Below are some key quantitative methods, concepts, and terms that students will cover in introductory research methods classes
Source: Fraenkel, J.R. and Wallen, N.E. How to Design and Evaluate Research in Education (Sixth Edition)
Descriptive Statistics:
- Statistics vs. Parameters
- Two fundamental types of numerical data (Quantitative Data and Categorical Data)
- Techniques for summarizing quantitative data (Frequency Polygons, Skewed Polygons, Histograms and Stem-Leaf Plots, The Normal Curve, Averages, Spreads, Standard Scores and the Normal Curve, Correlatin)
- Techniques for summarizing categorical data (The Frequency Table, Bar Graphs and Pie Charts, The Crossbreak Table)
Key Terms:
68-95-99.7 Rule 200, Averages, Bar Graph, Boxplot, Correlation Coefficient, Crossbreak Table/Contingency Table, Descriptive Statistics, Distribution Curves, Eta, Five-Number Summary, Frequency Distribution, Frequency Polygon, Grouped Frequency Distribution, Histogram, Mean, Measures of Central Tendency, Median, Mode, Negatively Skewed, Normal Curve, Normal Distribution, Outlier, Parameter, Pearson Product Moment Coefficient/Pearson r, Percentile, Pie Chart, Positively Skewed, Probability, Quantitative Data, Range, Scatterplot, Standard Deviation, Standard Score, Statistic, Stem-Leaf Plot, T Score, Variability, Variance, z Score
- Statistics vs. Parameters
- Two fundamental types of numerical data (Quantitative Data and Categorical Data)
- Techniques for summarizing quantitative data (Frequency Polygons, Skewed Polygons, Histograms and Stem-Leaf Plots, The Normal Curve, Averages, Spreads, Standard Scores and the Normal Curve, Correlatin)
- Techniques for summarizing categorical data (The Frequency Table, Bar Graphs and Pie Charts, The Crossbreak Table)
Key Terms:
68-95-99.7 Rule 200, Averages, Bar Graph, Boxplot, Correlation Coefficient, Crossbreak Table/Contingency Table, Descriptive Statistics, Distribution Curves, Eta, Five-Number Summary, Frequency Distribution, Frequency Polygon, Grouped Frequency Distribution, Histogram, Mean, Measures of Central Tendency, Median, Mode, Negatively Skewed, Normal Curve, Normal Distribution, Outlier, Parameter, Pearson Product Moment Coefficient/Pearson r, Percentile, Pie Chart, Positively Skewed, Probability, Quantitative Data, Range, Scatterplot, Standard Deviation, Standard Score, Statistic, Stem-Leaf Plot, T Score, Variability, Variance, z Score
Inferential Statistics:
- The logic of inferential statistics (Sampling Error, Distribution of Sample Means, Standard Error of the Mean, Confidence Intervals, Confidence Intervals and Probability, Comparing more than one Sample, The Standard Error of the Difference between Sample Means)
- Hypothesis Testing (The Null Hypothesis)
- Practical vs. Statistical Significance (One- and Two-Tailed Tests, Use of the Null Hypothesis)
- Inference Techniques (Parametric Techniques for Analyzing Quantitative Data, Nonparametric Techniques for Analyzing Categorical Data, Parametric Techniques for Analyzing Categorical Data, Nonparametric Techniques, for Analyzing Categorical Data, Summary of Techniques, Power of a Statistical Test)
Key Terms:
Analysis of Covariance (ANCOVA), Analysis of Variance (ANOVA), Chi-Square Test, Confidence Interval, Contingency Coefficient, Degrees of Freedom, Friedman Two-Way Analysis of Variance, Inferential Statistics, Kruskal-Wallis One-Way Analysis of Variance, Level of Significance, Mann-Whitney U Test, Multivariate Analysis of Covariance (MANCOVA), Nonparametric Technique, Null Hypothesis, One-Tailed Test, Parametric Technique, Power of a Statistical Test, Practical Significance, Probability, Research Hypothesis, Sampling Distribution, Sampling Error, Sign Test, Standard Error of the Difference, Standard Error of the Mean, Statistical Significance, T-Test for a Difference in Proportions, T-Test for Correlated Means, T-Test for Correlated Proportions, T-Test for Independent Means, T-Test for Independent Proportions, Two-Tailed Test, Type I Error, Type II Error, Wilk's Lambda.
- The logic of inferential statistics (Sampling Error, Distribution of Sample Means, Standard Error of the Mean, Confidence Intervals, Confidence Intervals and Probability, Comparing more than one Sample, The Standard Error of the Difference between Sample Means)
- Hypothesis Testing (The Null Hypothesis)
- Practical vs. Statistical Significance (One- and Two-Tailed Tests, Use of the Null Hypothesis)
- Inference Techniques (Parametric Techniques for Analyzing Quantitative Data, Nonparametric Techniques for Analyzing Categorical Data, Parametric Techniques for Analyzing Categorical Data, Nonparametric Techniques, for Analyzing Categorical Data, Summary of Techniques, Power of a Statistical Test)
Key Terms:
Analysis of Covariance (ANCOVA), Analysis of Variance (ANOVA), Chi-Square Test, Confidence Interval, Contingency Coefficient, Degrees of Freedom, Friedman Two-Way Analysis of Variance, Inferential Statistics, Kruskal-Wallis One-Way Analysis of Variance, Level of Significance, Mann-Whitney U Test, Multivariate Analysis of Covariance (MANCOVA), Nonparametric Technique, Null Hypothesis, One-Tailed Test, Parametric Technique, Power of a Statistical Test, Practical Significance, Probability, Research Hypothesis, Sampling Distribution, Sampling Error, Sign Test, Standard Error of the Difference, Standard Error of the Mean, Statistical Significance, T-Test for a Difference in Proportions, T-Test for Correlated Means, T-Test for Correlated Proportions, T-Test for Independent Means, T-Test for Independent Proportions, Two-Tailed Test, Type I Error, Type II Error, Wilk's Lambda.
Statistics in Perspective:
- Approaches to Research
- Comparing Groups (Techniques, Interpretation)
- Relating Variables within a Group (Techniques, Interpretation)
- Comparing Groups: Categorical Data (Techniques, Interpretation)
- Relating Variables within a Group (Categorical Data)
Key Terms:
Correlation Coefficient, Curvilinear Relationship, Effect Size (ES), Inferential Statistics, Linear Relationship, Scatterplot.
- Approaches to Research
- Comparing Groups (Techniques, Interpretation)
- Relating Variables within a Group (Techniques, Interpretation)
- Comparing Groups: Categorical Data (Techniques, Interpretation)
- Relating Variables within a Group (Categorical Data)
Key Terms:
Correlation Coefficient, Curvilinear Relationship, Effect Size (ES), Inferential Statistics, Linear Relationship, Scatterplot.
Experimental Research:
- The Uniqueness of Experimental Research
- Essential Characteristics of Experimental Research (Comparison of Groups, Manipulation of the Independent Variable, Randomization)
- Control of Extraneous Variables
- Group Designs in Experimental Research (Weak Experimental Designs, True Experimental Designs, Quasi-Experimental Designs, Factorial Designs)
- Control of Threats to Internal Validity
- Evaluating the Likelihood of a Threat to Internal Validity in Experimental Studies
- Control of Experimental Treatments
Key Terms:
Comparison Group, Control, Control Group, Counterbalanced Designs, Criterion Variable, Dependent Variable, Experiment, Experimental Group, Experimental Research, Extraneous Variables, Factorial Design, Gain Score, Independent Variable, Interaction, Matching Design, Moderator Variables, Nonequivalent Control Group Design, One-Group Pretest-Posttest Design, One-Shot Case Study Design, Outcome Variable, Pretest Treatment Interaction, Quasi-Experimental Designs, Random Assignment, Randomized Posttest-Only Control Group Design, Randomized Pretest-Posttest Control Group Design, Randomized Solomon Four-Group Design, Random Selection, Regressed Gain Score, Static-Group Comparison Design, Static-Group Pretest-Posttest Design, Statistical Matching, Time-Series Design, Treatment Variable.
- The Uniqueness of Experimental Research
- Essential Characteristics of Experimental Research (Comparison of Groups, Manipulation of the Independent Variable, Randomization)
- Control of Extraneous Variables
- Group Designs in Experimental Research (Weak Experimental Designs, True Experimental Designs, Quasi-Experimental Designs, Factorial Designs)
- Control of Threats to Internal Validity
- Evaluating the Likelihood of a Threat to Internal Validity in Experimental Studies
- Control of Experimental Treatments
Key Terms:
Comparison Group, Control, Control Group, Counterbalanced Designs, Criterion Variable, Dependent Variable, Experiment, Experimental Group, Experimental Research, Extraneous Variables, Factorial Design, Gain Score, Independent Variable, Interaction, Matching Design, Moderator Variables, Nonequivalent Control Group Design, One-Group Pretest-Posttest Design, One-Shot Case Study Design, Outcome Variable, Pretest Treatment Interaction, Quasi-Experimental Designs, Random Assignment, Randomized Posttest-Only Control Group Design, Randomized Pretest-Posttest Control Group Design, Randomized Solomon Four-Group Design, Random Selection, Regressed Gain Score, Static-Group Comparison Design, Static-Group Pretest-Posttest Design, Statistical Matching, Time-Series Design, Treatment Variable.
Single-Subject Research:
- Essential Characteristics of Single-Subject Research
- Single-Subject Designs (The Graphing of Single Subject Designs, The A-B Design, The A-B-A Design, The A-B-A-B Design, The B-A-B Design, The A-B-C-B Design, Multiple Baseline Designs)
- Threats to Internal Validity in Single-Subject Research (Control of Threats to Internal Validity in Single-Subject Research, External Validity in Single-Subject Research: The Importance of Replication, Other Single-Subject Designs)
Key Terms:
A-B Design, A-B-A Design, A-B-A-B Design, A-B-C-B Design, B-A-B Design, Baseline, External Validity, Multiple-Baseline Design, Single-Subject Design.
- Essential Characteristics of Single-Subject Research
- Single-Subject Designs (The Graphing of Single Subject Designs, The A-B Design, The A-B-A Design, The A-B-A-B Design, The B-A-B Design, The A-B-C-B Design, Multiple Baseline Designs)
- Threats to Internal Validity in Single-Subject Research (Control of Threats to Internal Validity in Single-Subject Research, External Validity in Single-Subject Research: The Importance of Replication, Other Single-Subject Designs)
Key Terms:
A-B Design, A-B-A Design, A-B-A-B Design, A-B-C-B Design, B-A-B Design, Baseline, External Validity, Multiple-Baseline Design, Single-Subject Design.
Correlational Research:
- The Nature of Correlational Research
- Purposes of Correlational Research (Explanatory Studies, Prediction Studies, More Complex Correlational Techniques)
- Basic Steps in Correlational Research (Problem Selection, Sample, Instruments, Design and Procedures, Data Collection, Data Analysis and Interpretation)
- What do Correlation Coefficients tell us?
- Threats to Internal Validity in Correlational Research (Subject Characteristics, Location, Instrumentation, Testing, Mortality)
- Evaluating Threats to Internal Validity in Correlational Studies
Key Terms:
Coefficient of Determination, Coefficient of Multiple Correlation, Correlation Coefficient, Criterion Variable, Discriminant Function Analysis, Factor Analysis, Multiple Regression, Partial Correlation, Path Analysis, Prediction, Prediction Equation, Prediction Studies, Predictor Variable, Regression Line, Standard Error of Estimate.
- The Nature of Correlational Research
- Purposes of Correlational Research (Explanatory Studies, Prediction Studies, More Complex Correlational Techniques)
- Basic Steps in Correlational Research (Problem Selection, Sample, Instruments, Design and Procedures, Data Collection, Data Analysis and Interpretation)
- What do Correlation Coefficients tell us?
- Threats to Internal Validity in Correlational Research (Subject Characteristics, Location, Instrumentation, Testing, Mortality)
- Evaluating Threats to Internal Validity in Correlational Studies
Key Terms:
Coefficient of Determination, Coefficient of Multiple Correlation, Correlation Coefficient, Criterion Variable, Discriminant Function Analysis, Factor Analysis, Multiple Regression, Partial Correlation, Path Analysis, Prediction, Prediction Equation, Prediction Studies, Predictor Variable, Regression Line, Standard Error of Estimate.
Causal-Comparative Research:
- What is Causal-Comparative Research? (Similarities and Differences between Causal-Comparative and Correlational Research, Similarities and Differences between Causal-Comparative and Experimental Research)
- Steps Involved in Causal-Comparative Research (Problem Formulation, Sample, Instrumentation Design)
- Threats to Internal Validity in Causal-Comparative Research (Subject Characteristics, Other Threats)
- Evaluating Threats to Internal Validity in Causal-Comparative Studies
- Data Analysis
- Associations between Categorical Variables
- What is Causal-Comparative Research? (Similarities and Differences between Causal-Comparative and Correlational Research, Similarities and Differences between Causal-Comparative and Experimental Research)
- Steps Involved in Causal-Comparative Research (Problem Formulation, Sample, Instrumentation Design)
- Threats to Internal Validity in Causal-Comparative Research (Subject Characteristics, Other Threats)
- Evaluating Threats to Internal Validity in Causal-Comparative Studies
- Data Analysis
- Associations between Categorical Variables
Survey Research:
- What is a Survey?
- Why are Surveys conducted?
- Types of Surveys (Cross-sectional Surveys, Longitudinal Surveys)
- Survey Research and Correlational Research
- Steps in Survey Research (Defining the Problem, Identifying the Target Population, Choosing the Mode of Data Collection, Selecting the Sample, Preparing the Instrument, Preparing the Cover Letter, Training Interviewers, Using an Interview to Measure Ability)
- Nonresponse (Total Nonresponse, Item Nonresponse)
- Problems in the Instrumentation Process in Survey Research
- Evaluating Threats to Internal Validity in Survey Research
- Data Analysis in Survey Research
Key Terms:
Census, Closed-Ended Question, Cohort Study, Contingency Question, Cross-Sectional Survey, Interview Schedule, Longitudinal Survey, Nonresponse, Open-Ended Question, Panel Study, Trend Study, Unit of Analysis.
- What is a Survey?
- Why are Surveys conducted?
- Types of Surveys (Cross-sectional Surveys, Longitudinal Surveys)
- Survey Research and Correlational Research
- Steps in Survey Research (Defining the Problem, Identifying the Target Population, Choosing the Mode of Data Collection, Selecting the Sample, Preparing the Instrument, Preparing the Cover Letter, Training Interviewers, Using an Interview to Measure Ability)
- Nonresponse (Total Nonresponse, Item Nonresponse)
- Problems in the Instrumentation Process in Survey Research
- Evaluating Threats to Internal Validity in Survey Research
- Data Analysis in Survey Research
Key Terms:
Census, Closed-Ended Question, Cohort Study, Contingency Question, Cross-Sectional Survey, Interview Schedule, Longitudinal Survey, Nonresponse, Open-Ended Question, Panel Study, Trend Study, Unit of Analysis.
