Appendix B Statistical Methods
|
|
- Marjory Sims
- 5 years ago
- Views:
Transcription
1 Appendix B Statistical Methods Figure B. Graphing data. (a) The raw data are tallied into a frequency distribution. (b) The same data are portrayed in a bar graph called a histogram. (c) A frequency polygon is plotted over the histogram. (d) The resultant frequency polygon is shown by itself. Empiricism depends on observation; precise observation depends on measurement; and measurement requires numbers. Thus, scientists routinely analyze numerical data to arrive at their conclusions. Over empirical studies are cited in this text, and all but a few of the simplest ones required a statistical analysis. Statistics is the use of mathematics to organize, summarize, and interpret numerical data. We discussed statistics briefly in Chapter, but in this appendix we take a closer look. To illustrate statistics in action, imagine a group of students who want to test a hypothesis that has generated quite an argument in their psychology class. The hypothesis is that university students who watch a great deal of television aren t as bright as those who watch TV infrequently. For the fun of it, the class decides to conduct a correlational study of itself, collecting survey and psychological test data. All of the classmates agree to respond to a short survey on their TV viewing habits. Because everyone at that school has had to take the Scholastic Aptitude Test (SAT), the class decides to use scores on the SAT verbal subtest as an index of how bright students are. The SAT is one of a set of tests that high school students in the United States take before applying to college or university. Universities frequently use test scores like these, along with the students high school grades and other relevant information, when considering admitting students to university. In this class, all of the students agree to allow the records office at the university to furnish their SAT scores to the professor, who replaces each student s name with a subject number (to protect students right to privacy). Let s see how they could use statistics to analyze the data collected in their pilot study (a small, preliminary investigation). Graphing Data After collecting the data, the next step is to organize the data to get a quick overview of our numerical results. Let s assume that there are students in the class, and when they estimate how many hours they spend per day watching TV, the results are as follows: c One of the simpler things that they can do to organize data is to create a frequency distribution an orderly arrangement of scores indicating the frequency of each score or group of scores. Figure B.(a) shows a frequency distribution for the data on TV viewing. The column on the left lists the possible scores (estimated hours of TV viewing) in order, and the column on the right lists the number of subjects or participants with each score. Graphs can provide an even better overview of the data. One approach is to portray the data in a histogram, which is a bar graph that presents data from a frequency distribution. Such a histogram, summarizing our TV viewing data, is presented in Figure B.(b). Another widely used method of portraying data graphically is the frequency polygon a line figure used to present data from a frequency distribution. Figures B.(c) and B.(d) show how the TV viewing data can be converted from a histogram to a frequency polygon. In both the bar graph and the line figure, the horizontal axis lists the possible scores and Score Tallies of score Scores (estimated hours of TV viewing per day) Scores (estimated hours of TV viewing per day) Scores (estimated hours of TV viewing per day) (a) distribution (b) Histogram (c) Conversion of histogram into frequency polygon (d) polygon A-8 APPENDI B NEL 77_7_App_pA-A pp.indd 8 // :: AM
2 the vertical axis is used to indicate the frequency of each score. This use of the axes is nearly universal for frequency polygons, although sometimes it is reversed in histograms (the vertical axis lists possible scores, so the bars become horizontal). The graphs improve on the jumbled collection of scores that they started with, but descriptive statistics, which are used to organize and summarize data, provide some additional advantages. Let s see what the three measures of central tendency tell us about the data. Measuring Central Tendency c In examining a set of data, it s routine to ask, What is a typical score in the distribution? For instance, in this case, we might compare the average amount of TV watching in the sample to national estimates, to determine whether the subjects appear to be representative of the population. The three measures of central tendency the median, the mean, and the mode give us indications regarding the typical score in a data set. As explained in Chapter, the median is the score that falls in the centre of a distribution, the mean is the arithmetic average of the scores, and the mode is the score that occurs most frequently. All three measures of central tendency are calculated for the TV viewing data in Figure B.. As you can see, in this set of data, the mean, median, and mode all turn out to be the same score, which is. Although our example in Chapter emphasized that the mean, median, and mode can yield different estimates of central tendency, the correspondence among them seen in the TV viewing data is quite common. Lack of agreement usually occurs when a few extreme scores pull the mean away from the centre of the distribution, as shown in Figure B.. The curves plotted in Figure B. are simply smoothed-out =. Mode (most frequent score) Median (middle of score distribution) Mean (arithmetic average of summed scores) frequency polygons based on data from many subjects. They show that when a distribution is symmetric, the measures of central tendency fall together, but this is not true in skewed or unbalanced distributions. Figure B.(b) shows a negatively skewed distribution, in which most scores pile up at the high end of the scale (negative skew refers to the direction in which the curve s tail points). A positively skewed distribution, in which scores pile up at the low end of the scale, is shown in Figure B.(c). In both types of skewed distributions, a few extreme scores at one end pull the mean, and to a lesser degree the median, away from the mode. In these situations, the mean may be misleading and the median usually provides the best index of central tendency. In any case, the measures of central tendency for the TV viewing data are reassuring, since they all agree and they fall reasonably close to national estimates Figure B. Measures of central tendency. Although the mean, median, and mode sometimes yield different results, they usually converge, as in the case of the TV viewing data. Figure B. Measures of central tendency in skewed distributions. In a symmetrical distribution (a), the three measures of central tendency converge. However, in a negatively skewed distribution (b) or in a positively skewed distribution (c), the mean, median, and mode are pulled apart as shown here. Typically, in these situations, the median provides the best index of central tendency. Low Mean Mode Median Scores High Low Mean Mode High Median Scores Low Mode Mean High Median Scores (a) Symmetrical distribution (b) Negatively skewed distribution (c) Positively skewed distribution NEL APPENDI B A- 77_7_App_pA-A pp.indd // :: AM
3 Figure B. The standard deviation and dispersion of data. Although both of these distributions of golf scores have the same mean, their standard deviations will be different. In (a) the scores are bunched together and there is less variability than in (b), yielding a lower standard deviation for the data in distribution (a). regarding how much young adults watch TV (Nielsen Media Research, 8). Given the small size of the student group, this agreement with national norms doesn t prove that the sample is representative of the population, but at least there s no obvious reason to believe that it is unrepresentative. Measuring Variability c Of course, the subjects in the sample did not report identical TV viewing habits. Virtually all data sets are characterized by some variability. Variability refers to how much the scores tend to vary or depart from the mean score. For example, the distribution of golf scores for a mediocre, erratic golfer would be characterized by high variability, while scores for an equally mediocre but consistent golfer would show less variability. The standard deviation is an index of the amount of variability in a set of data. It reflects the dispersion of scores in a distribution. This principle is portrayed graphically in Figure B., where the two distributions of golf scores have the same mean but the upper one has less variability because the scores are bunched up in the centre (for the consistent golfer). The distribution in Figure B.(b) is characterized by more variability, as the erratic golfer s scores are more spread out. This distribution will yield a higher standard deviation than the distribution in Figure B.(a). (a) (b) Mean 7 8 Golf scores Mean The formula for calculating the standard deviation is shown in Figure B., where d stands for each score s deviation from the mean and S stands for summation. A step-by-step application of this formula to our TV viewing data, shown in Figure B., reveals that the standard deviation for our TV viewing data is.. The standard deviation has a variety of uses. One of these uses will surface in the next section, where we discuss the normal distribution. The Normal Distribution c The hypothesis in the study was that brighter students watch less TV than relatively dull students. To test this hypothesis, the students decided to correlate N = Σ = Mean = TV viewing score ( ) Σ N = = Standard deviation = Σd = N =.7 =.. Deviation from mean ( d ) Deviation squared ( d ) Σd = 7 8 Golf scores Figure B. Steps in calculating the standard deviation. () Add the scores (S) and divide by the number of scores (N) to calculate the mean (which comes out to. in this case). () Calculate each score s deviation from the mean by subtracting the mean from each score (the results are shown in the second column). () Square these deviations from the mean and total the results to obtain (Sd ), as shown in the third column. () Insert the numbers for N and Sd into the formula for the standard deviation and compute the results. A- APPENDI B NEL 77_7_App_pA-A pp.indd // :: AM
4 TV viewing with SAT scores. But to make effective use of the SAT data, they need to understand what SAT scores mean, which brings us to the normal distribution. The normal distribution is a symmetrical, bellshaped curve that represents the pattern in which many human characteristics are dispersed in the population. A great many physical qualities (e.g., height, nose length, and running speed) and psychological traits (intelligence, spatial reasoning ability, introversion) are distributed in a manner that closely resembles this bell-shaped curve. When a trait is normally distributed, most scores fall near the centre of the distribution (the mean), and the number of scores gradually declines as one moves away from the centre in either direction. The normal distribution is not a law of nature. It s a mathematical function, or theoretical curve, that approximates the way nature seems to operate. The normal distribution is the bedrock of the scoring system for most psychological tests, including the SAT. As we discuss in Chapter, psychological tests are relative measures; they assess how people score on a trait in comparison to other people. The normal distribution gives us a precise way to measure how people stack up in comparison to each other. The scores under the normal curve are dispersed in a fixed pattern, with the standard deviation serving as the unit of measurement, as shown in Figure B.. About 8% of the scores in the distribution fall within plus or minus standard deviation of the mean, while % of the scores fall within plus or minus standard deviations of the mean. Given this fixed pattern, if you know the mean and standard deviation of a normally distributed trait, you can tell where any score falls in the distribution for the trait. Although you may not have realized it, you probably have taken many tests in which the scoring system is based on the normal distribution, such as IQ tests. On the SAT, for instance, raw scores (the number of items correct on each subtest) are converted into standard scores that indicate where a student falls in the normal distribution for the trait measured. In this conversion, the mean is set arbitrarily at and the standard deviation at, as shown in Figure B.7. Therefore, a score of on the SAT verbal subtest means that the student scored standard deviation below the mean, while an SAT score of indicates that the student scored standard deviation above the mean. Thus, SAT scores tell us how many standard deviations above or below the mean a specific student s score was. This system also provides the metric for IQ scales and many other types of psychological tests (see Chapter ). Test scores that place examinees in the normal distribution can always be converted to percentile scores,.7%.% 8.% 7 8 Standard deviations Number of scores in interval if total number = Scores in interval (%) 7 8 Percentiles Figure B. The normal distribution. Many characteristics are distributed in a pattern represented by this bell-shaped curve (each dot represents a case). The horizontal axis shows how far above or below the mean a score is (measured in plus or minus standard deviations). The vertical axis shows the number of cases obtaining each score. In a normal distribution, most cases fall near the centre of the distribution, so that 8.% of the cases fall within plus or minus standard deviation of the mean. The number of cases gradually declines as one moves away from the mean in either direction, so that only.% of the cases fall between and standard deviations above or below the mean, and even fewer cases (.%) fall between and standard deviations above or below the mean. NEL APPENDI B A- 77_7_App_pA-A pp.indd // :: AM
5 Figure B.7 The normal distribution and SAT scores. The normal distribution is the basis for the scoring system on many standardized tests. For example, on the SAT, the mean is set at and the standard deviation at. Hence, an SAT score tells you how many standard deviations above or below the mean a student scored. For example, a score of 7 means that person scored standard deviations above the mean. Figure B.8 Scatter diagrams of positive and negative correlations. Scatter diagrams plot paired and Y scores as single points. Score plots slanted in the opposite direction result from positive (top row) as opposed to negative (bottom row) correlations. Moving across both rows (to the right), you can see that progressively weaker correlations result in more and more scattered plots of data points..%.%.%.%.%.%.%.% Standard deviations 7 8 SAT scores which are a little easier to interpret. A percentile score indicates the percentage of people who score at or below a particular score. For example, if you score at the th percentile on an IQ test, % of the people who take the test score the same or below you, while the remaining % score above you. There are tables available that permit us to convert any standard deviation placement in a normal distribution into a precise percentile score. Figure B. gives some percentile conversions for the normal curve. Of course, not all distributions are normal. As we saw in Figure B., some distributions are skewed in one direction or the other. As an example, consider what would happen if a classroom exam was much too easy or much too hard. If the test was too easy, scores would be bunched up at the high end of the scale, as in Figure B.(b). If the test was too hard, scores would be bunched up at the low end, as in Figure B.(c). Measuring Correlation d To determine whether TV viewing is related to SAT scores, the students have to compute a correlation coefficient a numerical index of the degree of relationship between two variables. As discussed in Chapter, a positive correlation means that two variables say and Y co-vary in the same direction. This means that high scores on variable are associated with high scores on variable Y and that low scores on are associated with low scores on Y. A negative correlation indicates that two variables co-vary in the opposite direction. This means that people who score high on variable tend to score low on variable Y, whereas those who score low on tend to score high on Y. In their study, the psychology students hypothesized that as TV viewing increases, SAT scores will decrease, so they should expect a negative correlation between TV viewing and SAT scores. The magnitude of a correlation coefficient indicates the strength of the association between two variables. This coefficient can vary between and.. The coefficient is usually represented by the letter r (e.g., r.). A coefficient near tells us that there is no relationship between two variables. A coefficient of. or. indicates that there is a perfect, one-to-one correspondence between two variables. A perfect correlation is found only rarely when working with real data. The closer the coefficient is to either. or., the stronger the relationship is. The direction and strength of correlations can be illustrated graphically in scatter diagrams (see Figure B.8). A scatter diagram is a graph in which paired and Y scores for each subject are plotted as single points. Figure B.8 shows scatter diagrams for Direct relationship Y Y Y Y Y Positive correlation Inverse relationship r =. r =.8 r =. r =. Y Y Y Y Y Negative correlation r =. r =.8 r =. r =. A- APPENDI B NEL 77_7_App_pA-A pp.indd // :: AM
6 positive correlations in the upper half and for negative correlations in the bottom half. A perfect positive correlation and a perfect negative correlation are shown on the far left. When a correlation is perfect, the data points in the scatter diagram fall exactly in a straight line. However, positive and negative correlations yield lines slanted in the opposite direction because the lines map out opposite types of associations. Moving to the right in Figure B.8, you can see what happens when the magnitude of a correlation decreases. The data points scatter farther and farther from the straight line that would represent a perfect relationship. What about the data relating TV viewing to SAT scores? Figure B. shows a scatter diagram of these data. Having just learned about scatter diagrams, perhaps you can estimate the magnitude of the correlation between TV viewing and SAT scores. The scatter diagram of our data looks a lot like the one shown in the bottom right corner of Figure B.8, suggesting that the correlation will be in the vicinity of.. The formula for computing the most widely used measure of correlation the Pearson product moment correlation is shown in Figure B., along with the calculations for the data on TV viewing and SAT scores. The data yield a correlation of r.. This coefficient of correlation reveals that there is a weak inverse association between TV viewing and performance on the SAT. Among the sample of participants, as TV viewing increases, SAT scores decrease, but the trend isn t very strong. We can get a better idea of how strong this correlation is by examining its predictive power. Correlation and Prediction d As the magnitude of a correlation increases (gets closer to either. or.), our ability to predict one variable based on knowledge of the other variable steadily increases. This relationship between the magnitude of a correlation and predictability can be quantified precisely. All we have to do is square the correlation coefficient (multiply it by itself) and this gives us the coefficient of determination, the percentage of variation in one variable that can be predicted based on the other variable. Thus, a correlation of.7 yields a coefficient of determination of. (.7.7.), indicating that variable can account for % of the variation in variable Y. Figure B. shows how the coefficient of determination goes up as the magnitude of a correlation increases. Unfortunately, a correlation of. doesn t give us much predictive power. The students can account for only a little over % of the variation in variable Y. So, if they tried to predict individuals SAT scores based on how much TV those individuals watched, their predictions wouldn t be very accurate. Although a low correlation doesn t have much practical, predictive utility, it may still have theoretical value. Just knowing that there is a relationship between two variables can SAT score 7 Subject number Formula for Pearson product-moment correlation coefficient Estimated hours of TV viewing per day TV viewing score ( ) Figure B. Scatter diagram of the correlation between TV viewing and SAT scores. The hypothetical data relating TV viewing to SAT scores are plotted in this scatter diagram. Compare it to the scatter diagrams shown in Figure B.8 and see whether you can estimate the correlation between TV viewing and SAT scores in the students data (see the text for the answer). N = Σ = Σ = ΣY = 8 ΣY = 7 ΣY = 8 8 Figure B. r = = SAT score ( Y ) Y = [8][ 7] = ( N ) ΣY ( ) Σ ( ΣY ) [(N ) Σ (Σ ) ][(N ) ΣY (ΣY ) ] () (8 8) () (8) [ () () () ] [() ( 7) (8) ] Y Computing a correlation coefficient. The calculations required to compute the Pearson product moment coefficient of correlation are shown here. The formula looks intimidating, but it s just a matter of filling in the figures taken from the sums of the columns shown above the formula. NEL APPENDI B A- 77_7_App_pA-A pp.indd // :: AM
7 Figure B. Correlation and the coefficient of determination. The coefficient of determination is an index of a correlation s predictive power. As you can see, whether positive or negative, stronger correlations yield greater predictive power. Coefficient of determination..7.. High Negative correlation Moderate Low Low Negligible predictive power Positive correlation Moderate High Correlation Increasing Increasing be theoretically interesting. However, we haven t yet addressed the question of whether the observed correlation is strong enough to support the hypothesis that there is a relationship between TV viewing and SAT scores. To make this judgment, we have to turn to inferential statistics and the process of hypothesis testing. Hypothesis Testing Inferential statistics go beyond the mere description of data. Inferential statistics are used to interpret data and draw conclusions. They permit researchers to decide whether their data support their hypotheses. In Chapter, we showed how inferential statistics can be used to evaluate the results of an experiment; the same process can be applied to correlational data. In the study of TV viewing, the students hypothesized that they would find an inverse relationship between the amount of TV watched and SAT scores. Sure enough, that s what they found. However, a critical question remains: Is this observed correlation large enough to support the hypothesis, or might a correlation of this size have occurred by chance? We have to ask a similar question nearly every time we conduct a study. Why? Because we are working with only a sample. In research, we observe a limited sample (in this case, participants) to draw conclusions about a much larger population (students in general). In any study, there s always a possibility that if we drew a different sample from the population, the results might be different. Perhaps our results are unique to our sample and not generalizable to the larger population. If we were able to collect data on the entire population, we would not have to wrestle with this problem, but our dependence on a sample necessitates the use of inferential statistics to precisely evaluate the likelihood that our results are due to chance factors in sampling. Thus, inferential statistics are the key to making the inferential leap from the sample to the population (see Figure B.). Although it may seem backward, in hypothesis testing, we formally test the null hypothesis. As applied to correlational data, the null hypothesis is the assumption that there is no true relationship between the variables observed. In the students study, the null hypothesis is that there is no genuine Figure B. Population: The complete set Sampling Sample: A subset of the population Inference The relationship between the population and the sample. In research, we are usually interested in a broad population, but we can observe only a small sample from the population. After making observations of our sample, we draw inferences about the population, based on the sample. This inferential process works well as long as the sample is reasonably representative of the population. A- APPENDI B NEL 77_7_App_pA-A pp.indd // :: AM
8 association between TV viewing and SAT scores. They want to determine whether their results will permit them to reject the null hypothesis and thus conclude that their research hypothesis (that there is a relationship between the variables) has been supported. In such cases, why do researchers directly test the null hypothesis instead of the research hypothesis? Because our probability calculations depend on assumptions tied to the null hypothesis. Specifically, we compute the probability of obtaining the results that we have observed if the null hypothesis is indeed true. The calculation of this probability hinges on a number of factors. A key factor is the amount of variability in the data, which is why the standard deviation is an important statistic. Statistical Significance When we reject the null hypothesis, we conclude that we have found statistically significant results. Statistical significance is said to exist when the probability that the observed findings are due to chance is very low, usually fewer than chances in. This means that if the null hypothesis is correct and we conduct our study times, drawing a new sample from the population each time, we will get results such as those observed only times out of. If our calculations allow us to reject the null hypothesis, we conclude that our results support our research hypothesis. Thus, statistically significant results typically are findings that support a research hypothesis. The requirement that there be fewer than chances in that research results are due to chance is the minimum requirement for statistical significance. When this requirement is met, we say the results are significant at the. level. If researchers calculate that there is less than chance in that their results are due to chance factors in sampling, the results are significant at the. level. If there is less than a in chance that findings are attributable to sampling error, the results are significant at the. level. Thus, there are several levels of significance that you may see cited in scientific articles. Because we are dealing only in matters of probability, there is always the possibility that our decision to accept or reject the null hypothesis is wrong. The various significance levels indicate the probability of erroneously rejecting the null hypothesis (and inaccurately accepting the research hypothesis). At the. level of significance, there are chances in that we have made a mistake when we conclude that our results support our hypothesis, and at the. level of significance, the chance of an erroneous conclusion is in. Although researchers hold the probability of this type of error quite low, the probability is never zero. This is one of the reasons that competently executed studies of the same question can yield contradictory findings. The differences may be due to chance variations in sampling that can t be prevented. What do we find when we evaluate the data linking TV viewing to students SAT scores? The calculations indicate that, given the sample size and the variability in the data, the probability of obtaining a correlation of. by chance is greater than %. That s not a high probability, but it s not low enough to reject the null hypothesis. Thus, the findings are not strong enough to allow us to conclude that the students have supported their hypothesis. Statistics and Empiricism In summary, conclusions based on empirical research are a matter of probability, and there s always a possibility that the conclusions are wrong. However, two major strengths of the empirical approach are its precision and its intolerance of error. Scientists can give you precise estimates of the likelihood that their conclusions are wrong, and because they re intolerant of error, they hold this probability extremely low. It s their reliance on statistics that allows them to accomplish these goals. Key Terms Coefficient of determination, A- Correlation coefficient, A- Descriptive statistics, A- distribution, A-8 polygon, A-8 Histogram, A-8 Inferential statistics, A- Mean, A- Median, A- Mode, A- Negatively skewed distribution, A- Normal distribution, A- Null hypothesis, A- Percentile score, A- Positively skewed distribution, A- Scatter diagram, A- Standard deviation, A- Statistical significance, A- Statistics, A-8 Variability, A- NEL APPENDI B A- 77_7_App_pA-A pp.indd // :: AM
CHAPTER ONE CORRELATION
CHAPTER ONE CORRELATION 1.0 Introduction The first chapter focuses on the nature of statistical data of correlation. The aim of the series of exercises is to ensure the students are able to use SPSS to
More informationChapter 1: Introduction to Statistics
Chapter 1: Introduction to Statistics Variables A variable is a characteristic or condition that can change or take on different values. Most research begins with a general question about the relationship
More information3 CONCEPTUAL FOUNDATIONS OF STATISTICS
3 CONCEPTUAL FOUNDATIONS OF STATISTICS In this chapter, we examine the conceptual foundations of statistics. The goal is to give you an appreciation and conceptual understanding of some basic statistical
More informationLesson 9 Presentation and Display of Quantitative Data
Lesson 9 Presentation and Display of Quantitative Data Learning Objectives All students will identify and present data using appropriate graphs, charts and tables. All students should be able to justify
More informationStandard Scores. Richard S. Balkin, Ph.D., LPC-S, NCC
Standard Scores Richard S. Balkin, Ph.D., LPC-S, NCC 1 Normal Distributions While Best and Kahn (2003) indicated that the normal curve does not actually exist, measures of populations tend to demonstrate
More informationSTATISTICS AND RESEARCH DESIGN
Statistics 1 STATISTICS AND RESEARCH DESIGN These are subjects that are frequently confused. Both subjects often evoke student anxiety and avoidance. To further complicate matters, both areas appear have
More informationCHAPTER 3 DATA ANALYSIS: DESCRIBING DATA
Data Analysis: Describing Data CHAPTER 3 DATA ANALYSIS: DESCRIBING DATA In the analysis process, the researcher tries to evaluate the data collected both from written documents and from other sources such
More informationResults & Statistics: Description and Correlation. I. Scales of Measurement A Review
Results & Statistics: Description and Correlation The description and presentation of results involves a number of topics. These include scales of measurement, descriptive statistics used to summarize
More informationChapter 7: Descriptive Statistics
Chapter Overview Chapter 7 provides an introduction to basic strategies for describing groups statistically. Statistical concepts around normal distributions are discussed. The statistical procedures of
More informationBusiness Statistics Probability
Business Statistics The following was provided by Dr. Suzanne Delaney, and is a comprehensive review of Business Statistics. The workshop instructor will provide relevant examples during the Skills Assessment
More informationStatistical Methods and Reasoning for the Clinical Sciences
Statistical Methods and Reasoning for the Clinical Sciences Evidence-Based Practice Eiki B. Satake, PhD Contents Preface Introduction to Evidence-Based Statistics: Philosophical Foundation and Preliminaries
More informationStill important ideas
Readings: OpenStax - Chapters 1 13 & Appendix D & E (online) Plous Chapters 17 & 18 - Chapter 17: Social Influences - Chapter 18: Group Judgments and Decisions Still important ideas Contrast the measurement
More informationStatistics for Psychology
Statistics for Psychology SIXTH EDITION CHAPTER 3 Some Key Ingredients for Inferential Statistics Some Key Ingredients for Inferential Statistics Psychologists conduct research to test a theoretical principle
More informationOn the purpose of testing:
Why Evaluation & Assessment is Important Feedback to students Feedback to teachers Information to parents Information for selection and certification Information for accountability Incentives to increase
More informationHomework Exercises for PSYC 3330: Statistics for the Behavioral Sciences
Homework Exercises for PSYC 3330: Statistics for the Behavioral Sciences compiled and edited by Thomas J. Faulkenberry, Ph.D. Department of Psychological Sciences Tarleton State University Version: July
More informationBiostatistics. Donna Kritz-Silverstein, Ph.D. Professor Department of Family & Preventive Medicine University of California, San Diego
Biostatistics Donna Kritz-Silverstein, Ph.D. Professor Department of Family & Preventive Medicine University of California, San Diego (858) 534-1818 dsilverstein@ucsd.edu Introduction Overview of statistical
More informationUnit 7 Comparisons and Relationships
Unit 7 Comparisons and Relationships Objectives: To understand the distinction between making a comparison and describing a relationship To select appropriate graphical displays for making comparisons
More informationUndertaking statistical analysis of
Descriptive statistics: Simply telling a story Laura Delaney introduces the principles of descriptive statistical analysis and presents an overview of the various ways in which data can be presented by
More informationChapter 2 Norms and Basic Statistics for Testing MULTIPLE CHOICE
Chapter 2 Norms and Basic Statistics for Testing MULTIPLE CHOICE 1. When you assert that it is improbable that the mean intelligence test score of a particular group is 100, you are using. a. descriptive
More informationDescribe what is meant by a placebo Contrast the double-blind procedure with the single-blind procedure Review the structure for organizing a memo
Business Statistics The following was provided by Dr. Suzanne Delaney, and is a comprehensive review of Business Statistics. The workshop instructor will provide relevant examples during the Skills Assessment
More informationUnit 1 Exploring and Understanding Data
Unit 1 Exploring and Understanding Data Area Principle Bar Chart Boxplot Conditional Distribution Dotplot Empirical Rule Five Number Summary Frequency Distribution Frequency Polygon Histogram Interquartile
More information1 The conceptual underpinnings of statistical power
1 The conceptual underpinnings of statistical power The importance of statistical power As currently practiced in the social and health sciences, inferential statistics rest solidly upon two pillars: statistical
More informationReadings: Textbook readings: OpenStax - Chapters 1 13 (emphasis on Chapter 12) Online readings: Appendix D, E & F
Readings: Textbook readings: OpenStax - Chapters 1 13 (emphasis on Chapter 12) Online readings: Appendix D, E & F Plous Chapters 17 & 18 Chapter 17: Social Influences Chapter 18: Group Judgments and Decisions
More informationStill important ideas
Readings: OpenStax - Chapters 1 11 + 13 & Appendix D & E (online) Plous - Chapters 2, 3, and 4 Chapter 2: Cognitive Dissonance, Chapter 3: Memory and Hindsight Bias, Chapter 4: Context Dependence Still
More informationDescribe what is meant by a placebo Contrast the double-blind procedure with the single-blind procedure Review the structure for organizing a memo
Please note the page numbers listed for the Lind book may vary by a page or two depending on which version of the textbook you have. Readings: Lind 1 11 (with emphasis on chapters 10, 11) Please note chapter
More informationData and Statistics 101: Key Concepts in the Collection, Analysis, and Application of Child Welfare Data
TECHNICAL REPORT Data and Statistics 101: Key Concepts in the Collection, Analysis, and Application of Child Welfare Data CONTENTS Executive Summary...1 Introduction...2 Overview of Data Analysis Concepts...2
More informationMedical Statistics 1. Basic Concepts Farhad Pishgar. Defining the data. Alive after 6 months?
Medical Statistics 1 Basic Concepts Farhad Pishgar Defining the data Population and samples Except when a full census is taken, we collect data on a sample from a much larger group called the population.
More informationMeasurement and Descriptive Statistics. Katie Rommel-Esham Education 604
Measurement and Descriptive Statistics Katie Rommel-Esham Education 604 Frequency Distributions Frequency table # grad courses taken f 3 or fewer 5 4-6 3 7-9 2 10 or more 4 Pictorial Representations Frequency
More informationDescriptive Statistics Lecture
Definitions: Lecture Psychology 280 Orange Coast College 2/1/2006 Statistics have been defined as a collection of methods for planning experiments, obtaining data, and then analyzing, interpreting and
More informationStatistics. Nur Hidayanto PSP English Education Dept. SStatistics/Nur Hidayanto PSP/PBI
Statistics Nur Hidayanto PSP English Education Dept. RESEARCH STATISTICS WHAT S THE RELATIONSHIP? RESEARCH RESEARCH positivistic Prepositivistic Postpositivistic Data Initial Observation (research Question)
More informationStudents will understand the definition of mean, median, mode and standard deviation and be able to calculate these functions with given set of
Students will understand the definition of mean, median, mode and standard deviation and be able to calculate these functions with given set of numbers. Also, students will understand why some measures
More informationCHAPTER - 6 STATISTICAL ANALYSIS. This chapter discusses inferential statistics, which use sample data to
CHAPTER - 6 STATISTICAL ANALYSIS 6.1 Introduction This chapter discusses inferential statistics, which use sample data to make decisions or inferences about population. Populations are group of interest
More informationResearch Methods 1 Handouts, Graham Hole,COGS - version 1.0, September 2000: Page 1:
Research Methods 1 Handouts, Graham Hole,COGS - version 10, September 000: Page 1: T-TESTS: When to use a t-test: The simplest experimental design is to have two conditions: an "experimental" condition
More informationChapter 2--Norms and Basic Statistics for Testing
Chapter 2--Norms and Basic Statistics for Testing Student: 1. Statistical procedures that summarize and describe a series of observations are called A. inferential statistics. B. descriptive statistics.
More informationReadings: Textbook readings: OpenStax - Chapters 1 11 Online readings: Appendix D, E & F Plous Chapters 10, 11, 12 and 14
Readings: Textbook readings: OpenStax - Chapters 1 11 Online readings: Appendix D, E & F Plous Chapters 10, 11, 12 and 14 Still important ideas Contrast the measurement of observable actions (and/or characteristics)
More informationStatistics: Making Sense of the Numbers
Statistics: Making Sense of the Numbers Chapter 9 This multimedia product and its contents are protected under copyright law. The following are prohibited by law: any public performance or display, including
More informationISC- GRADE XI HUMANITIES ( ) PSYCHOLOGY. Chapter 2- Methods of Psychology
ISC- GRADE XI HUMANITIES (2018-19) PSYCHOLOGY Chapter 2- Methods of Psychology OUTLINE OF THE CHAPTER (i) Scientific Methods in Psychology -observation, case study, surveys, psychological tests, experimentation
More informationSection 6: Analysing Relationships Between Variables
6. 1 Analysing Relationships Between Variables Section 6: Analysing Relationships Between Variables Choosing a Technique The Crosstabs Procedure The Chi Square Test The Means Procedure The Correlations
More informationChapter 1: Exploring Data
Chapter 1: Exploring Data Key Vocabulary:! individual! variable! frequency table! relative frequency table! distribution! pie chart! bar graph! two-way table! marginal distributions! conditional distributions!
More informationDescribe what is meant by a placebo Contrast the double-blind procedure with the single-blind procedure Review the structure for organizing a memo
Please note the page numbers listed for the Lind book may vary by a page or two depending on which version of the textbook you have. Readings: Lind 1 11 (with emphasis on chapters 5, 6, 7, 8, 9 10 & 11)
More informationChapter 23. Inference About Means. Copyright 2010 Pearson Education, Inc.
Chapter 23 Inference About Means Copyright 2010 Pearson Education, Inc. Getting Started Now that we know how to create confidence intervals and test hypotheses about proportions, it d be nice to be able
More informationNever P alone: The value of estimates and confidence intervals
Never P alone: The value of estimates and confidence Tom Lang Tom Lang Communications and Training International, Kirkland, WA, USA Correspondence to: Tom Lang 10003 NE 115th Lane Kirkland, WA 98933 USA
More informationStatistical Methods Exam I Review
Statistical Methods Exam I Review Professor: Dr. Kathleen Suchora SI Leader: Camila M. DISCLAIMER: I have created this review sheet to supplement your studies for your first exam. I am a student here at
More informationCHAPTER 2. MEASURING AND DESCRIBING VARIABLES
4 Chapter 2 CHAPTER 2. MEASURING AND DESCRIBING VARIABLES 1. A. Age: name/interval; military dictatorship: value/nominal; strongly oppose: value/ ordinal; election year: name/interval; 62 percent: value/interval;
More informationChapter 20: Test Administration and Interpretation
Chapter 20: Test Administration and Interpretation Thought Questions Why should a needs analysis consider both the individual and the demands of the sport? Should test scores be shared with a team, or
More informationEmpirical Knowledge: based on observations. Answer questions why, whom, how, and when.
INTRO TO RESEARCH METHODS: Empirical Knowledge: based on observations. Answer questions why, whom, how, and when. Experimental research: treatments are given for the purpose of research. Experimental group
More informationAPPENDIX N. Summary Statistics: The "Big 5" Statistical Tools for School Counselors
APPENDIX N Summary Statistics: The "Big 5" Statistical Tools for School Counselors This appendix describes five basic statistical tools school counselors may use in conducting results based evaluation.
More informationStatistics: Interpreting Data and Making Predictions. Interpreting Data 1/50
Statistics: Interpreting Data and Making Predictions Interpreting Data 1/50 Last Time Last time we discussed central tendency; that is, notions of the middle of data. More specifically we discussed the
More informationStatistical Techniques. Masoud Mansoury and Anas Abulfaraj
Statistical Techniques Masoud Mansoury and Anas Abulfaraj What is Statistics? https://www.youtube.com/watch?v=lmmzj7599pw The definition of Statistics The practice or science of collecting and analyzing
More informationStatistics is the science of collecting, organizing, presenting, analyzing, and interpreting data to assist in making effective decisions
Readings: OpenStax Textbook - Chapters 1 5 (online) Appendix D & E (online) Plous - Chapters 1, 5, 6, 13 (online) Introductory comments Describe how familiarity with statistical methods can - be associated
More informationWDHS Curriculum Map Probability and Statistics. What is Statistics and how does it relate to you?
WDHS Curriculum Map Probability and Statistics Time Interval/ Unit 1: Introduction to Statistics 1.1-1.3 2 weeks S-IC-1: Understand statistics as a process for making inferences about population parameters
More informationbivariate analysis: The statistical analysis of the relationship between two variables.
bivariate analysis: The statistical analysis of the relationship between two variables. cell frequency: The number of cases in a cell of a cross-tabulation (contingency table). chi-square (χ 2 ) test for
More informationC-1: Variables which are measured on a continuous scale are described in terms of three key characteristics central tendency, variability, and shape.
MODULE 02: DESCRIBING DT SECTION C: KEY POINTS C-1: Variables which are measured on a continuous scale are described in terms of three key characteristics central tendency, variability, and shape. C-2:
More informationPsychology Research Process
Psychology Research Process Logical Processes Induction Observation/Association/Using Correlation Trying to assess, through observation of a large group/sample, what is associated with what? Examples:
More informationLesson 11 Correlations
Lesson 11 Correlations Lesson Objectives All students will define key terms and explain the difference between correlations and experiments. All students should be able to analyse scattergrams using knowledge
More informationQuantitative Methods in Computing Education Research (A brief overview tips and techniques)
Quantitative Methods in Computing Education Research (A brief overview tips and techniques) Dr Judy Sheard Senior Lecturer Co-Director, Computing Education Research Group Monash University judy.sheard@monash.edu
More informationStatistics is the science of collecting, organizing, presenting, analyzing, and interpreting data to assist in making effective decisions
Readings: OpenStax Textbook - Chapters 1 5 (online) Appendix D & E (online) Plous - Chapters 1, 5, 6, 13 (online) Introductory comments Describe how familiarity with statistical methods can - be associated
More informationSection 3.2 Least-Squares Regression
Section 3.2 Least-Squares Regression Linear relationships between two quantitative variables are pretty common and easy to understand. Correlation measures the direction and strength of these relationships.
More informationData, frequencies, and distributions. Martin Bland. Types of data. Types of data. Clinical Biostatistics
Clinical Biostatistics Data, frequencies, and distributions Martin Bland Professor of Health Statistics University of York http://martinbland.co.uk/ Types of data Qualitative data arise when individuals
More informationWelcome to OSA Training Statistics Part II
Welcome to OSA Training Statistics Part II Course Summary Using data about a population to draw graphs Frequency distribution and variability within populations Bell Curves: What are they and where do
More informationPsy201 Module 3 Study and Assignment Guide. Using Excel to Calculate Descriptive and Inferential Statistics
Psy201 Module 3 Study and Assignment Guide Using Excel to Calculate Descriptive and Inferential Statistics What is Excel? Excel is a spreadsheet program that allows one to enter numerical values or data
More informationEating and Sleeping Habits of Different Countries
9.2 Analyzing Scatter Plots Now that we know how to draw scatter plots, we need to know how to interpret them. A scatter plot graph can give us lots of important information about how data sets are related
More information11/18/2013. Correlational Research. Correlational Designs. Why Use a Correlational Design? CORRELATIONAL RESEARCH STUDIES
Correlational Research Correlational Designs Correlational research is used to describe the relationship between two or more naturally occurring variables. Is age related to political conservativism? Are
More informationStats 95. Statistical analysis without compelling presentation is annoying at best and catastrophic at worst. From raw numbers to meaningful pictures
Stats 95 Statistical analysis without compelling presentation is annoying at best and catastrophic at worst. From raw numbers to meaningful pictures Stats 95 Why Stats? 200 countries over 200 years http://www.youtube.com/watch?v=jbksrlysojo
More informationInferential Statistics
Inferential Statistics and t - tests ScWk 242 Session 9 Slides Inferential Statistics Ø Inferential statistics are used to test hypotheses about the relationship between the independent and the dependent
More informationMeasuring the User Experience
Measuring the User Experience Collecting, Analyzing, and Presenting Usability Metrics Chapter 2 Background Tom Tullis and Bill Albert Morgan Kaufmann, 2008 ISBN 978-0123735584 Introduction Purpose Provide
More informationStatisticians deal with groups of numbers. They often find it helpful to use
Chapter 4 Finding Your Center In This Chapter Working within your means Meeting conditions The median is the message Getting into the mode Statisticians deal with groups of numbers. They often find it
More informationAssessing Agreement Between Methods Of Clinical Measurement
University of York Department of Health Sciences Measuring Health and Disease Assessing Agreement Between Methods Of Clinical Measurement Based on Bland JM, Altman DG. (1986). Statistical methods for assessing
More informationApplied Statistical Analysis EDUC 6050 Week 4
Applied Statistical Analysis EDUC 6050 Week 4 Finding clarity using data Today 1. Hypothesis Testing with Z Scores (continued) 2. Chapters 6 and 7 in Book 2 Review! = $ & '! = $ & ' * ) 1. Which formula
More informationAP Psych - Stat 1 Name Period Date. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
AP Psych - Stat 1 Name Period Date MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) In a set of incomes in which most people are in the $15,000
More informationTwo-Way Independent ANOVA
Two-Way Independent ANOVA Analysis of Variance (ANOVA) a common and robust statistical test that you can use to compare the mean scores collected from different conditions or groups in an experiment. There
More informationPRINCIPLES OF STATISTICS
PRINCIPLES OF STATISTICS STA-201-TE This TECEP is an introduction to descriptive and inferential statistics. Topics include: measures of central tendency, variability, correlation, regression, hypothesis
More informationIntroduction to Statistical Data Analysis I
Introduction to Statistical Data Analysis I JULY 2011 Afsaneh Yazdani Preface What is Statistics? Preface What is Statistics? Science of: designing studies or experiments, collecting data Summarizing/modeling/analyzing
More informationMULTIPLE LINEAR REGRESSION 24.1 INTRODUCTION AND OBJECTIVES OBJECTIVES
24 MULTIPLE LINEAR REGRESSION 24.1 INTRODUCTION AND OBJECTIVES In the previous chapter, simple linear regression was used when you have one independent variable and one dependent variable. This chapter
More informationRegression CHAPTER SIXTEEN NOTE TO INSTRUCTORS OUTLINE OF RESOURCES
CHAPTER SIXTEEN Regression NOTE TO INSTRUCTORS This chapter includes a number of complex concepts that may seem intimidating to students. Encourage students to focus on the big picture through some of
More informationClever Hans the horse could do simple math and spell out the answers to simple questions. He wasn t always correct, but he was most of the time.
Clever Hans the horse could do simple math and spell out the answers to simple questions. He wasn t always correct, but he was most of the time. While a team of scientists, veterinarians, zoologists and
More informationConvergence Principles: Information in the Answer
Convergence Principles: Information in the Answer Sets of Some Multiple-Choice Intelligence Tests A. P. White and J. E. Zammarelli University of Durham It is hypothesized that some common multiplechoice
More informationVariability. After reading this chapter, you should be able to do the following:
LEARIG OBJECTIVES C H A P T E R 3 Variability After reading this chapter, you should be able to do the following: Explain what the standard deviation measures Compute the variance and the standard deviation
More information9 research designs likely for PSYC 2100
9 research designs likely for PSYC 2100 1) 1 factor, 2 levels, 1 group (one group gets both treatment levels) related samples t-test (compare means of 2 levels only) 2) 1 factor, 2 levels, 2 groups (one
More informationStatistics: Bar Graphs and Standard Error
www.mathbench.umd.edu Bar graphs and standard error May 2010 page 1 Statistics: Bar Graphs and Standard Error URL: http://mathbench.umd.edu/modules/prob-stat_bargraph/page01.htm Beyond the scatterplot
More informationSPRING GROVE AREA SCHOOL DISTRICT. Course Description. Instructional Strategies, Learning Practices, Activities, and Experiences.
SPRING GROVE AREA SCHOOL DISTRICT PLANNED COURSE OVERVIEW Course Title: Basic Introductory Statistics Grade Level(s): 11-12 Units of Credit: 1 Classification: Elective Length of Course: 30 cycles Periods
More informationUnderstandable Statistics
Understandable Statistics correlated to the Advanced Placement Program Course Description for Statistics Prepared for Alabama CC2 6/2003 2003 Understandable Statistics 2003 correlated to the Advanced Placement
More informationGeorgina Salas. Topics EDCI Intro to Research Dr. A.J. Herrera
Homework assignment topics 51-63 Georgina Salas Topics 51-63 EDCI Intro to Research 6300.62 Dr. A.J. Herrera Topic 51 1. Which average is usually reported when the standard deviation is reported? The mean
More informationt-test for r Copyright 2000 Tom Malloy. All rights reserved
t-test for r Copyright 2000 Tom Malloy. All rights reserved This is the text of the in-class lecture which accompanied the Authorware visual graphics on this topic. You may print this text out and use
More informationCCM6+7+ Unit 12 Data Collection and Analysis
Page 1 CCM6+7+ Unit 12 Packet: Statistics and Data Analysis CCM6+7+ Unit 12 Data Collection and Analysis Big Ideas Page(s) What is data/statistics? 2-4 Measures of Reliability and Variability: Sampling,
More informationChapter 1: Explaining Behavior
Chapter 1: Explaining Behavior GOAL OF SCIENCE is to generate explanations for various puzzling natural phenomenon. - Generate general laws of behavior (psychology) RESEARCH: principle method for acquiring
More informationUsing Analytical and Psychometric Tools in Medium- and High-Stakes Environments
Using Analytical and Psychometric Tools in Medium- and High-Stakes Environments Greg Pope, Analytics and Psychometrics Manager 2008 Users Conference San Antonio Introduction and purpose of this session
More informationStudent Performance Q&A:
Student Performance Q&A: 2009 AP Statistics Free-Response Questions The following comments on the 2009 free-response questions for AP Statistics were written by the Chief Reader, Christine Franklin of
More informationTypes of questions. You need to know. Short question. Short question. Measurement Scale: Ordinal Scale
You need to know Materials in the slides Materials in the 5 coglab presented in class Textbooks chapters Information/explanation given in class you can have all these documents with you + your notes during
More informationStatistical Significance, Effect Size, and Practical Significance Eva Lawrence Guilford College October, 2017
Statistical Significance, Effect Size, and Practical Significance Eva Lawrence Guilford College October, 2017 Definitions Descriptive statistics: Statistical analyses used to describe characteristics of
More informationPolitical Science 15, Winter 2014 Final Review
Political Science 15, Winter 2014 Final Review The major topics covered in class are listed below. You should also take a look at the readings listed on the class website. Studying Politics Scientifically
More informationOne-Way ANOVAs t-test two statistically significant Type I error alpha null hypothesis dependant variable Independent variable three levels;
1 One-Way ANOVAs We have already discussed the t-test. The t-test is used for comparing the means of two groups to determine if there is a statistically significant difference between them. The t-test
More informationKnowledge discovery tools 381
Knowledge discovery tools 381 hours, and prime time is prime time precisely because more people tend to watch television at that time.. Compare histograms from di erent periods of time. Changes in histogram
More informationExamining differences between two sets of scores
6 Examining differences between two sets of scores In this chapter you will learn about tests which tell us if there is a statistically significant difference between two sets of scores. In so doing you
More informationPsychology Research Process
Psychology Research Process Logical Processes Induction Observation/Association/Using Correlation Trying to assess, through observation of a large group/sample, what is associated with what? Examples:
More informationHARRISON ASSESSMENTS DEBRIEF GUIDE 1. OVERVIEW OF HARRISON ASSESSMENT
HARRISON ASSESSMENTS HARRISON ASSESSMENTS DEBRIEF GUIDE 1. OVERVIEW OF HARRISON ASSESSMENT Have you put aside an hour and do you have a hard copy of your report? Get a quick take on their initial reactions
More informationMODULE S1 DESCRIPTIVE STATISTICS
MODULE S1 DESCRIPTIVE STATISTICS All educators are involved in research and statistics to a degree. For this reason all educators should have a practical understanding of research design. Even if an educator
More informationUnderstanding Correlations The Powerful Relationship between Two Independent Variables
Understanding Correlations The Powerful Relationship between Two Independent Variables Dr. Robert Tippie, PhD I n this scientific paper we will discuss the significance of the Pearson r Correlation Coefficient
More informationOne-Way Independent ANOVA
One-Way Independent ANOVA Analysis of Variance (ANOVA) is a common and robust statistical test that you can use to compare the mean scores collected from different conditions or groups in an experiment.
More informationIntroduction to statistics Dr Alvin Vista, ACER Bangkok, 14-18, Sept. 2015
Analysing and Understanding Learning Assessment for Evidence-based Policy Making Introduction to statistics Dr Alvin Vista, ACER Bangkok, 14-18, Sept. 2015 Australian Council for Educational Research Structure
More information