lecture 3 depression/BD

• Level of Measurement (LOM) determines the type of statistics you can use:

  • Nominal: attributes are named
  • Ordinal: attributes can be ordered
  • Interval: distance is meaningful
  • Ratio: absolute zero
• LOM and parametric vs. nonparametric:

  • Categorical and ordinal dependent variable -> non-parametric
  • Interval and ratio dependent variable -> more complicated
  • If the distribution is normal -> parametric
  • If the distribution is non-normal -> non-parametric
• Parametric statistics:

  • Estimate parameters of a population based on the normal distribution
  • Univariate: mean, standard deviation, skewness, kurtosis
  • Bivariate: correlation, linear regression, t-tests
  • Multivariate: multiple linear regression, ANOVAs
  • More powerful, more assumptions, vulnerable to violations
• Non-parametric statistics:

  • Do not assume sampling from a population that is normally distributed
  • Univariate: median, frequencies
  • Bivariate: Spearman’s correlation, Chi square test
  • Less powerful, fewer assumptions, less vulnerable to assumption violations
• How many variables are you working on?

  • One -> Univariate (mean, median, mode, histogram, bar chart)
  • Two -> Bivariate (correlation, t-test, scatterplot, clustered bar chart)
  • More than two -> Multivariate (reliability analyses, factor analysis, multiple linear regression)
• Central Tendency:

  • Mode: most frequent
  • Median: 50th percentile
  • Mean: average
  • Use depends on data type and distribution shape
• Mode (Mo):

  • Most common score, not affected by outliers
  • Suitable for all data levels
• Frequencies (f) and percentages (%):

  • Number of responses in each category
  • Percentage of responses in each category
  • Can be visualized with a bar or pie chart
• Median (Mdn):

  • Mid-point of the distribution, not badly affected by outliers
  • Might not represent central tendency if data is skewed
• Mean:

  • Average score, sensitive to outliers
  • Used for normally distributed ratio or interval data
• Standard deviation (SD):

  • Square root of the variance
  • Calculated with Σ √ ( (x - x̄)2/ (N- 1) )
  • Used for normally distributed interval or ratio data
• Options for nominal LOM:

  • Describe most frequent, least frequent, frequencies, percentages, cumulative percentages, ratios
• Descriptives for ordinal data:

  • Similar to nominal, can use percentiles
• Descriptives for interval data:

  • Central tendency, shape/spread, treated as continuous
• Descriptives for ratio data:

  • Same as interval data, can use ratios
• Summary of descriptive statistics:

  • Level of measurement and normality determine parametric treatment
  • Describe central tendency and distribution using various measures
• Central tendency can be described using frequencies, percentages, mode, median, and mean
• Distribution can be described using minimum and maximum values, range, quartiles, standard deviation, and variance
• Skewness is a measure of the lean of the distribution, with a tail to the right indicating positive skew and to the left indicating negative skew
• Kurtosis indicates how flat or peaked the data distribution is, with positive kurtosis for peaked data and negative kurtosis for flat data
• In a normal distribution, mean = median = mode; positive skew means mode < median < mean, and negative skew means mean < median < mode
• Non-normal distributions can be described using non-parametric descriptive statistics like quartiles, percentiles, and interquartile ratio
• Transformations can be used to convert data into a normal distribution for more powerful tests, but this may complicate interpretation
• Graphical techniques like bar charts, pie charts, histograms, stem and leaf plots, and box plots can be used to represent data visually