Stats

• Data

  • Quantitative: Expressed in numbers or values
  • Qualitative: Expressed on a quality scale or observed
  • Sample: Known proportion of population to be studied

  Normal Distribution

  • Special frequency distribution
  • Plotted graph is symmetrical 'bell shaped curve'
  • Same mean (average), mode and median (middle) values
  • True normal distribution is symmetrical: 50% values above mean, 50% below
  • 95% values within 2 standard deviations of mean
• Spread of Dispersion

  Standard Deviation

  • Spread of measurements about mean in normal distribution
  • Reduces anomalies effect
  • Indicates if difference is significant
  • Distance from mean to inflexion point on curve
  • 68% lie in 1 SD of mean, 95% in 1.96 SD
  • Low SD = data has narrow range, grouped around mean (greater reliability), makes a narrow curve
  • High SD = data has larger range, less well grouped (lower reliability), makes a wide curve

  Range

  • Largest - smallest
  • Severely affected by outliers
  • May skew calculation
• Spearman’s Rank Correlation Coefficient

  • Statistical relationship between two quantitative variables
  • Measured from same sample
  • Null hypothesis (H_0):
  • No statistically significant correlation between measurement 1 and 2
  • Negative r value = negative correlation
  • Positive r value = positive correlation
  • R value will be between +1 and -1
  • n = Number of individuals in sample
  • d_i = Difference in rank of two measurements made on individual

  
• Students T-test (unpaired)

  • Shows if there is a statistically significant difference between means
  • Sample is under 25 in normal distribution
  • Formula
  • X_1 = first mean
  • X_2 = second mean
  • S_1 = first SD
  • S_2 = second SD
  • n_1 = first measurement number
  • n_2 = second measurement number
  • Null hypothesis (H_0):
  • No statistically significant difference between two means
  • Rejected if t value exceeds critical value (P = 0.05)

  
• Chi-squared

  • Measurements relate to individual numbers in particular categories
  • Compares observed with theoretical expected results
  • Calculation generate X^2 value,
  • Higher = greater difference between observed and expected
  • Null hypothesis: no statistical difference between observed and expected
  • Calculate expected value
  • Mean of expected values
  • Inheritance, add expected values and apply ratio
  • n-1 = degrees of freedom
  • O = observe value
  • e = expected value
  • Conclusion
  • Claim bio reason caused difference
  • Number exceeds critical at 95% confidence (0.05), reject null
  • If less, accept