Lesson 1 Introduction to Statistics Psychology • Scientific Study of • Affect: Feelings • Behavior: Observable; what people do • Cognition: Thoughts • SCIENCE OF BEHAVIOR Theory • Empiricism • Direct observation • Systematic, careful • Surveys, naturalistic observation, etc. • Observation and Measurement are two components of empiricism that we use in psychology Three General Principles Three General Principles of Science 1.Prediction: We only accept explanations that have been shown to successfully predict behavior. Three General Principles Three General Principles of Science 2.Replication: We must be able to replicate (confirm) the findings—another person should be able to do the exact same research. Three General Principles Three General Principles of Science 3.Self-correction: Science is self-correcting; there should never be anything hidden from the public or other researchers. Science changes over time. Psychology changes over time. Psychology Journals • Most recent research • Frequently published • Specific topics • Peer-review process • Systematic format Psychology Journals Four basic parts of journal articles: 1. 2. 3. 4. Introduction Method Results Discussion Journal Articles: Introduction • Describes a research question • Introduces the theory we are testing • We do not study people • We study variables Variables • A variable is a characteristic or condition that can change or take on different values. • Research: The detection and interpretation of relationships between variables. Correlations • Covariation: Co (together) + Variation (changing) • Correlation: Co (together) + Relation (connection; association) • Outside temperature and electric bill Correlations • Academic performance • Positive correlation between study time and GPA • As one variable increases, so does the other • Negative correlation between alcohol consumption and GPA • As one variable increases, the other decreases • Study time and alcohol consumption related to academic performance Correlations • Correlation ≠ Causation! • We know there is a relationship, but we do not know which variable is causing the other • A theory is an attempt to explain why a relationship exists • Cause and effect • Must be further tested Correlations • Does alcohol consumption cause grades to suffer? • Alcohol = cause • Academic performance = effect • This is only ONE possible explanation • Relationship could be in opposite direction • Or third variable causing both Journal Articles: Introduction • To recap • Describe research that has been conducted • Relationships between variables • Describe theory (cause and effect) and how it was developed • Justify why the theory is a reasonable possibility Journal Articles: Method • How did we test the theory? • Participants • Materials • Procedure Method: Participants • Describe the people we studied • Population = group of interest • Sample = subset of population Population • The entire group of individuals is called the population. • Group theory applies to • Defined by researcher • Does not refer to people in a specific geographic area Sample • A sample is selected to represent the population in a research study. • The goal is to use the results obtained from the sample to help answer questions about the population. • Two defining characteristics of a sample: 1. Everyone comes from population of interest 2. People we actually observe and measure Method: Participants • In this section of Method – We report demographic information (subject characteristics) • Averages, etc. Descriptive Statistics 1. Organize observations 2. Summarize observations Descriptive Statistics • Statistics – Descriptive numbers from a sample – Representative sample is important • Parameters – Descriptive information for a population A statistic is an estimate of a parameter. Method: Materials • How will we measure our variables? Measurement • Turning human experience into numbers—forces objective observation • Our theory is based on constructs • Concepts that can’t be observed directly • Operational definitions • Defining variables in terms of the operations used to measure it or manipulate them • Defining something by how it is quantified Measurement • The process of measuring a variable requires a set of categories called a scale of measurement and a process that classifies each individual into one category. Measurement • Discrete variables (such as class size) consist of indivisible categories • Categorical • Continuous variables (such as time or weight) are infinitely divisible into whatever units a researcher may choose. • Exists along a continuum, as the name implies Real Limits • To define the units for a continuous variable, a researcher must use real limits which are boundaries located exactly half-way between adjacent categories. 4 Types of Measurement Scales 1. A nominal scale is an unordered set of categories identified only by name. 2. An ordinal scale is an ordered set of categories. 4 Types of Measurement Scales 3. An interval scale is an ordered series of equal-sized categories. No true zero point. 4. A ratio scale is an interval scale where a value of zero indicates none of the variable. Allows for ratio comparisons of measurements. Discrete Continuous Nominal (qualitative) Ordinal Interval Ratio Gender Class ranking n/a Number of children Favorite Color XS, S, M, L, XL Handedness Degree obtained Religion No, Maybe, Yes Number of people sleeping in stats class Political party Place in race (only integer values) SSN Letter grades n/a (Ordinal variables are created based on continuous data; the resulting variables are discrete, though they measure a continuous construct) Number of kittens in a litter Temperature in F or C Time on clock Scales designed with equal intervals (some debate about whether attitude scales are truly interval or actually ordinal) Temperature in Kelvin Height Distance Speed Time passed Income earned Method: Procedures • Hypothesis à specific prediction • Hypothesis ≠ Theory • Theory à broader concept Correlational Studies • Is there a relationship between two variables? • What is the nature of this relationship? • Simply observes the two variables as they exist naturally. Experiments • The goal is to demonstrate a cause-and-effect relationship between two variables. • One variable is manipulated while another variable is observed and measured. Experiments • Manipulated variable à independent variable • Observed (measured) variable à dependent variable Experiments • Two defining characteristics: 1. The independent variable is manipulated • • Example: Does exercise improve cognitive abilities? Example: Does crowd size affect conformity? Experiments • Two defining characteristics: 1. The independent variable is manipulated 2. Controlled conditions • • Extraneous variables ~ other variables present in the study that are not of interest to the researcher Confound ~ occurs when extraneous variables are not equally distributed across conditions Experiments • Two categories of extraneous variables: • Environmental variables • Participant variables Experiments • How do we control individual differences? 1. Never study individuals; study groups 2. Experimental vs. control group 3. Random assignment à Every person has an equal chance of being part of either group Quasi-experiments • Quasi-experimental studies also compare scores from different groups. • No manipulated variable to differentiate groups (not ‘real’ experiments). • Variable that differentiates groups is usually a preexisting participant variable (such as male/female) or a time variable (such as before/after). Journal Article Recap • Introduction • Research question • Do energy drinks affect cognitive performance? • Population • College students • Method (Participants) • Sample • From population of interest (college students) Journal Article Recap • Method (Materials) • Energy drinks • Introductory statistics exam • Method (Procedure) • Independent variable à Energy drinks • Experimental group (energy drink) vs. Control group (no drink) • Dependent variable à Cognitive performance • Operational definition is score on intro stats exam Results Section • Results • If theory is correct, two groups should differ on DV • If energy drinks affect performance, the scores on the statistics test should be different for the experimental vs. control group • Sounds like a simple question… Data • The measurements obtained in a research study are called the data. • The goal of statistics is to help researchers organize and interpret the data. Descriptive Statistics • Descriptive statistics are methods for organizing and summarizing data. • Tables • Graphs • Averages Inferential Statistics • Inferential statistics • sample data à general conclusions (inferences) about populations Sampling Error • Discrepancy between sample statistic and its population parameter à sampling error • The amount of difference between a statistics and its corresponding population parameter Sampling Error • Error ≠ mistake! • Error is a reflection of how different our statistic is from the parameter • Mathematical concept of error • Here’s the “kicker” • Because we rarely (if ever) know the true parameter, we never really know how much sampling error we have Sampling Error • Implications 1. Samples are never identical to the population they come from. 2. Two samples from the same population will yield different results. • Sampling error is always present • • Can’t eliminate it Can minimize it Sampling Error • Minimize 1. Representative sample/random selection • This is the ideal • Easier said than done 2. Sample size • Bigger = better Results Section • We know that the results will never be perfect • We are never 100% certain about what we learned • We can never “prove” anything • Statistics, in psychology, are based on probability, never certainty • In general, we have to be at least 95% certain about our results • Some results are incorrect, but we may not know which ones… Energy Drinks (3 pt. margin of error) Energy Drinks (5 pt. margin of error) Discussion Section • Summarize results* – The group that received an energy drink (did vs. did not) score significantly higher on the exam • Explain what the results mean* – Energy drinks (do vs. do not) improve academic performance • Implications • Future research – Improvements – New questions *we will be doing a lot of this! A few notes about Notation • Individual measurements or scores obtained will be identified by the letter X (or X, Y, Z, etc. if there are multiple scores for each individual). • The number of scores in a data set will be identified by N for a population or n for a sample. • The Greek letter sigma, Σ, will be used to indicate "the sum of." • For example, ΣX identifies the sum of the scores. Order of Operations Review (PEMDΣAS) 1. All calculations within parentheses are done first. 2. Squaring or raising to other exponents is done second. 3. Multiplying, and dividing are done third, and should be completed in order from left to right. 4. Summation with the Σ notation is done next. 5. Any additional adding and subtracting is done last and should be completed in order from left to right.
