🪛Intro to Political Research Unit 2 – Quantitative Data Analysis in Political Research

Key Concepts and Definitions

• Quantitative data analysis involves using statistical methods to analyze numerical data and draw meaningful conclusions
• Variables are characteristics or attributes that can be measured or observed and vary among individuals or groups
• Dependent variables are the outcome or response variables that are influenced by the independent variables
• Independent variables are the predictor or explanatory variables that are manipulated or controlled to observe their effect on the dependent variables
• Confounding variables are extraneous factors that can influence the relationship between the independent and dependent variables and need to be controlled for in the analysis
• Operationalization is the process of defining abstract concepts in terms of measurable variables (political ideology measured on a scale from liberal to conservative)
• Reliability refers to the consistency and stability of measurements over time or across different observers
• Validity refers to the extent to which a measure accurately represents the concept it is intended to measure (survey questions measuring political knowledge)

Data Types and Measurement Scales

• Nominal data consists of categories or labels with no inherent order or numerical value (political party affiliation)
• Ordinal data has categories that can be ranked or ordered but the differences between categories are not necessarily equal (level of agreement with a statement on a Likert scale)
• Interval data has ordered categories with equal intervals between them but no true zero point (temperature measured in Celsius or Fahrenheit)
• Ratio data has ordered categories, equal intervals, and a true zero point representing the absence of the attribute being measured (income, age)
• Discrete data can only take on specific, separate values with no intermediate values possible (number of votes cast in an election)
• Continuous data can take on any value within a range and can be measured to any level of precision (percentage of vote share)
  • Continuous data is often rounded or grouped into categories for analysis (income brackets)
• Measurement scales determine the appropriate statistical methods that can be used to analyze the data
  • Nominal and ordinal data require non-parametric methods that do not assume a normal distribution
  • Interval and ratio data can be analyzed using parametric methods that assume a normal distribution

Descriptive Statistics

• Descriptive statistics summarize and describe the main features of a dataset without drawing conclusions about a larger population
• Measures of central tendency describe the typical or average value in a dataset
  • Mean is the arithmetic average calculated by summing all values and dividing by the number of observations
  • Median is the middle value that separates the upper and lower halves of a dataset when arranged in order
  • Mode is the most frequently occurring value or values in a dataset
• Measures of dispersion describe how spread out or variable the data points are
  • Range is the difference between the maximum and minimum values in a dataset
  • Variance is the average squared deviation from the mean, measuring how far individual data points are from the mean
  • Standard deviation is the square root of the variance, expressed in the same units as the original data
• Frequency distributions organize and display the number of observations falling into each category or range of values
  • Histograms are graphical representations of frequency distributions for continuous data
  • Bar charts display the frequency or percentage of observations in each category for categorical data
• Percentiles and quartiles divide a dataset into equal parts based on the percentage of observations below a certain value (median is the 50th percentile or 2nd quartile)

Probability and Sampling

• Probability is the likelihood of an event occurring, expressed as a number between 0 and 1 or as a percentage
• Probability distributions describe the likelihood of different outcomes for a random variable
  • Normal distribution is a symmetric bell-shaped curve with most values clustered around the mean (IQ scores, height)
  • Binomial distribution describes the probability of a fixed number of successes in a fixed number of independent trials with two possible outcomes (voting yes or no on a ballot measure)
• Sampling is the process of selecting a subset of individuals from a larger population to study
• Sampling methods can be probability-based or non-probability-based
  • Simple random sampling gives every individual an equal chance of being selected
  • Stratified sampling divides the population into subgroups and selects a random sample from each subgroup
  • Cluster sampling divides the population into clusters and randomly selects entire clusters to study
  • Convenience sampling selects individuals who are easily accessible or willing to participate (online polls)
• Sampling error is the difference between a sample statistic and the true population parameter due to random variation
• Sampling bias occurs when some members of the population are systematically more or less likely to be selected than others, leading to a non-representative sample

Hypothesis Testing

• Hypothesis testing is a statistical method used to make decisions or draw conclusions about a population based on sample data
• Null hypothesis ($H_0$) is a statement of no effect or no difference, assumed to be true unless there is strong evidence against it
• Alternative hypothesis ($H_a$ or $H_1$) is a statement that contradicts the null hypothesis and is accepted if the null hypothesis is rejected
• One-tailed tests have an alternative hypothesis that specifies the direction of the effect or difference (greater than or less than)
• Two-tailed tests have an alternative hypothesis that does not specify the direction of the effect or difference (not equal to)
• Test statistic is a standardized value calculated from the sample data that is used to determine the likelihood of observing the data if the null hypothesis is true (z-score, t-score, chi-square)
• p-value is the probability of observing a test statistic as extreme or more extreme than the one calculated from the sample data, assuming the null hypothesis is true
  • A small p-value (typically < 0.05) indicates strong evidence against the null hypothesis and leads to its rejection in favor of the alternative hypothesis
  • A large p-value (> 0.05) indicates weak evidence against the null hypothesis and leads to its retention
• Type I error (false positive) occurs when the null hypothesis is rejected when it is actually true
• Type II error (false negative) occurs when the null hypothesis is not rejected when it is actually false

Correlation and Regression Analysis

• Correlation measures the strength and direction of the linear relationship between two variables
• Pearson correlation coefficient (r) ranges from -1 to +1, with 0 indicating no linear relationship
  • Positive correlation means that as one variable increases, the other variable also tends to increase
  • Negative correlation means that as one variable increases, the other variable tends to decrease
• Spearman rank correlation coefficient (ρ) is a non-parametric measure used for ordinal data or data with outliers
• Correlation does not imply causation, as there may be confounding variables or reverse causality
• Regression analysis models the relationship between a dependent variable and one or more independent variables
• Simple linear regression fits a straight line to the data to predict the dependent variable from one independent variable
  • Slope ($\beta_1$) represents the change in the dependent variable for a one-unit increase in the independent variable
  • Intercept ($\beta_0$) represents the predicted value of the dependent variable when the independent variable is zero
• Multiple regression includes two or more independent variables to predict the dependent variable
• Coefficient of determination ($R^2$) measures the proportion of variance in the dependent variable that is explained by the independent variable(s)
• Residuals are the differences between the observed values and the predicted values from the regression line
  • Residual plots can be used to check assumptions of linearity, homoscedasticity, and normality

Data Visualization Techniques

• Data visualization helps to communicate patterns, trends, and relationships in data through graphical representations
• Scatter plots display the relationship between two continuous variables, with each data point represented by a dot
  • Positive correlation appears as an upward-sloping pattern
  • Negative correlation appears as a downward-sloping pattern
  • No correlation appears as a random scatter of points with no clear pattern
• Line graphs show changes in a continuous variable over time or another continuous variable
  • Multiple lines can be used to compare different groups or categories
• Bar graphs compare values across different categories or groups, with the height or length of each bar representing the value
• Pie charts show the proportion or percentage of the whole for each category, with each slice representing a category
• Box plots (box-and-whisker plots) display the distribution of a continuous variable, including the median, quartiles, and outliers
• Heat maps use color intensity to represent values in a two-dimensional matrix, often used for correlation matrices
• Geographic maps can display data values or categories for different regions or locations
  • Choropleth maps use color shading to represent data values for different areas
  • Dot density maps use dots to represent the density or concentration of a variable across a geographic area
• Interactive visualizations allow users to explore and manipulate data displays, such as zooming, filtering, or hovering for more information

Interpreting and Reporting Results

• Interpret results in the context of the research question and hypotheses, considering the practical and theoretical implications
• Report the sample size, descriptive statistics, and inferential statistics (test statistics, p-values, confidence intervals) for each analysis
• Use appropriate language to describe the strength and direction of relationships or differences (e.g., weak positive correlation, statistically significant difference)
• Avoid overstating or understating the findings, and acknowledge limitations or alternative explanations
• Use tables and figures to summarize and visualize key results, following guidelines for clear and informative presentation
  • Include clear titles, labels, and legends
  • Use consistent formatting and appropriate scales
  • Highlight key findings or patterns
• Discuss the generalizability of the results to the larger population or other contexts, considering the sampling method and sample characteristics
• Suggest future directions for research based on the findings and limitations of the current study
• Provide a clear and concise summary of the main findings and conclusions in the abstract and discussion sections
• Follow reporting guidelines or standards for the specific field or publication outlet (e.g., APA style)