Statistics and Data Classification Quiz

Defining Data

• Classify data as numerical or categorical
• Numerical data can be further classified as discrete or continuous
• Categorical data can be further classified as ordinal or nominal
• Binary/dichotomous data has two possible values
• Derived variables are created from categories using a threshold or cutoff
• Transformed variables involve transformations like log transformations or standardized scores

Outcome and Exposure

• Outcome variables are response or dependent variables (Y)
• Exposure variables are explanatory or independent variables (X)
• Case control groups can be outcome or exposure dependent
• Treatment groups are exposure dependent
• Predictor is the exposure variable

Descriptive Statistics

• Frequency distributions show the frequency of each data value.
• Histograms are bar graphs showing the frequency of data within ranges.
• Bin width is the size of each bar in a histogram
• Frequency represents the number of data points in a bin
• Range is the difference between highest and lowest data values
• Mode is the most frequent data value
• Density is the frequency normalized so that the area under the chart equals one.
• Skewness describes the asymmetry of the distribution.
  • Positive skew (right-hand skew) - data tailing off to the right
  • Negative skew (left-hand skew) - data tailing off to the left
  • Normal distribution has no skew.
• Modality describes how many peaks the graph has
  • Unimodal (one peak)
  • Bimodal (two peaks)
  • Multimodal (multiple peaks)
  • Uniform (truly random) data is represented by a flat line

Sample Statistics

• Central tendency measures the center of data.
  • Mean is the average of all values (Σ X / N)
  • Median is the middle value when sorted.
  • Mode is the most frequent value.
• When data is not normally distributed, the median is preferred.
• Dispersion measures the spread of data.
  • Variance calculates the average of squared differences from the mean.
  • Standard deviation is the square root of variance.
• 68.27% of observations fall within one standard deviation of mean.
• 95.45% of observations fall within two standard deviations of mean.
• 99.7% of observations fall within three standard deviations of mean.
• Geometric mean is a better measure of central tendency for skewed data

Measures of Dispersion

• Interquartile range (IQR) is the difference between the 25th and 75th percentile.
• Box plot visually represents distribution, showing the median, quartiles and outliers.

Categorical Summaries and Displays

• Bar charts are for categorical data
• Histograms are for continuous data
• Contingency tables present the relationship between two categorical variables
• Conditional distribution
• Relative frequency distribution can use row percentages or column percentages
• Case control studies consider whether they have the outcome.

Scatter Plot

• Scatter plot shows relationship between two co-varying variables
• Evaluate relationship direction and strength

Correlation Coefficient

• Quantifies the linear relationship strength between two variables.
• r takes values from -1 to +1
• r = 1 perfect positive linear relationship
• r = -1 perfect negative linear relationship
• r = 0 no linear relationship

Z-scores

• Linear transformation of a measurement
• centre and spread change, but shape doesn't change
• Compare scores from different normal distributions
• Reference range calculation
• A Z-score measures the distance from the mean, in standard deviation units.

Standard Normal Distribution

• Displays probability of observing a z-score.
• Total area under the curve is one.

Logged Variables

• Logarithmic scales represent equal multiplicative change
• Pulls low values apart and high values together
• Log transformation reduces positive skew and eases analysis
• Back transformation converts log values back to original scale
• Geometric mean is suitable for positively skewed data.

Prevalence and Incidence

• Prevalence is the proportion of the population with a disease at a specific time.
• Incidence is the rate of new cases of a disease during a specified period.
• Cumulative incidence (also risk) is the proportion getting the disease in a specific time period.

Observational and Experimental Designs

• Experimental studies (interventional) manipulate a variable to observe its effect.
• Observational studies observe natural variation in a population.
• Cohort and case-control studies are subtypes of observational studies
• Cross-sectional studies collect data at a single point in time.

Sample Size and Power/Regression/Systematic Review

• Sample size and power analysis inform the needed sample size to detect an effect.
• Regression models examine relationships between variables.
• Systematic review synthesizes findings from multiple studies.

Meta-analysis

• Meta-analysis combines results from multiple studies.

Hypothesis Testing

• Null hypothesis states no difference or association.
• Alternative hypothesis asserts a difference or association.
• P-value is the probability of observing results as extreme as, or more extreme than, those observed, if the null hypothesis is true.
• Test statistic measures how far the data are from the null.
• Degrees of freedom affect the shape of the distribution and are often related to sample size.

Point Estimates and Parameters

• Statistical inference uses samples to make statements about populations.
• Point estimates (sample values) are best guesses for population parameters (unknown values)
• Confidence interval estimates the range likely encompassing a specific population parameter.

Confidence Intervals

• Confidence intervals provide range of likely values for population parameter
• Widens with decreasing sample size.
• 95% CI means that, in repeated sampling, 95% of such estimated ranges will contain true value.

Sampling Considerations

• Random errors reflect variability in repeated sampling
• Standard error estimates how much point estimates deviate from population parameters during repeated sampling.

Statistical Assumptions and Methods

• Methods like t-tests have underlying assumptions like data normality, independence, and homogeneity of variances.
• Using correct statistical method and applying appropriate corrections is critical
• Non-parametric methods may be needed when assumptions cannot be met.

Chi-squared Test of Independence

• Assesses independence between two categorical variables.
• Examines if there's an association between variables.
• Calculations involve (observed - expected)²/ expected for all cells.
• Assumes no more than 20% of expected values are less than 5 in each cell.
• Degrees of freedom (df) are calculated as (rows- 1) x (columns - 1)

Clinical Trials

• A clinical trial is a specific type of experimental study.

Risk Difference

• The difference in probabilities between two groups.

Risk Ratio

• The ratio of probabilities between two groups.

Odds Ratio

• The ratio of odds between two groups.

Rank-Based Tests

• Non-parametric tests rank observations