Handout One: Quantitative Research Methodology-Question, Design, Data, Analysis, & Inference EPSE 592 Experimental Designs and Analysis in Educational Research Instructor: Dr. Amery Wu

Learning Strategies for Successful Outcomes Contextualizing through preview Building through mastery Digesting by slicing Consolidating by review and application Internalizing through communication

Research Question Give me a research question of your Interest. Contextualizing Learning by a Research Example Give me a research question of your Interest.

What is “Data”? “Data” is originally a Latin noun meaning “something given.” Today, the word data is used in English as a plural noun meaning “facts or pieces of information”. In statistics, data is conceived of as information given, observed, or obtained.

Types of Data Continuous data (numerical or quantitative data) refer to the information indicated by numbers that represent the amount of the studied phenomenon. Categorical data (discrete or qualitative data) refer to the information indicated by numbers or symbols that represent the type of the studied phenomenon, where the types can be ordered (ordinal) or disordered (nominal).

A Plan for Data Collection What is Research Design? A Plan for Data Collection A plan of what type of data to gather, from whom, how and when to collect the data, and how to analyze the obtained data in order to answer the research questions, hence making intended inferences.

Types of Research Design Experimental (clinical trials): typically used when the intended inference is uni-directional and causal, e.g., smoking causes lung cancer. Observational (correlational, survey): typically used when the intended inference is dual-directional and relational, e.g., smoking is related to lung cancer. With observational data, some particular conditions must be met in order to make directional or causal inferences.

Modeling the Data (Statistical Analysis) Data = Model + Residual Types of Modeling Describing or summarizing: uncovering the data pattern hidden in one single variable of interest, no other variables are involved to explain/predict the pattern (e.g., central tendency and dispersion of income). Explaining or predicting: explaining and predicting the outcome (response, dependent) variable using other variable(s) (e.g., t-test, odds ratio, ANOVA, multiple regression).

Q: Are the following statistical techniques type 1) or 2) Models? correlation contingency table (chi-square table) percentage ranks percentile mean variance t-test Median mode

Data

Model Data Fit Data Model Residual = + 9 1 8 = + 10 6 4 = + 5 7 -2 = + • • • 5 7 -2 = + Since the data is given, a statistician’s task is to, within the availability of data, maximize the fit between the model and data, which is equivalent to minimize the residual (because of the additive property)

Descriptive vs. Inferential Types of Statistical Inferences Causal vs. Relational Causal inference entails the claim about the direction between variables, i.e., cause→ effect, IV →DV, or factor →outcome. In a manipulationist view, causal relationship is conceptualized as “change in the IV leading to change in the DV.” experimental design/data is often required. Relational inference is the claim about the bi-directional relationship/association between observational data. Descriptive vs. Inferential Descriptive inference is claims made about the given sample. Inferential inference is claims made about the target population based on the given sample using hypothesis testing technique.

Activity Classify the following statistical methods into one of the four categories (A-D) Mode Percentage Two-tailed correlation test Correlation Chi-square test Variance Histogram ANOVA One-sample t- test Percentile Two-sample t-test Ranks Simple regression Mean Skewness Bar chart

Activity Place each of the research elements listed below in one of the boxes next to the vertices of the pentagon, draw lines (connecting vertices) and arrows to explain the relationships among these concepts. Note that the terms are not ordered. Research Design Data Inference Statistical Analysis Research Question

What Do Statisticians/Methodologist Do? Ask questions: formulating good and researchable questions Design: participating in research design to make sure data obtained is valid for answering the research question (intended inferences) Model: using statistical techniques to describe, summarize, explain or predict data Communicate: clearly and accurately disseminating the research results and their implications to the stakeholders and audience.