involves a pooled proportion where x = number of samples who possess the characteristic
• Additional Sample Problems:

  1. Study on breastfeeding rates in low-income countries

  2. Investigation on the Patriots' coin toss winning rate

  3. Comparison of defects in cars from two assembly procedures
• Independent Variable: Continous

  Dependent Variable: OrdinalANOVA (F-test)

  Spearman Correlatation Coefficient
• Independent Variable: Continous

  Dependent Variable: Dichotomous

  Paire T-test
• Independent Variable: Continous

  Dependent Variable: Nominal

  ANOVA (F-test)
• UUU - Phenylalanine (PHE)
• UUC - Phenylalanine (Phe)
• UUA & UUG - Leucine (LEU)
• UU (UCAG) - Serine or Ser
• UAU or UAC - Tyrosine (Tyr)