Psychological Statistics Lecture Notes PDF

Nueva Ecija University of Science and Technology College of Arts and Sciences MATHEMATICS AND SCIENCES DEPARTMENT Psy 102 – Psychological Statistics  LESSON OBJECTIVES: At the end of the lesson, the students are expected to: ü Familiarize with the basic concepts, meanin...

Nueva Ecija University of Science and Technology College of Arts and Sciences MATHEMATICS AND SCIENCES DEPARTMENT Psy 102 – Psychological Statistics  LESSON OBJECTIVES: At the end of the lesson, the students are expected to: ü Familiarize with the basic concepts, meaning, nature and importance of statistics; ü Distinguish type of data and levels of measurement; ü Identify type of variable given a research problem  Introduction The term statistics may have different meanings to different people. A psychologist for example who investigates an intervention program to help reduce anxiety and depression, statistics are used as evidence of the effectiveness of the program. To an appliance store manager, statistics may refer to the brand of electric fan or refrigerator most consumers buy. To a school principal, statistics are information regarding increase or decrease in school enrolment, faculty salary, dropout rate and absenteeism. To a college student, statistics are his scores on quizzes, exams and assignments. While they use it in different ways and purposes, they are all using statistics correctly.  Statistics as a Tool in Research STATISTICS – the science/methods of collecting, presenting, analyzing and interpreting data. When you collect data, you utilize questionnaires, interviews, tests, observations and experiments. When you present data, you organize data in the forms of tables, graphs or charts. When you analyze data, you extract relevant significant information from the gathered data. Lastly, when you interpret data, you draw conclusions or inferences. Statistics may be divided into two broad categories – descriptive and inferential statistics.  Statistics as a Tool in Research Descriptive statistics is concerned with summary calculations. It largely involves gathering, classification and presentation of data. Examples: class average of examination, average salary, range of family income, percentage of students who obtained a grade higher than 90  Statistics as a Tool in Research Inferential statistics involves making inferences, estimates or predictions about a large set of data (called a population) using the information gathered from a smaller set of data (called a sample). Aside from providing a description of a particular data set, predictions and inferences are also made. Examples: t-test, correlation and regression analyses, analysis of variance (ANOVA), and non- parametric tests such as chi-squares. In statistics, the descriptive measure of the population is called a parameter while a descriptive measure of a sample is called statistic.  Variables and Measurement Variables are the characteristics or conditions that the experimenter manipulates, controls or observes. It is the characteristic or attribute of the person or objects, which assumes different values (numerical/quantitative) or labels (qualitative). The process of assigning the value or label is called measurement.  Variables and Measurement Independent variable – variables that (probably) cause, influence, or affect outcomes. It is also called treatment, manipulated, antecedent or predictor variable. Dependent variable – variables that depend on the independent variables. They are the outcomes or results of the influence of the independent variable. It is also called criterion, outcome or effect variable.  Variables and Measurement Example: Do anxious students get lower scores on the test? Anxiety Test Scores (Independent) (Dependent)  Variables and Measurement Moderating variable – variables that influence the direction and/or magnitude of the relationship between the independent and the dependent variable. Example: Do anxious students get lower scores on the test, whether they have low or high IQ? (i.e. Students who are anxious have lower test scores, only for those with low IQ, but not with high IQ).  Variables and Measurement Anxiety Test Scores (Independent) (Dependent) IQ (Moderator)  Variables and Measurement Mediating variable – “stand between” variable. The variable that explains the relationship between the independent and the dependent variable. Example: Does effort mediate or explain why anxious students get lower scores on the test? (i.e. If students are anxious, they will not exert effort in studying, and this will lead to lower scores)  Variables and Measurement Anxiety Test Scores (Independent) (Dependent) Effort (Mediator)  Variables and Measurement Control variable – a special type of independent variable that is measured in a study because it potentially influence the dependent variable Example: Do anxious students get lower test sores when gender and type of school are held constant. (i.e. When gender and type of school are held constant, do anxious students get lower scores)  Variables and Measurement Anxiety Test Scores (Independent) (Dependent) Gender Type of School  Exercise Directions: Identify the independent and dependent variables in the following research problem/question. 1. Does gender affect work performance of the employees in Company A? 2. Is there a significant relationship between employee’s perceived work climate and work engagement?  Exercise 3. Do motivation and self-efficacy influence work performance making gender and type of school constant? 4. Is number of hours reviewing related to test scores regardless of the time of day? 5. Do gender and type of school interact in influencing math and science performance?  Types of Variables Qualitative variable yields categorical or qualitative response. It refers to the attributes or characteristics of the sample. Examples: Gender (male, female), Likert Scale (strongly disagree, disagree, agree, strongly agree) Quantitative variable yields numerical or continuous response representing an amount or quantity. Examples: age, temperature, length of service  Types of Variables Discrete variables assume finite or countable values. It takes integral values and usually gives rise to counting numbers such as number of children (0,1,2,3) , number of female students enrolled (i.e. 15). Continuous variables cannot take on finite values, but the values are related with points on an interval. Thus, it takes any value within a specified range of values. It usually gives rise to measurement such as height (i.e. 5’8”), temperature (i.e. 37.8 degrees Celsius)  Levels of Measurements The level of measurement refers to the relationship among the values that are assigned to the attributes for a variable. It is important to understand this for two very important reasons: 1. It helps you decide how to interpret the data from that variable. 2. It helps you decide what statistical analysis is appropriate on the values that were assigned.  Levels of Measurements A. Nominal Nominal level is the crudest form of measurement. It consists of numbers which indicates categories. Variables can be named, but not quantified. The categories are mutually exclusive, that is, being in one category automatically excludes the other. Nominal variables are coded with numbers, but the magnitude of the number is arbitrary. Thus, the numbers have no mathematical value assigned to them. If for example one basketball player wears jersey number 23 (the center) and another player wears jersey number 18 (the guard), it does not make sense to add these numbers.  Levels of Measurements A. Nominal Examples: 1. Sex: 1-male, 2-female 2. Marital Status: 1-single , 2-married, 3-divorced 3. Employee tenure: 1-permanent, 2-temporary 4. Language spoken: 1-English, 2-Filipino, 3-Mandarin 5. Type of school graduated from :1-public, 2-private Note: If the variable has only two values, it is referred to as Dichotomous variable.  Levels of Measurements B. Ordinal It is a sort of improvement of nominal level in terms of precision of measurement. The values given to measurement can be ordered, from “bottom to top” or “low to high” manner. Values assigned represent a rough quantitative sense to their measurement, but the differences between scores are not necessarily equal. The variables are in order, but not fixed. Nevertheless, we can use statements such as “greater than” or “less than”. For instance, Student A ranked 1st on the test while Student B ranked 2nd. While it is true that we do not know how much better Student A is as compared to Student B, we can infer that the score of Student A is greater than the score of Student B.  Levels of Measurements B. Ordinal Examples: 1. Socio-economic status : 1-low 2-average 3-high 4. Highest educational 2. Letter grades : A,B,C,D,E,F attainment: 3. Likert Scale (5-point scale) 1-elementary Strongly Agree 5 2- high school Agree 4 3- college Neither agree nor disagree 3 4- masteral Disagree 2 Strongly Disagree 1 5. Evaluation: Low, High (Dichotomized)  Levels of Measurements C. Interval Interval level possesses the properties of the nominal and ordinal data. It has equal intervals providing information about how much better one value is compared with another. Measurements are not only classified and ordered, but the distances between each scale are equal. However, zero is arbitrary. For instance, ℃ does not mean the absence of temperature, rather the temperature where water freezes, or an IQ of 0 does not indicate the absence of knowledge , rather the person belongs to the low (or very low) performer category. Moreover, aside from determining that one value if greater or less than another, addition and subtraction have meanings.  Levels of Measurements C. Interval Examples: 1. Temperature (i.e., ℃). The distance between 10 ℃ - 20 ℃ is the same as the distance between 50 ℃ - 60 ℃. But, it does not mean that a temperature of 50 ℃ is 5 times hotter than 10 ℃. 2. IQ scores. The IQ scores of four Students A, B , C and D are 90, 140, 80,and 130, respectively. The difference between 90 and 140 is the same as the difference between 80 and 130 but we cannot claim that the second student is twice as intelligent than the first.  Levels of Measurements D. Ratio Ratio level possesses all the properties of the nominal, ordinal and interval levels. In addition, this has an absolute zero point which indicates the total absence of the property being measured. Numbers can be compared as multiples of one another. For instance, If Carlo is 5 years old and his father is 30, then, his father is six times older. Moreover, all mathematical procedures are appropriate with ratio scales. Examples: age, income, exam scores, grades of students, height, and weight. Note: In statistical practice, ratio variables are subjected to operations that treat them as interval and ignore their ratio properties.  Levels of Measurements The table below summarizes the characteristics of the various levels of measurement. Levels of Measurement Classify Order Equal Limits Absolute Zero A. Nominal Yes No No No B. Ordinal Yes Yes No No C. Interval Yes Yes Yes No D. Ratio Yes Yes Yes Yes  Basic Quantitative Research Design Research design - the collective reference to what type of study a researcher intends to conduct. It likewise includes the format of research question needed to prepare paralleled to the content of the research instrument, the type of hypotheses to be tested, the nature of variables to be manipulated or hold constant, the data gathering techniques to be employed, as well as the statistical tools to be utilized, and other pertinent parts of the paper which embodied the framework of the study.  Basic Quantitative Research Design TYPES OF QUANTITATIVE RESEARCH DESIGNS Descriptive Research – involves the description, recording, analysis, interpretation of conditions that presently exist. Descriptive research purely involves the "present" conditions and definitely not the past. It generally involves some type of comparison, contrast, attempt to discover a relationship that exactly exists between two variables. ∎ Descriptive-Normative ∎ Descriptive-Developmental ∎ Descriptive-Correlational ∎ Descriptive-Documentary ∎ Descriptive-Evaluative ∎ Descriptive-Comparative  Basic Quantitative Research Design TYPES OF QUANTITATIVE RESEARCH DESIGNS Experimental Research – involves involves the manipulation of at least one independent variable, controls other relevant variables, and observes the effect on one or more dependent variables. The relationship between cause and effect is explained based on what transpires as the independent variable (x) is manipulated which brings the changes to the dependent variable (y). ∎ Pre-experimental research ∎ True-experimental research ∎ Quasi-experimental research  Basic Quantitative Research Design TYPES OF QUANTITATIVE RESEARCH DESIGNS Historical Research – involves any activity which appeals to past experiences or occurrences to better understand the present phenomena and plan for future innovation. It, therefore, is concerned with describing past events, facts, records, and actions in a spirit of inquiring critically for the whole truth. Ex-post facto (Causal-Comparative) Research - involves groups of the variable with qualities that already exist being compared to some dependent variable. Known as "after the fact" research, an ex post facto is considered quasi- experimental because the subjects are not randomly assigned.  Basic Quantitative Research Design TYPES OF QUANTITATIVE RESEARCH DESIGNS Participatory Research – a long, slow, difficult but creative process. It recognizes people's capabilities to discover, organize, and use knowledge. As a research methodology, It considerably requires researchers to analyze and decide about what values and views about research, an understanding which consequently and inevitably spells the direction out of the careful and strict investigation.  References Dela Rosa, E. D. (2019). Learning Module in Statistics with SPSS Applications. Philippine Copyright 2019. Cortez and Galman (2017). Writing Research in the Major Fields – A guide in writing undergraduate thesis. Philippine Copyright 2017.