... Lilian Otieno, Resident Lecturer I am tasked to distinguish between parametric and non-parametric statistics and explain when to use each method in analysis of data. I shall first seek to define what parametric and non-parametric statistics mean and then compare and contrast them in the analysis of data. Parametric statistics is a branch of statistics that assumes that the data has come from a type of probability distribution and makes inferences about the parameters of the distribution. Most well-known elementary statistical methods are parametric. (According to Wikipedia, the online dictionary). In statistical analysis, parametric significance tests are only valid if certain assumptions are met. If they are not, nonparametric tests can be used. A parameter is a measure of an entire population, such as the mean height of every man in London. In statistical analysis, one practically never has measurements from a whole population and has to infer the characteristics of the population from a sample. Generally speaking parametric methods make more assumptions than non-parametric methods. If those extra assumptions are correct, parametric methods can produce more accurate and precise estimates. They are said to have more statistical power. However, if assumptions are incorrect, parametric methods can be very misleading. For that reason they are often not considered robust. On the other hand, parametric formulae are often simpler to write down and faster to compute. In some,...
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................................................................................................... 5 2.1. 2.2. 2.3. Mergers and acquisitions activity in recent years .................................................. 5 Overview of efficient market hypothesis .............................................................. 7 Abnormal operating performance ......................................................................... 9 3. Event study approach ............................................................................................... 12 3.1. 3.2. Event study technique ........................................................................................ 12 Test statistics ..................................................................................................... 14 Parametric tests...
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...Nonparametric Hypothesis Testing RES/342 Nonparametric Hypothesis Testing During the course of the last three weeks, the team explored the hypothesis testing segment of statistics research. The first part of this assignment was the one sample hypothesis testing. The second was the two or more sample hypothesis testing, and finally in this third week, we will look at nonparametric hypothesis testing. This week’s project is a continuation of the previous projects and entails to build on the identical research question that we will frame a research hypothesis from the same provided data sets (Wage and Wage Earners) using ratio or interval numerical data; however, this week we will use a nonparametric hypothesis test to find our answer. In the next following paragraphs, the team will clearly affirm a hypothesis statement that will provide the base for our survey, perform a five-step hypothesis test on information concerning our choice and apply the concepts of nonparametric testing learned in this course, and describe how the results of our findings answer our research question. Finally, we will conclude this study with a brief summary that will examine the main points, the purpose, and conclusions of this final third week’s study on nonparametric testing. Perform the five-step hypothesis test on the data Nonparametric tests are statistical tests that analyze data that does not require assumptions about the distribution of shape of the population from which...
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...WEIGHTED AVERAGE SCORE Table showing weighted average score for elements of work ethics. |Factors |Strongly agree |Agrees |Neutral |Disagree |Strongly disagree| |Performance Appraisal |8 |55 |6 |20 |11 | |Performance Measurement |12 |65 |8 |10 |5 | |Mission statements |10 |33 |15 |40 |2 | |Work culture |35 |40 |5 |18 |2 | |Quality Concerns |5 |28 |1 |32 |34 | Table showing weighted average score for elements of work ethics. |Factors |Strongly agree |Agrees (4) |Neutral (3) |Disagree |Strongly disagree|Total |Rank | | |(5) | | |(2) |(1) | | | |Performance Appraisal |40 |220 |18 |40 |22 |340 = 22.6 |1 | | | | | | | |15 ...
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...Statistics Practical 2a Comments on Z-tests and t-tests 1. You should have realized from the lectures that in practice, a z-test is seldom used, while the ‘default’ test for single sample or two-samples mean(s) is the ttest. This is because in most practical situations, the population variance is seldom known and therefore we need to estimate that by the sample variance, thus justifying a t-test rather than a z-test. It is always good to perform the standard exploratory data analysis before commencing any hypothesis testing involving t-tests. It is often useful to check through summary statistics (like the minimum and maximum of the data), as well as a quick plot of the data (box-plots), to check for any problematic data or outliers. The use of a t-test requires the assumption that the data is distributed like a normal distribution – essentially a bell-shaped curve for the histogram. Therefore it is extremely informative to look at the histogram of the data before commencing on testing, as this will indicate whether the use of the t-test is justified. Before commencing any testing, evaluate what are your hypotheses that you are interested in. If you are testing the mean for a single sample, are you testing the mean to be 0, or are you testing the mean against some non-zero value. If so, do remember to change the input in SPSS correspondingly. Similarly if you are testing the means for two samples, are you testing for the difference to be zero, or against a non-zero difference...
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...HYPOTHESIS TESTS Lecture Notes Asst. Prof. Jay Kaiser S. Lariosa Non-Parametric Statistics 2 Spearman Rank Correlation Source: Elementary Number Theory 4th ed., by David M. Burton Prepared by Asst. Prof. Jay Kaiser S. Lariosa Pearson’s r 3 • The Pearson product-moment correlation coefficient is designed to measure the strength of the association between two quantitative variables. • The two variables being compared must be measured on either interval or ratio scale. Source: Elementary Number Theory 4th ed., by David M. Burton Prepared by Asst. Prof. Jay Kaiser S. Lariosa Spearman Rank Correlation Coefficient 4 • • Is a nonparametric counterpart of the Pearson’s r. This coefficient measures the extent of association between two variables each measured on an ordinal scale. Source: Elementary Number Theory 4th ed., by David M. Burton Prepared by Asst. Prof. Jay Kaiser S. Lariosa Spearman’s r 5 • The procedure for calculating the Spearman rank correlation coefficient consists of two sets of rankings on the same subjects. • The strength of association between these two rankings is measured by the coefficient. Source: Elementary Number Theory 4th ed., by David M. Burton Prepared by Asst. Prof. Jay Kaiser S. Lariosa 6 Spearman’s rs rs 1 • 6 d 2 n3 n where: • • • • rs = Spearman rank correlation coefficient d2 = squared differences between the two ranks n = number of objects being compared...
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...3.5 Inferential Statistics: The Plot Thickens We have been talking about ways to calculate and describe characteristics about data. Descriptive statistics tell us information about the distribution of our data, how varied the data are, and the shape of the data. Now we are also interested in information related to our data parameters. In other words, we want to know if we have relationships, associations, or differences within our data and whether statistical significance exists. Inferential statistics help us make these determinations and allow us to generalize the results to a larger population. We provide background about parametric and nonparametric statistics and then show basic inferential statistics that examine associations among variables and tests of differences between groups. Parametric and Nonparametric Statistics In the world of statistics, distinctions are made in the types of analyses that can be used by the evaluator based on distribution assumptions and the levels of measurement data. For example, parametric statistics are based on the assumption of normal distribution and randomized sampling that results in interval or ratio data. The statistical tests usually determine significance of difference or relationships. These parametric statistical tests commonly include t-tests, Pearson product-moment correlations, and analyses of variance. Nonparametric statistics are known as distribution-free tests because they are not based on the assumptions...
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...EDITORIAL Analyzing and Interpreting Data From Likert-Type Scales L ikert-type scales are frequently used in medical education and medical education research. Common uses include end-of-rotation trainee feedback, faculty evaluations of trainees, and assessment of performance after an educational intervention. A sizable percentage of the educational research manuscripts submitted to the Journal of Graduate Medical Education employ a Likert scale for part or all of the outcome assessments. Thus, understanding the interpretation and analysis of data derived from Likert scales is imperative for those working in medical education and education research. The goal of this article is to provide readers who do not have extensive statistics background with the basics needed to understand these concepts. Developed in 1932 by Rensis Likert1 to measure attitudes, the typical Likert scale is a 5- or 7-point ordinal scale used by respondents to rate the degree to which they agree or disagree with a statement (T A B L E). In an ordinal scale, responses can be rated or ranked, but the distance between responses is not measurable. Thus, the differences between ‘‘always,’’ ‘‘often,’’ and ‘‘sometimes’’ on a frequency response Likert scale are not necessarily equal. In other words, one cannot assume that the difference between responses is equidistant even though the numbers assigned to those responses are. This is in contrast to interval data, in which the difference between...
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...1. 2. QBUS5001 3. QBUSS5002 topic1 - 12 EXCEL 4. word ----- 5. zh.lai@foxmail.com R-XIANG George Jackie HD QBUS5001 ~ Jack 2015/6/7 目录 ........................................................................................................................................................................................... 1 TOPIC 1 ....................................................................................................................................................................................... 4 TOPIC 2 PROBABILITY ........................................................................................................................................................ 4 2.1 EVENTS & PROBABILITIES 2.2 JOINT ............................................................................................................................................ 4 MARGINAL& CONDITIONAL PROBABILITIES 2.3 PROBABILITIES TREES ....................................................................................... 4 .......................................................................................................................................................... 4 2.4 BAYER’S THEOREM ......................................................................................................................................................................... 4 2.5 POPULATION MEAN & VARIANCE ................
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...assumptions that were checked, and the results obtained. The more practice you get with this process, the easier it will be for you to write up the results of your analyses. Details on how to structure a report are available on AUTonline. Part A 1. A market researcher is interested in the coffee drinking habits of males and females. He asks a sample of male and female office workers to record the number of cups of coffee they consume during a week. (a) Which parametric statistical technique could the researcher use to determine if males and females differ in terms of the number of cups of coffee consumed in a week? Justify your answer and describe how you would obtain this statistic using SPSS. Independent-samples t-tests (b) What are the key values you would look for in the output? (c) What assumptions should you check for when using the technique that you chose in question 2(a) above. Interval scaled data with normally distributed scores Random sampling data (d) What non-parametric technique (chapter 16) could be used to address this research question? (p109) Mann-Whitney U Test 2. The following output was obtained using SPSS....
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...Investigating age differences effect on emotion detection for the over and under forties using Baron Cohen's “Eyes Test” (Baron-Cohen, Wheelwright & Hill, 2001) Abstract: This research focuses on the area of emotion detection in psychology. Independent variables being tested is the participants’ age [over and under 40 years of age]. Dependent variables being tested is participants’ scores in the eyes test. Participants were picked from a convenience sample with a large sum selected from adults attending Buckingham University Previous research suggests that there is a steady decline in emotion detection from a young age into elderly age. The key prediction is that under 40s will score better on the eyes test revised for adults than the over 40s. Results yielded no difference in emotion detection via the eyes test revised for adults between the over and under 40s. Introduction: Theory of mind, which is the ability to relate independent mental states to self and others to predict and or explain behavior, has long been researched since 1983 by Wimmer and Perner (1983). Since then their methods have been improved and altered in order to better understand theory of mind. Initially Baron–Cohen and colleagues (1985) simplified the test procedure from Wimmer’s (1983) research, then once more in 2001 where issues with data collection, number of items and responses in the test were all addressed. The revised eyes test for adults consisted of each participant identifying the gender...
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...laws in India are wearing a helmet in case of two wheelers, putting a seat belt in case of cars, driving on the right side of the road including overtaking from the right direction, over speeding in certain restricted areas, not obeying the traffics signals and stooping the car after the finish line. It is mainly because of these violations that major accidents occur. It should be recognized that the highway is a social situation, in which people are interacting. However the drivers are unknown to each other in most of the cases and the interaction between them very brief and non-recurring. The communication between them is very limited and that also through mechanical aids like lights and horns. The main objective of these laws is to minimize the confusion and conflict between vehicles and the people. When this is achieved then accidents will automatically reduce. Therefore our study tells the statistics of some major traffic violations in Chennai and the percentage of people violating it from a sample of people. REVIEW OF LITERATURE The major violations of traffic rules may be due to various reasons but there are some key factors...
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...Weighted Rank Correlation measures in Hierarchical Cluster Analysis Livia Dancelli, Marica Manisera, and Marika Vezzoli Abstract When the aim is to group rankings, matching-type measures must be used in cluster analysis techniques. Among these, rank-based correlation coefficients, as the Spearman’s ρ , can be considered. To this regard, we think that Weighted Rank Correlation measures are remarkably useful, since they evaluate the agreement between two rankings emphasizing the concordance on top ranks. In this paper, we employ an appropriate Weighted Rank Correlation measure to evaluate the dissimilarity between rankings in a hierarchical cluster analysis, in order to segment subjects expressing their preferences by rankings. An illustrative example on selected rankings shows that the resulting groups contain subjects whose preferences are more similar on the most important ranks. The procedure is then applied to real data from an extensive 2011 survey carried out in the Italian McDonald’s restaurants. Key words: rank-based correlation coefficients, matching-type measures, hierarchical cluster analysis 1 Introduction Cluster analysis aims at identifying groups of individuals or objects that are similar to each other but are different from individuals in other groups (among others, [4]). This is useful, for example, in market segmentation studies, also when consumers’ preferences are expressed by grades, leading to rankings of products or services provided by individuals...
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...methodology involves the use of CAPM model to estimate the returns of stocks. The stock portfolio is composed of 10, 25 and 50 stocks. Because of thin trade stock motivation the trade to trade adjustment was made. The estimation is based on 250 trading days total and 247 of this period corresponds to parameter estimation and the rest, t-1, t, t+1 is used for event study. The parameter estimations were based on OLS with heteroskedasticity correction. The abnormality is detected by analyzing difference between market return and expected return from CAPM model. Returns for event days are the subjects of test statistics. The examined statistics were based on t-test with cross sectional independence, t-test with standardized abnormal return and t-test with adjusted standardized abnormal return. These tests are the parametric tests for abnormality, the authors also conducted non-parametric test such as rank test, sign test and generalized sign test. The event days are specified by simulation and uniform distribution is assumed. After event day specification the impact of 0.5% and 2% are added to abnormal return on the event day. The simulation is repeated 1000 times to achieve a distribution...
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...correctness of information is important. QUANTATIVE ANALYSIS Ickovics et al 2003 utilize both descriptive and inferential statistics to scrutinize the data, the reason for the study was to evaluate the difference among the two groups, for the inferential statistics the McNemar test was used, which was suitable for the degree of enquiry due to the matched group, the Cohort design was also implemented as they intended to quantify between groups. Also as relates to the variables outcome. (Polit & Beck 2008). The paired T test was also proper for the study due to the fact its purpose is to test the differences among the two groups that are either paired or matched on the essence of the characteristics. The F test was also implemented, it occurs as the test used when apply multiple linear regression as this F statistics has been utilized while stipulating the influence between birth weight and preterm delivery (p1054). The purpose of linear regression is to describe the amount of the outcome variable is distinct to the independent variable (Burns & Groove, 2007) Descriptive statistics were used by the author to relate the dispensing of the statistical data among topics such as age, race, and parity, they also possess illustrative analysis to explain the issues of statistical variables among the distributing of outcomes variables among the specimens. A parametric as well as...
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