Two Halves to Statistics Descriptive statistics: Numbers and calculations which help to describe, characterize, or summarize features/characteristics of data. Inferential statistics: Numbers and calculations which use sample data to predict the true population data. Allows us to draw inferences about what the descriptive statistics mean. Both halves use data. Data: measurements or observations. Typically these are numeric. What is the singular form of data? Datum! Also called a “score” or a “raw score.”

Descriptive Statistics Numbers and calculations which help to describe, characterize, or summarize features/characteristics of data. Typically, these are presented graphically, in tables, or as summary statistics. Examples: Median age in Merced County is 28. Average household size in Merced, CA is 3.18 people. 48.5% of the undergrad population at UCM is male.

Inferential Statistics Main point of statistics: To get useful information that can be used for scientific purposes, policy purposes, etc. In doing so, we are interested in properties of a population of interest. Population: A set of all individuals, items, or groups of interest to scientists, policy-makers, etc. Example: All people in the US. The United States Census. All students at UC Merced.

Inferential Statistics In real life, we do not know the true characteristics of a population of interest, so we collect data. Ideally, we’d collect the data from everyone in the population of interest! This is almost always impossible or at least highly impractical. Instead, we collect data from a sample and infer something about the population of interest by analyzing the data from the sample.

Inferential Statistics Sample: A set of selected individuals, items, or data taken from the population of interest. Example: How to sample from all people in the US? Randomly calling people in the US! How to sample from all students at UC Merced? Stand outside the library and ask questions of passersby. Pick a class and ask questions of those in the class… like this one!

Inferential Statistics Some other definitions: The characteristics of a population we are interested in are called population parameters. Example: Proportion of Europeans suffering from depression. Mean weight of teenagers in the US. Since we often do not have a full population of data, we get at it through a sample. The sample version of a parameter is called a sample statistic. Proportion of people in our sample of Europeans suffering from depression. Mean weight of those in our sample of US teenagers. The sample statistic is an estimate of the population parameter. More on this will be discussed later in the semester.

Research Methods Ultimately, statistics is a toolbox in the workshop of a scientist. What is science? Science: A systematic study of relationships through strict observation, evaluation, interpretation, and theoretical explanation. Three kinds of research methods we will talk about: Experimental Quasi-experimental Correlational Each kind of research method use different tools in the statistics toolbox.

Research Methods Experimental method – cause-effect analyses To truly determine cause-and-effect relationships, conditions underlying the study must be carefully controlled. Three requirements for an experiment: Randomization Manipulation Comparison

Research Methods Randomization: Manipulation: Comparison: This refers to randomly assigning participants to conditions. Manipulation: This refers to systematically manipulating variables in the experiment. Comparison: This refers to comparing the experimental group (or groups) to what is called a control group.

Research Methods When designing an experiment, several features must be defined and put into their respective contexts. The very first thing we do when designing an experiment is to define the topic of interest. A usual situation would be one where the researcher is interested in determining if one thing (X) causes another thing (Y). To do this, a researcher would set up conditions designed to assess if: X causes Y not-X does not cause Y.

Research Methods Experimental method – cause-effect analyses Research Question: the question of interest Example: Did the IV (Type of Teaching Method) cause a difference in the DV (Reading Achievement Scores)? Independent Variable (IV): a variable that is manipulated; the proposed cause. Also called an input variable. Example: New or Traditional Teaching Method Experimental Group: the group exposed to IV Example: New Teaching Method Control Group: the group not exposed to IV Example: Traditional Teaching Method

Research Methods Experimental method – continued Random assignment: participants have an equal chance of being assigned to groups; renders groups equivalent Example: students are randomly assigned via random number generator to a class. Dependent Variable (DV): a variable that is measured; the proposed effect. Also called an outcome variable. Example: exam performance for the students. Operational definition: describes specifically how DV is measured Example: exam performance is specifically defined as a score between 0 and 100 on a test.

Research Methods Quasi-experimental method It is very similar to the experimental method with one key difference. The independent variable is either non-manipulated, non-random, or lacks a control group. Example: Do boys and girls (IV) differ in number of aggressive behaviors (DV)? Why is this a quasi-experiment? Example: Are there differences between the PSY 10 labs in test scores?

Research Methods Correlational method - analyses for prediction Quantifies the strength and direction of a relationship between two (or more) variables X = the predictor; Y = the criterion There is no manipulation Variables measured as they naturally occur Lack of random assignment Typically, the “predictor” happens before the “criterion.” This doesn’t have to hold, because the variables may be measured at the same time. If it doesn’t hold, there should be a theory for why one variable is the predictor and the other is the criterion. Example: What is the relationship between SAT scores and freshman college GPA? What is the predictor here? What is the criterion?

Measurement Measurement is the assignment of numbers (or other symbols) to characteristics (or objects) according to certain pre-specified rules. One-to-one correspondence between the numbers and the characteristics being measured. The rules for assigning numbers should be standardized and applied uniformly. Rules must not change over objects or time.

Scales of Measurement More simply, we can think of these as types of variables. We can think of these as the degree to which measured variables conform to the usual abstract number system Includes: identity, order, equal distance, and absolute zero The reason this is important is because it determines the type of statistical analyses that are possible.