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Central Philippine University College of Arts and Sciences Social Sciences Department PSY 1102 - PSYCHOLOGICAL STATISTICS By PRINCE JOASH L. DACLES, RPm OVERVIEW OF SCIENTIFIC METHOD AND STATISTICS METHOD TO ACQUIRE KNOWLEDGE (Methods of Knowing) - TIARES -this are ways in which a person can know things or discover answers to questions 1. Method of Tenacity - involves holding on to ideas simply because they have been accepted as facts for a long time or because of superstition (based on habit or superstition). It is often referred to as belief perseverance. In general, the more frequently we are exposed to statements, the more we tend to believe them. Also, it involves the persistence of superstitions. The only problem is that the information acquired might not be accurate and there is no method for correcting erroneous ideas for belief based on tenacity is difficult to change. 2. Method of Intuition - it is when information is accepted as true because it “feels right”. With intuition, a person relies on hunches, instinct or gut feeling to answer question. It is the quickest way to obtain answer because if we have no information at all and cannot refer to supporting data or use rational justification, we often resort to intuition. Many ethical decisions or moral questions are resolved by method of intuition. The problem with this method is that it has no mechanism for separating from inaccurate knowledge. 3. Method of Authority - a person relies on information or answer from an expert in the subject area. This method is an excellent starting point; often, it is the quickest and easiest way to obtain answers. But this method cannot provide accurate data and for some authority or experts information can be biased. Also, answer obtained from an expert could represent subjective, personal opinion rather than true expert knowledge. Additional limitation is that we assume, by virtue of the person’s status as an authority, that expertise can be generalized to include the question we are asking. Moreover, people often accepts an expert’s statement without question, as a result, false information is sometimes taken as truth. People sometimes accept the word of an authority because they have complete trust in the authority figure. In this situation, the method of authority is often called the method of faith because people accept on faith any information that is given, it is an unquestioned trust in the authority figure. But, always remember, not all experts are experts. 4. Method of Rationalism - or rational method/rationalism, involves seeking answer by logical reasoning beginning with a set of known facts or assumptions and use logic to reach a conclusion or get an answer to question (consist of an argument, premise statements, logical conclusion). Rational methods is the practice of employing reason as a source of knowledge. Answers obtained using the rational method are not simply accepted as true without verification. Instead all conclusions are tested by ensuring that they conform to the rules of logic. Because the rational method does not involve directly observing or actively gathering information, it has been said that logic is a way of establishing truth in the absence of evidence. Example Syllogism: All statistics professors are interesting people Mr. X is a statistic professor. Therefore, Mr. X is an interesting person 5. Method of Empiricism - or empirical method/empiricism, attempts to answer question by direct observation or personal experience. This method is a product of empirical viewpoint in philosophy, which holds that all knowledge is acquired through the senses. Table 1. Nonscientific Methods of Acquiring Knowledge Method Way of Knowing or Acquiring Tenacity From habit or superstition Intuition From a hunch or feeling Authority From an expert Rationalism From reasoning; a logical conclusion Empiricism From direct sensory observation 6. Method of Science - The Scientific Method -It is an approach to acquiring knowledge that involves formulating specific questions and then systematically finding answers. The scientific method contains many elements of nonscientific methods of acquiring knowledge. This method is carefully developed system for asking and answering questions so that the answers we discover are as accurate as possible. Scientific method defines as a method of acquiring knowledge that uses observation to develop a hypothesis, the use the hypothesis to make logical predictions that can be empirically tested by making additional, systematic observations. Typically, the new observations lead to a new hypothesis, and the cycle continues. At the heart of science lies the scientific experiment. The method of science is rather straightforward. By some means, usually by reasoning deductively from existing theory or inductively form existing facts or through intuition, the scientist arrives at a hypothesis about some feature of reality. He or she then designs an experiment to objectively test the hypothesis. The data from the experiment are then analyzed statistically, and the hypothesis is either supported or rejected. STEPS OF THE SCIENTIFIC METHODS 1. Observe behavior or other phenomenon - it begins with casual or informal observation. At this stage, people commonly tend to generalize beyond the actual observations. The process of generalization is an almost automatic human response known as induction or inductive reasoning - specific to general observations. 2. Form a tentative answer or explanation (hypothesis) - it begins with identifying factors or variables - are characteristics or conditions that change or have different values for different individual. After which, select an explanations to be evaluated in a scientific research study, at this point hypothesis - is a statement that describes or explains a relationships between or among variables, is formulated 3. Use your hypothesis to generate a testable prediction - single hypothesis lead to several predictions, and that each prediction refers to a specific situation or an event that can be observed and measured. In this stage, deduction or deductive reasoning - general to specific statements, is used. And, prediction generated from a hypothesis must be testable - that is, it must be possible to demonstrate that he prediction is either correct or incorrect by direct observation. Either the observation will provide support for the hypothesis or they will refute the hypothesis. For a prediction to be truly testable, both outcomes must be possible. 4. Evaluate prediction by making systematic planned observations - After a specific, testable prediction has been made (rational method), the next step is to evaluate the prediction using direct observation (empirical method). This is the actual research or data collection phase of the scientific method. The goal is to provide a fair and unbiased test of the research hypothesis by observing whether the prediction is correct. 5. Use the observations to support, refute or refine the original hypothesis - the final step is to compare the actual observation with the predictions that were made from the hypothesis. OTHER ELEMENTS OF SCIENTIFIC METHODS - EPO 1. Science is Empirical - answer are obtained by making observations. However, unlike the method of empiricism, the scientific method involves structures or systematic observation which is determined by the procedures and techniques that are used in the research study. Also, in that they are performed under specific set of conditions so that we can accurately answer the question we are addressing. 2. Science is Public - making observation available for evaluation by others, specifically scientists. In particular, other individuals should be able to repeat the same step-by-step process that led to the observation so that they can replicate/repeat - allow verification of the findings, the observation for themselves. The scientific community makes observations public by publishing reports in scientific journals or presenting their results at conference and meetings. 3. Science is Objective - observations are structured so that the researcher’s biases and beliefs do not influence the outcome of the study. Science has been called “a dispassionate search for knowledge,” - meaning that the researcher does not let personal feelings contaminate the observations. References: F.J. Gravetter & L-A.B. Forzano (2012), Understanding Research Methods for the Behavioral Sciences 2nd Edition, Cengage Learning Asia Pte. Ltd. Pagano, R. R. (2016). Understanding Statistics in the Behavioral Sciences: Cengage Learning STATISTICS In common usage, the word statistics simply refers to a mass or a collection of facts and figures, such as grades of students, enrolment figures, inflation rates over a certain period of time, production figures in a company and many others. Such statistics merely provides descriptive information. However, statistics is more than a mere mass of figures or a collection of facts. It is a science in itself (concerned with the concepts and methods of processing a collection of data in a more accurate, just and meaningful way). As a body of knowledge, statistics is concerned with the concepts and techniques employed in the collection, presentation, analysis and interpretation of data. Simply stated, it is a science of data. Data Gathering Tools Questionnaire, Interview, Observation, Experiment, Psychological Examinations, or a combination of any of the aforementioned Data Analysis- the resolution of information into simpler elements by the application of statistical principles/tools Data Interpretation- an explanation of what has been analyzed WHY STUDY STATISTICS -it can give a precise description of data -it can predict the behavior of an individual -it can be used to test a hypothesis Statistical Data - the raw materials for statistics. These are information derived from counts, measurements, observations, interviews, experiments and other techniques. Data originally measured are referred to as raw data. Any recorded information, whether numerical or categorical is called observation. The problem of measurement of concepts is a central concern in research. A concept is a relatively abstract idea, such as social class, academic achievement and leadership ability. Measurement refers to the assignment of numbers or scores to characteristics of persons, objects or observed events according to a set of rules. In the process of measuring concepts, variables arise as a result. A variable is characteristic of the objects under observation that takes on different values for different cases. It is a trait that can differ in quality or in quantity from one case to case. EXAMPLES OF CONCEPT AND VARIABLES -Social class is a concept and annual income is a variable that results in the process of measuring social class -Academic achievement is a concept and the average grade is a variable that results in the process of measuring academic achievement Other examples of commonly used variables in research include, gender, age at last birthday, number of years in school IQ scores and test scores. In contrast to a variable, a constant is a value that does not vary for different cases or over time. Examples of constants are the number of months in a year, the number of centimeters in one meter or the mathematical constant π (read as pi) TYPES OF VARIABLE A. Variables According to Functional Relationship 1. Independent also known as predictor variables or variates 2. Dependent also known as criterion variables *Other variables Intervening Variable - introduced by Tolman, a third variable that can often explain the relationship between two or other variable. Extraneous Variable - is any variable you’re not interested in studying that could also have some effect on the dependent variable. B. Variables According to Continuity of Values 1. Continuous (variables in which the researcher can make measurements of varying degrees of precision. Ex. height, weight, and width. 2. Discrete or discontinuous (variables whose values or levels cannot take the form of decimals) C. Variables According to Scale or Level of Measurement 1. Nominal The nominal scale is the lowest level of measurement in which observations are simply classified into categories with no necessary relationship existing between the categories. Thus, nominal variables express differences in type or variety and are also called classification variables since they are classified into exhaustive and mutually exclusive categories. The categories are simply qualitative distinctions which cannot be subjected to any arithmetic operations. (Ex. civil status, gender, religious affiliation, political party preference). Observations on these variables are simply qualitative categories expressing differences in types without implying that one category is greater or lesser than the other. Nominal Scale: A scale or level of measurement in which scores represent names only but not differences in amount A nominal-scale variable is a qualitative variable It must be analyzed by nonparametric tests. Ex. Telephone numbers, species of flowers, preferred hobby 2. Ordinal Variables that are measured on an ordinal level have the characteristics of a nominal variable plus the advantage that the categories can be ordered or ranked from low to high. Values of variables in the ordinal scale cannot, however, be added or subtracted and differences between ranks are not necessarily equal. (Ex. ranks given to participants in a contest as 1 st, 2nd, and 3rd ; socioeconomic status which may be classified as upper, middle and lower; stress level which may be classified as high, moderate, low; attitude and opinion scales in which responses to items are “never”, “sometimes”, “usually”, and “always”. Ordinal Scale: A measurement scale in which scores indicate only relative amounts or rank order. An ordinal-scale variable is the crudest type of quantitative variable. It must be analyzed by nonparametric tests. Ex. Street number (usually some possible addresses are missing), position in a spelling bee, seedlings of tennis players Note: Some variables fall between ordinal and interval levels. The values imply something about relative distances between them but the spacing is not perfect. They are frequently analyzed by parametric tests. Ex. Attitude scales, rating scales, letter grades 3. Interval Variables that are measured on an interval level have the characteristics of nominal and ordinal variables but in addition, the categories are measured in terms of a standard unit of measurement and thus, have equal intervals between categories. This means that the distance between two numbers or scores is a reflection of the distance between the values of the characteristics being measured. In interval scales, the distance between all adjacent values of the variable are equal and the zero point is arbitrary. (Ex. Test scores, IQ scores and Temperature in centigrade or Fahrenheit scale.) Interval Scale: A scale of measurement for which equal differences in scores represent equal differences in amount of the property measured, but with an arbitrary zero point. An interval-scale variable is a quantitative variable. It may be analyzed by parametric tests. Ex. Fahrenheit temperature, score on an advanced Spanish test as a measure of knowledge of Spanish, many aptitude test scores. 4. Ratio Variables that are measured on the ratio scale have all the properties of an interval scale plus a real zero or a true zero point which indicates the absence of the characteristic measured. Measurements in the ratio scale allow multiplication and division of values, aside from addition and subtraction, which are the only operation possible in the interval scale. A ratio scale has a meaningful zero point and ratios of measurement reflects ratios of magnitude. (Ex. income, number of children in a family, age, student enrolment, population size, length, weight, volume and rates.) Ratio Scale: A scale having interval properties except that a score of zero indicates a total absence of the quality being measured. Statements about ratios of scores are meaningful: Twice as big a number means twice as much of the variable. A ratio-scale variable is a quantitative variable. It may be analyzed by parametric tests. Ex. Distance, duration, volume. Why Does Level of Measurement Matter? Level of measurement is important because the kinds of statistical procedures that can be appropriately used depends on the level of measurement of the variable studies. POPULATION AND S-In research, a population is the complete set of individuals, objects or scores that the investigator is interested in studying. -it is an entire group of people, objects or events which have at least one characteristic in common, and must be defined specifically and unambiguously. -the number of observations in a population is called the size of the population, usually denoted by N -the term parameter refers to any numerical value describing a characteristic of a population and is usually represented by the Greek letters such as μ and σ. -a sample is a finite number of objects selected from the population that is a subset or part of the population. -the number of observations in a sample is called the size of the sample, usually denoted by n. -sample: persons, events, places or things used as sources of data -the term statistic is used to refer to any numerical value describing a characteristic of a sample. It is usually represented by lower case letters in the English alphabet, such as and s. Sampling is the process involved in taking a portion of the population, making observations on this smaller group and then generalizing the findings to the larger population. -the process of selecting the sample or the study units from a previously defined population -a study on the entire population of interest is called a census or complete enumeration ESSENTIAL CONCEPTS AND STEPS IN SAMPLING 1. Determine the population of individuals, or items, or cases where to find the data needed. (ex. You want to get the perceptions of the clergy from certain churches about issues of national development in the Philippines. The target population or universe are all members of the clergy of selected churches in the Phil) 2. Determine the kind of sample you want to have. (ex. a priest is the basic element of the total target population of priests) 3. Find out what is the appropriated size of the sample. 3.1. Compute the sample size. A sample of at least 30 is needed for statistical laws of probability to operate. Generally, a “large sample” is useful when the population is small, and a “small sample” for a large population. 3.2. Apply the formula for sample determination Example: Find n from an N of 1000. Gay (1976) offers some minimum acceptable sizes depending on the types of research as follows: a. descriptive research: 10 percent of the population(for a smaller population, a minimum of 20 percent may be required) b. correlational research: 30 subjects c. experimental research: 15 subjects per group. Some authorities believe that 30 subjects per group should be considered the minimum d. ex-post-facto or causal research: 15 subjects per group 4. Having the desired sample size, get the samples from the sampling frame, based on the sampling method that you want to use COMMON TERMINOLOGY RECAP 1. Population - it is the complete set of individuals, objects, or scores that the investigator is interested in studying. It is a larger group of individuals in which subjects are taken. 2. Sample - is a subset of the population. For economical reason, investigator usually collects data on a smaller groups of subjects. 3. Variable - is any property or characteristics of some events, object, or person that may have different values at different times depending on the conditions. 4. Constant - it does not have different values at different times. 5. Independent variable (IV) - the IV in an experiment is the variable that is systematically manipulated by the investigator. It can be manipulated. 6. Dependent variable (DV) - the dependent variable in an experiment is the variable that the investigator measures to determine the effect of the independent variable. It can be measured. 7. Data - it is the measurement that are made on the subjects of an experiment. The data as originally measured are often referred to as raw or original scores. 8. Statistic - is a number calculated on sample data that quantifies a characteristic of the sample. 9. Parameter - is a number calculated on population data that quantifies a characteristic of the population. MODE OF PRESENTATION AND RETENTION 2 CATEGORY OF SCIENTIFIC RESEARCH - most scientific research fall in this category 1. Observational studies - no active manipulation and cannot determine causality a) Naturalistic observation - to obtain accurate description of the situation being studied. Example: anthropological & etiological research. b) Parameter estimation - to estimated the level of one or more population characteristics. Example: surveys, public opinion polls, and market research. c) Correlational studies - focuses attention on two or more variables to determine whether they are related. 2. True experiments - it can determine causality, IV is manipulated and its effect on some dependent variable is studied. TWO MAJOR AREAS OF STATISTICS 1. Descriptive Statistics- concerned with the methods for collecting, organizing and describing a set of data so as to yield meaningful information. These methods include graphical and numerical techniques for summarizing data that is, reducing a large mass of data to simpler and more understandable terms. The construction of tables, charts and graphs and the computations of descriptive statistical measures like averages, proportions and percentages also fall in this area. 2. Inferential Statistics or Inductive Statistics- comprises those procedures for drawing inferences or making generalizations about characteristics of a population based on partial and incomplete information obtained from a sample of the population. It involves techniques which use the obtained sample data to infer to populations. The testing of predictions or hypotheses is a major function of inferential statistics. A major part of inferential statistics involves the computation of statistical tests, or procedures designed to permit the researcher to answer certain questions about the data. However, not all statistical procedures can be used with all types of data. In order to decide which statistical test to use, you need to understand the distinction between tests that make certain assumptions about the nature of the data to which they apply and tests that make far fewer assumptions. The tests that assume a number of characteristics about the parameters of the population from which the scores come are parametric tests. The tests that can be used for purely ordinal or nominal data are nonparametric tests. Parametric Tests Definition: Statistical tests that assume a number of characteristics about the parameters of the population from which the scores come Assumptions: Interval-or ratio data Independent or random sampling Normal distribution of scores in the population Equal variances of the scores in the population from which the samples Nonparametric Tests Statistical tests that make fewer assumptions about the population and can be used with nominal or ordinal data Independent or random sampling By Sampling Method/ techniques Population Sample Census (Complete Enumeration) come Advantages: By descriptive techniques Usually more powerful More versatile Robust to violations of assumptions By descriptive techniques Fewer assumptions Computationally simpler By inferential techniques Parameter Statistic μ--------------------------------------------Mean--------------------------------------------σ------------------------------------Standard Deviation------------------------------------s ρ--------------------------Pearson Coefficient of Correlation---------------------------r USING COMPUTER IN STATISTICS -The use of computers in statistics has increased greatly over the past decade. In fact today almost all research data in the behavioral sciences are analyzed by statistical computer programs rather than “by hand” with calculator. -Computers have disadvantage of saving time and labor, minimizing the chances of computational error, allowing easy graphical display of the data, and providing better management of large data sets. -Several computer programs available to do statistical analysis. The most popular are the Statistical Package for the Social Sciences (SPSS), Statistical Analysis System (SAS), SYSTAT, MINITAB, and Excel. Versions of these programs are available for both mainframes and microcomputers. QUESTION Why do I have to do any of these complicated calculations by hand? -Unfortunately, when you are using statistical software to calculate the value of a statistic, it does not help you understand that statistic. -Understanding statistics and its proper use is best achieved by doing calculations or step-by-step calculations using Excel. Of course, once you have learned everything you can from these calculations, using statistical software like SPSS to grind out correct values of the statistics seems eminently reasonable. References: P.A. dela Rama, Ph.D; Psy 202 - Advanced Psychological Statistics, Instructional Material in Advanced Statistics, Sillima University, Graduate School. Pagano, R. R. (2016). Understanding Statistics in the Behavioral Sciences: Cengage Learning