PSYC 204 Introduction to Psychological Statistics Lecture Notes PDF

PSYC 204 Introduction to Psychological Statistics Week 1: Introduction to statistics (Ch. 1) 2024-09-03 Dr. Jens Kreitewolf What is this lecture about? Key content from Chapter 1 1. What are statistics? 2. Different types of measurements and variables 3. Different research methods 4. Stat...

PSYC 204 Introduction to Psychological Statistics Week 1: Introduction to statistics (Ch. 1) 2024-09-03 Dr. Jens Kreitewolf What is this lecture about? Key content from Chapter 1 1. What are statistics? 2. Different types of measurements and variables 3. Different research methods 4. Statistical notation PSYC204 – Introduction to Psychological Statistics 2 What are statistics? Book says: “set of mathematical procedures for organizing, summarizing, and interpreting information” PSYC204 – Introduction to Psychological Statistics 3 Statistics: What is it good for? You need statistics... …to pass the exam …for your research project/thesis …to assess the quality of scientific studies …if you want to work in research …for what else? PSYC204 – Introduction to Psychological Statistics 4 Some real-life examples Statistics are used to predict important outcomes and make decisions about many things in your everyday life This week’s weather Political elections How likely you are to wreck your car (car insurance price) Can you think of other examples? PSYC204 – Introduction to Psychological Statistics 5 Some real-life examples Statistics are used to predict important outcomes and make decisions about many things in your everyday life ast to he p This week’s weather to u se t Political elections we r rror e p o r e* ! *with e How likely you are toowreck u h t yourfcar u tu i ve y th e (car insurance sg price) ict i sti c pred Stat Can you think of other examples? PSYC204 – Introduction to Psychological Statistics 6 Some Basic Terms Population: The entire group of individuals is called the population. Sample: PSYC 204 PSYC students 204 Students in the A smaller group selected from Discussion the population. Group 1 PSYC204 – Introduction to Psychological Statistics 7 Some Basic Terms Variable: is a characteristic or condition that can change or take on different values. PSYC 204 Data (pl.): PSYC students 204 Students in the Discussion The measurements obtained in a Group 1 research study are called the data. PSYC204 – Introduction to Psychological Statistics 8 PSYC204 – Introduction to Psychological Statistics 9 Descriptive Statistics Descriptive statistics are methods for organizing and summarizing data. A descriptive value for a population is called a parameter and a descriptive value for a sample is called a statistic. PSYC204 – Introduction to Psychological Statistics 10 Example: Time Zone Data (last semester) What time zone are you in? PSYC204 – Introduction to Psychological Statistics 11 Example: Time Zone Data (from previous semester) 244/404 students filled out the survey These data are just a sample from the population of students in the class. 3% were in UTC +8, is that a parameter or a statistic? PSYC204 – Introduction to Psychological Statistics 12 Descriptive Statistics Descriptive statistics are methods for organizing and summarizing data. A descriptive value for a population is called a parameter and a descriptive value for a sample is WholePSYC PSYC204 students 204 Class who called a statistic. answered = time zone survey Parameter What information would I = statistic need to get the population parameter? PSYC204 – Introduction to Psychological Statistics 13 Inferential Statistics Inferential statistics are methods for using sample data to make general conclusions (inferences) about populations. PSYC 204 students who Whole PSYC 204 answered time Class zone survey PSYC204 – Introduction to Psychological Statistics 14 Sampling Error The discrepancy between a sample statistic and its population parameter is called sampling error. PSYC 204 students who Whole PSYC 204 answered time Class zone survey PSYC204 – Introduction to Psychological Statistics 15 PSYC204 – Introduction to Psychological Statistics 16 Descriptive & Inferential Statistics —Comparison Descriptive statistics Inferential statistics Summarize data Study samples to make Organize data generalizations about the Simplify data population Interpret experimental data Familiar examples Tables Common terminology Graphs “Margin of error” Averages “Statistically significant” PSYC204 – Introduction to Psychological Statistics 17 Learning Check 1 A researcher is interested in the effect of amount of sleep on high school students’ exam scores. A group of 75 high school boys agree to participate in the study. The boys are _____. A. A statistic B. A variable C. A parameter D. A sample PSYC204 – Introduction to Psychological Statistics 18 Types of Variables Discrete variable Has separate, indivisible categories No values can exist between two neighboring categories Continuous variable Has an infinite number of possible values between any two observed values Is divisible into an infinite number of fractional parts PSYC204 – Introduction to Psychological Statistics 19 Types of Variables Whether a variable is discrete or continuous also depends on how we measure it… PSYC204 – Introduction to Psychological Statistics 20 Real Limits of Continuous Variables Because continuous variables can be subdivided again and again, we need limits: Real limits are the boundaries of each interval representing scores measured on a continuous number line. PSYC204 – Introduction to Psychological Statistics 21 Example: What whole number would 149.6 or 150.3 be assigned? PSYC204 – Introduction to Psychological Statistics 22 Example: What whole number would 149.6 or 150.3 be assigned? PSYC204 – Introduction to Psychological Statistics 23 Measuring variables and scales Measurement assigns individuals or events to categories The categories can be names such as introvert/extrovert or employed/unemployed (qualitative data) They can be numerical values such as 68 inches or 175 pounds (quantitative data) The categories used to measure a variable make up a scale of measurement Relationships between the categories determine different types of scales PSYC204 – Introduction to Psychological Statistics 24 Measuring variables and scales 1. A nominal scale is an unordered set of categories identified only by name. Nominal measurements only permit you to determine whether two individuals are the same or different. 2. An ordinal scale is an ordered set of categories. Ordinal measurements tell you the direction of difference between two individuals. 3. An interval scale is an ordered series of equal-sized categories. Interval measurements identify the direction and magnitude of a difference. The zero point is located arbitrarily on an interval scale. The ZERO doesn’t mean NONE of the quantity – What is an example of this? 4. A ratio scale is an interval scale where a value of zero indicates none of the variable. Ratio measurements identify the direction and magnitude of differences and allow ratio comparisons of measurements. PSYC204 – Introduction to Psychological Statistics 25 Measuring variables and scales Nominal Ordinal Interval Ratio 2 1 3 =≠ = ≠, < > = ≠, < >, + - = ≠, < >, + -, * / PSYC204 – Introduction to Psychological Statistics 26 Measuring variables and scales Nominal Ordinal Interval Ratio Can you think of other examples? 2 1 3 =≠ = ≠, < > = ≠, < >, + - = ≠, < >, + -, * / PSYC204 – Introduction to Psychological Statistics 27 Learning Check 2 A study assesses the optimal size (number of members) for study groups. The variable size of group is _____. A. Discrete and interval B. Continuous and ordinal C. Discrete and ratio D. Continuous and interval PSYC204 – Introduction to Psychological Statistics 28 Research Methods Descriptive research (individual variables) One (or more) variables measured per Example: Fluffiness of cats individual Statistics describe the observed variable May use categorical and/or numerical variables Not concerned with relationships between variables PSYC204 – Introduction to Psychological Statistics 29 Research Methods The correlational method One group of participants Measurement of two variables for Example: Fluffiness and Grooming each participant The goal is to describe type and magnitude of the relationship Patterns in the data reveal relationships Nonexperimental method of study PSYC204 – Introduction to Psychological Statistics 30 Research Methods The correlational method Can demonstrate the existence of a relationship between two variables Does not provide an explanation for the relationship Most importantly, does not demonstrate a cause-and-effect relationship between the two variables PSYC204 – Introduction to Psychological Statistics 31 Research Methods The experimental method Goal is to demonstrate a cause-and- effect relationship between two variables Group 1 Group 2 Manipulation: The level of one (control) (treatment) variable is determined by the experimenter Control rules out influence of other variables PSYC204 – Introduction to Psychological Statistics 32 Research Methods Methods of control – Random assignment of subjects – Matching of subjects – Holding the level of some potentially influential variables constant Control condition Group 1 Group 2 – Individuals do not receive the experimental (control) (treatment) treatment – They either receive no treatment or they receive a neutral, placebo treatment – Purpose: to provide a baseline for comparison with the experimental condition Experimental condition – Individuals do receive the experimental treatment PSYC204 – Introduction to Psychological Statistics 33 Research Methods Important Terminology: Independent variable (IV): the variable that is manipulated by the researcher Group 1 Group 2 Dependent variable (DV): the IV: (control) (treatment) one that is observed to assess the effect of treatment DV: Fluffiness PSYC204 – Introduction to Psychological Statistics 34 Other Types of Studies Other types of research studies, know as non-experimental or quasi- experimental, are similar to experiments because they also compare groups of scores. These studies do not use a manipulated variable to differentiate the groups. Instead, the variable that differentiates the groups is usually a pre-existing participant variable (such as male/female) or a time variable (such as before/after). Because these studies do not use the manipulation and control of true experiments, they cannot demonstrate cause and effect relationships. As a result, they are similar to correlational research because they simply demonstrate and describe relationships. PSYC204 – Introduction to Psychological Statistics 35 Learn Check 3 Researchers observed that students’ exam scores were higher the more sleep they had the night before. This study is _____. A. Descriptive B. Experimental comparison of groups C. Non-experimental group comparison D. Correlational PSYC204 – Introduction to Psychological Statistics 36 Learn Check 4 Stephens, Atkins, and Kingston (2009) found that participants were able to tolerate more pain when they shouted their favorite swear words over and over than when they shouted neutral words. For this study, what is the independent variable? a. The amount of pain tolerated b. The participants who shouted swear words c. The participants who shouted neutral words d. The kind of word shouted by the participants PSYC204 – Introduction to Psychological Statistics 37 Statistical Notation Statistics uses operations and notations you have already learned (Appendix A has a Mathematical Review) The individual measurements or scores obtained for a research participant will be identified by the letter X (or X and Y 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. PSYC204 – Introduction to Psychological Statistics 38 Statistical Notation Summing a set of values is a common operation in statistics and has its own notation. The Greek letter sigma, Σ, will be used to stand for "the sum of." For example, ΣX identifies the sum of the X scores. PSYC204 – Introduction to Psychological Statistics 39 Order of Operations 1. All calculations within parentheses (brackets) 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. PSYC204 – Introduction to Psychological Statistics 40 Learning Check 5 ΣX ! + 47 instructs you to _____. A. Square each score and add 47 to it, then sum those numbers B. Square each score add up the squared scores, then add 47 to that sum C. Add 47 to each score, square the result, and sum those numbers D. Add up the scores, square that sum, and add 47 to it PSYC204 – Introduction to Psychological Statistics 41 Thank you for your attention!