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# Week 1: Introduction to Statistics psy 3234

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This 5 page Class Notes was uploaded by Laura Castillo on Friday September 9, 2016. The Class Notes belongs to psy 3234 at Florida Atlantic University taught by Joseph Salvatore in Fall 2016. Since its upload, it has received 90 views. For similar materials see Exp Design and Stat Inference in Psychology at Florida Atlantic University.

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Date Created: 09/09/16

Introduction to Statistics 09/08/2016 ▯ Statistics, science, and observations What is Statistics? o Statistics is a set of procedures in math that are used to summarize, organize, and interpret information. o Psychologists use statistics for 2 general purposes: 1. organize and summarize info (usually a large amount) 2. Help researchers answer questions about human behavior ▯ ▯ Populations vs Samples What are populations and samples? o Psychological research begins with a question about a group or groups of people. Ex: Does self-esteem in college students lead to drinking? o Population: the entire set of individuals of interest in a particular study. Populations should ALWAYS be defined by the researcher first. o Normally impossibly to study a whole population of interest, so the researcher selects a sample of the population. o Sample: a set of individuals in a population that are selected for a study. The goal is to take the results of the study done on the sample and generalize it back to the population. What information does the population and sample provide researchers with? o Researchers are interested in behaviors, traits, and characteristics of certain populations, which can vary from one individual to another. These are called variables. o Variables: a condition or characteristic that changes or has different values for different individuals. Ex: Hair color, eye color, height, weight, age, environment, weather, sex, etc. To be able to examine or show the changes in variables, individual scores, or raw scores, need to be collected. (aka datum) o Data: the complete set of scores of measurements or observations. Parameters o Parameters: A characteristic that describes a population o Statistic: A characteristic that describes a sample Ex: The average score on a particular variable for a sample Types of Statistics o There are 2 general categories: 1. Descriptive Statistics: Statistical procedures that summarize and simplify data. 2. Inferential Statistics: Techniques that allow us to study samples and make generalizations about the population from which it was selected. Sampling Error o One of the problems with using samples? It provides limited information about the whole population. Not expected to give a perfect picture of the population. o Sampling Error: The amount of error that exists between a sample statistic and the corresponding population parameter. The characteristics of a sample depend on the people in the sample. Samples vary, so they’re going to be different from the population. That difference is the sampling error. ▯ Data Structures, Research Methods, and Statistics Levels of research o Occurs on 2 levels: Conceptual Level: refers to the abstract concepts that are relevant to the theory. Operational Level: refers to the way abstract concepts are explained in the research. Process of research 1. Theory 2. Hypothesis (operational definition) 3. Test hypothesis 4. Reject/support theory, retest with new operational definitions. o A theory may be correct on the conceptual level, even if it was disconfirmed on the operational level. Methods of Research o Correlational Method Studies the relationship between two or more variables Observational methods do not indicate the direction of a relationship, they only indicate if and what variables are related. o Experimental Method Has 3 components that allows a research to assume the direction of causation. Has an advantage over the observational method, but there are rules: a. Manipulate independent variable and measure the dependent variable. This fixes the direction from independent variable to dependent variable Independent Variable: variable that is manipulated by the researcher. Dependent Variable: variable that is being studied to see how changes in the independent variable change it. Control Condition: the condition that is not to be affected at all by the independent variable. Experimental Condition: conditions that are being treated by the experiment, aka being affected definitely by the independent variable. b. Random Assignment of Participants to Condition Means that all participants in the study have an equal chance of being placed in the different categories of the study. Gives us the ability to assume that individual differences between participants are randomly spread out among the categories of the study. c. Control Extraneous Variables An extraneous variable is one that is not the independent variable but can still affect the dependent variable. Ways to manage extraneous variables o Hold the EV constant All participants receive the same level of the EV. o Systematically vary the EV If it is a variable of interest, then it can be manipulated in such a way that the EV is used in addition to the IV. Relation Between Statistics, Methods of Research, and Causal Inference o Inferring causal inference depends entirely on the method with which the researcher gathers information. o Statistics only show whether the variables are related and does not inform us if the variables are causally related. The way the experiment is designed does. ▯ Variables and Measurement Discrete and Continuous Variables and Real Limits o Two types of variables: Discrete Variable: distinct categories that have no values between the neighboring categories. Ex: There can be 3, 4, or 5 children, but there can’t be 4.5 children. Continuous Variable: has infinite values in between the neighboring values. Ex: There’s an infinite possibility of values between 5 and 6 seconds. However, when you measure a continuous variable, it appears to give us a discrete value. This is because continuous variables exist on an interval. In order to remind us that continuous variables exist on an interval, we use the concepts of Real Limits. Real Limits: boundaries that divide intervals and the limits are located half way between the scores. Ex: If your score is 5.4, your upper real limit is 5.45 and your lower real limit is 5.35 Scales of Measurements o 4 scales of measurement used to quantify observations 1. Nominal Scale: observations are labeled into categories. Ex: hair color, sex, sport, fruit, etc. 2. Ordinal Scale: An ordered series of categories that are ranked Ex: rank your preference of fruit This scale does not indicate the difference between the categories. Ex: Does the difference between your preference for apples and oranges the same as your preference for apples and bananas? 3. Interval Scale: An ordered series of categories with equal intervals between categories. Ex: farenheight, rating of fruit on a 10 pt scale. The difference between 5 and 10 is the same as the difference between 10 and 15 Doesn’t have a true zero point. Aka there’s no way to measure the true absence of a phenomenon Ex: 0 degrees farenheight doesn’t mean there’s no temperature. 4. Ratio Scale: An ordered series of categories with equal intervals and a true zero point. Ex: A researcher measures the weight of 5 puppies: 7lbs, 12lbs, 20lbs, 25lbs, 34lbs. This is a ratio scale and there is a true zero. ▯ Statistical Notation Raw Scores: the actual and unchanged score by the individual. Ex: each person’s weight. o The score for a particular variable are listed as the letter X o When 2 variables are studied, the second variable is known as Y. o Each pair of values represents the value for the participant. o N is used to represent the number of scores in a population. o n is used to represent the scores of a sample Ex: n = 3 if there are 3 participants in a sample for X and Y o Σ (sigma): the symbol to represent the sum of scores. The expression ΣX= the sum of the scores for X. Ex: Scores for X = 2, 3, 4. ΣX= 2 + 3 + 4 = 9. Two important notes: The Σ is always followed by a symbol or a mathematical expression which identifies exactly values are to be added, or summed. Sometimes the mathematical expression will be more complicated than just X. Ex: Σ(X-1) 2 When the summation process involves more complex procedures, remember the correct order of operations (PEMDAS: Please Excuse My Dear Aunt Sally) i. P: Parentheses ii. E: Exponents (squaring/cubing) iii. M/D: Multiplication or division, whichever comes first iv. A/S: Addition or subtraction, whichever comes first v. Σ: summation

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