NCMB 315 Week 7

• Quantitative data analysis four purposes:

  • To describe data
  • To estimate population values
  • To test hypotheses
  • To provide evidence regarding measurement properties of quantified variables.
• Levels of measurement

  • Nominal
  • Ordinal
  • Interval
  • Ratio
• Nominal


  Lowest level, involves using numbers simply to categorize attributes, the numerical value is simply a placeholder
• Ordinal


  Ranks people on attributes, categories imply some sort of ranking
• Interval


  Ranks people on an attribute and specifies the distance between them; no true zero value (arbitrary zero)
• Ratio


  Highest level of measurement, has a meaningful zero and provides information about the absolute magnitude of the attribute
• Descriptive statistics


  Used to synthesize and describe data, provides simple description and summary about the sample and observations
• Parameter


  Population value
• Statistic


  Sample value
• Univariate


  One variable
• Symmetrical distribution


  When folded over, the two halves of a frequency polygon would be superimposed
• Normal distribution


  Bell or normal shaped curve, unimodal, gaussian
• Asymmetrical distribution


  • (+) skew - longer tail points to the right
  • (-) skew - longer tail points to the left
• Central tendency


  Provides an overall summary but does not clarify the patterns of data
• Indexes of central tendency

  • Mode
  • Median
  • Mean
• Mode


  Most numerical value that occurs most frequently, most popular value
• Median


  Middle value, does not take into account individual values and is insensitive to extremes
• Mean


  The sum of all values divided by the number of participants, the most stable
• Variability (dispersion)


  How the values are different from the mean
• Range


  The highest minus of the lowest score in a distribution
• Standard deviation


  Captures the degree to which the scores deviate from one another, shows the homogeneity or heterogeneity of the dataset
• Bivariate


  Two variables
• Crosstabulations


  A two-dimensional frequency distribution in which the frequencies of two variables are crosstabulated
• Correlation


  Used to describe the relationship between two variables - to what extent are the two variables related to each other
• Pearson's r


  The product-moment correlation coefficient, the most widely used correlation statistic, computed with continuous measures
• Spearman's Rho


  A correlation index used for ordinal level data or when sample sizes are very small
• Inferential statistics


  Based on the laws of probability, provide a means for drawing inferences about a population, given data from a sample
• Parameter estimation


  Used to estimate population parameter - e.g. a mean, a proportion, or a difference in means between two groups
• Point estimation


  Involves calculating a single statistic to estimate the parameter
• Interval estimation


  Provides a range of values within which the parameter has a specified probability of lying (dependent on confidence interval)
• Confidence interval (CI)


  An interval estimation based on confidence level
• Hypothesis testing


  Type I and Type II errors
• Type I error


  False-positive (accept), occurs if an investigator rejects a null hypothesis that should be accepted
• Type II error


  False-negative (reject), occurs if an investigator fails to reject a null hypothesis that should be rejected
• Confidence interval


  • Provides a range of values within which the parameter has a specified probability of lying (dependent on confidence interval)
  • Used in sampling computation
  • Based on confidence level (most common is 95 confidence level) - can have the same sampling estimation as parameter estimation
• Parameter estimation


  When the population SD is unknown, the interval estimate can be determined using student's t-distribution
• Sample problem


  • The mean age of the sample of 25 students is 18 years, and the standard deviation is 1.3 years. Find the interval estimate of the population mean using 95% CL (2.064)
• Degree of freedom


  n - 1
• Margin of error formula


  E - margin of arrow, t - statistics, s - sample SD, n - sample size
• Type II error


  False-negative, occurs if an investigator accepts a null hypothesis that should be rejected