R&M Solutons

Size: px
Start display at page:

Download "www.rmsolutions.net R&M Solutons"

Transcription

1 Ahmed Hassouna, MD Professor of cardiovascular surgery, Ain-Shams University, EGYPT. Diploma of medical statistics and clinical trial, Paris 6 university, Paris.

2 1A- Choose the best answer The duration of CCU stay after acute MI: hours. A) What is the expected probability for a patient to stay for <24 hours? 1) about 2.5 % 2) about 5% 3) about 95% B) What is the expected probability for a patient to stay for more than 72 hours? 1) same as the probability to stay for less than 24 hours. 2) triple the probability to stay for less than 24 hours. 3) We cannot tell C) What is the probability for a patient to stay for less than 24 hours and for more than 72 hours? 1) about 2.5 % 2) about 5% 3) about 95%

3 2A- Choose the WRONG answer A randomized controlled unilateral study was conducted to compare the analgesic effect of drug (X) to placebo. The analgesic gave significantly longer duration of pain relief ( hours), compared to placebo (2 + 1 hours) ; P = 0.05 (Student s test, one-tail). 1) A unilateral study means that the researchers were only concerned to show the superiority of the analgesic over placebo, but not the reverse. 2) A one-tail statistics implies that a smaller difference between compared analgesic effects is needed to declare statistical significance, compared to a bilateral design. 3) The statistical significance of the difference achieved will not change if the design was bilateral.

4 3A- Choose the best answer A) The primary risk of error: 1) It is the risk to conclude upon a difference in the study that does not exist in the reality. 2) It is the risk not to conclude upon a difference in the study despite that this difference does exist in the reality. 3) Both definitions are wrong B) The secondary risk of error: 1) It is the risk to conclude upon a difference in the study that does not really exist. 2) It is the risk not to conclude upon a difference in the study despite that this difference does exist in the reality. 3) Bothe definitions are wrong C) The power of the study: 1) It is the ability of the study to accurately conclude upon a statistically significant difference. 2) It is the ability of the study not to miss a statistically significant difference. 3) Both definitions are wrong

5 4A- Choose the best answer A randomized controlled unilateral study was conducted to compare the analgesic effect of drug (X) to placebo. The analgesic gave significantly longer duration of pain relief ( hours), compared to placebo (2 + 1 hours) ; P = 0.05 (onetail). This P value means that: 1) There is a 95% chance that this result is true 2) There is a 5% chance that this result is false. 3) The probability that this result is due to chance is once, every 20 times this study is repeated. 4) The probability that this longer duration of pain relief is not a true difference in favor of the analgesic but rather a variation of that obtained with placebo is once, every 20 times this study is repeated.

6 5A- Choose the best answer: Although the previous study was a RCT, the researchers wanted to compare 40 pre trial demographic variables among study groups. How many times do you expect that those pre trial variables would be significantly different between patients receiving analgesic and those receiving placebo? a) None, as randomization ensures perfect initial comparability. b) It can happen to have 1 significantly different variable by pure chance. c) It would be quite expected to have 2 significantly different variables. d) We cannot expect any given number.

7 6A- Choose the best answer: Another group of researchers has repeated the same study and found a statistically more significant difference in favor of analgesic; P value < In view of the smaller P value, and provided that both studies were appropriately designed, conducted and analyzed, choose the BEST answer: a) The results of the second study have to be more considered than the first for being truer. b) The results of the second study have to be more considered than the first for being more accurate. c) The results of the second study have to be more considered than the first for being more credible. d) Both studies have to have an equal consideration, for being both statistically significant

8 The relative Z values (scores)

9 One of the empirically verified truths about life: it is a finding and not an invention. It is a name given to a characteristic distribution which followed by the majority of biological variables and, not a quality of such distribution. Birth weight classes (gm.) Birth weight frequency Total weight (a) Centers (b) Range* Absolute Relative (%) (gm.) (number) Total

10 m 1 SD 2 SD 3 SD

11 Birth weight classes (gm.) Birth weight frequency Total weight (a) Centers (b) Range* Absolute Relative (%) (gm.) (number) Total (66 births; 69.5%) (92 births; 96.8%) The mean birth weight m = 3200 gm. and the SD = 450 gm. Let us check for the Normality of the distribution: 2/3 of birth weights are included in the interval: m + 1SD: gm. 95% of birth weights are included in the interval: m + 2SD: gm. Nearly all birth weights are comprised within a distance of + 3 SD from the mean

12 A- Beginning by the observation No 2 samples are alike. The more the sample increases in size (n), the more it will resemble the population from which it was drawn and the more the distribution of the sample itself will acquire the characteristic inverted bell shape of the Normal distribution. However, it is not only a question of size but other factors do matter like the units and measurement scale and hence, in order to compare Normal distributions we have to have a reference that is no more under the influence of both: measurement units and scale.

13 B- Reaching a suggestion Statisticians have suggested a Standard Normal distribution with a mean of 0 and a SD of 1; which means that the SD becomes the unit of measurement: moving 1 unit on this scale (from 0 to 1 ) will also mean that we went 1 SD further away from the mean and so on. Those units have to have a name and were called Z units (scores, values). Statisticians have then calculated the probabilities for observations to lay at all possible Z units and put it in the Z table. The rough (size, unit and scaledependent) estimation of probabilities that differ from one Normal distribution to another, were now replaced by exact (standard) figures. As example, exactly 68.26%, 95% and 99% of observations were found to lay WITHIN A DISTANCE of 1, 1.96 and 2.6 SD from either sides of the mean SD SD 47.5% 47.5% 2.5% 2.5% The probability for a value to lie AT (OR FURTHER AWAY) from SD is obtained by simple deduction: % = 5%; 2.5% on each side.

14 C- Ending with the application: Standardizing values (the wire technique) Any OBSERVED Normal distribution is EXPECTED to follow the Standard Normal distribution and the more it deviates from those expectations, the more it will be considered as being different and the question that we are here to answer is about the extent and consequently the statistical significance of such a difference or deviation. In fact, the unknown probabilities of our observed (x) values can now be calculated when the latter are transformed into standardized Z values; with already known tabulated probabilities: Z = (x-m)/sd Returning to our example: what is the expected probability of having a child whose birth weight is as large as > gm.? We begin by standardizing the child s weight: Z = ( ) / 450 = Then we check the table for the probability of having a Z score of +1.96; which is simply equal to the probability of having such a low birth weight child of 2300 gm. or less. <2300 gm. >4100 gm. > < 47.5% 47.5% 2.5% 2.5% How to consult the Z table? The probability of having a child whose birth weight lay in the interval formed by the mean SD = = >2300 and 4100< is 95%.

15 The (Z) table gives the probability for a value to be smaller than Z; in the interval between 0 and Z. Z value

16 The Z scores are directly proportional of observed deviation The larger (or smaller) is a value as compared to the mean, the more distinct is its position on the standard scale: i.e. the larger is the Z value Z= (x-m)/sd = ( ) /450 = 1, = ( ) /450 = 1.96, Put it another way, the larger is the Z value (+/-), the less is its chance to belong to this particular distribution. Q1: What is the probability of having a child who is as heavy as 5 kg? Z = ( ) /450 = 4 Q2: If this probability is minimal, (not even listed) what can you suggest? May be this child does not belong to the same population from which we have drawn our sample? Is his mother diabetic?; i.e. we can now suggest a qualitative decision based on such an extreme deviation gm. 3650gm gm. 5000gm.

17 The duration of CCU stay after acute MI: hours. The expected probability for a patient to stay for <24 hours, for more than 72 hours or for both less than 24 hours and more than 72 hours? Z = (24-48)/ 12 = (72-48)12 = 2. Depending on the question posed: A) The probability of having either a larger (+) or smaller (-) Z value of 2 is calculated by adding 50% to the probability given by the table (47.5%) and subtracting the whole from 1 = 1- (47.5% + 50%) = 2.5%. B) The probability of having both larger and smaller Z values (i.e. staying for >72 hours and staying for <24 hours) is calculated by multiplying the probability given in the table by 2 and subtracting the whole from 1= 1-(47.5%x2) = 5% % % 50%

18 1B- Choose the best answer The duration of CCU stay after acute MI: hours. A) What is the expected probability for a patient to stay for <24 hours? 1) about 2.5 % 2) about 5% 3) about 95% Z = (x-m)/sd= (24-48)/12 = -2; probability = 1-( )= nearly 2.5% B) What is the expected probability for a patient to stay for more than 72 hours? 1) same as the probability to stay for less than 24 hours. 2) triple the probability to stay for less than 24 hours. 3) We cannot tell Z = (x-m)/sd= (72-48)/12 = +2; probability = 1-( )= nearly 2.5% C) What is the probability for a patient to stay for less than 24 hours and for more than 72 hours? 1) about 2.5 % 2) about 5% 3) about 95% Summing both previous probabilities = 1- (47.5x2) = 5%

19 The Normal law: conditions of application The Normal law is followed by the majority of biological variables and Normality can be easily checked out by various methods, starting from simple graphs to special tests. As a general rule, quantitative variables are expected to follow the Normal law whenever the number of values per group >30. For a binominal (p,q) qualitative variable with (N) total number of values (N), Normality can be assumed whenever Np, Nq >5. The presence of Normality allows the application of many statistical tests for the analysis of data. These are called parametric tests for necessitating fulfillment of some parameters before being used, including Normality. Non-parametric (distribution-free) tests are equally effective for data analysis and hence, one should not distort data to achieve Normality.

20 The null hypothesis

21 The statistical problem A sample must be representative of the aimed population. One of the criticisms of RCT is that they are too ordered to be a good reflection of the disordered reality. Even if the requirements of representativeness are thought to be fulfilled by randomization, a question will always remain: how much likely does our sample really represent the aimed population? As example, when a comparative study shows that treatment A is 80% effective in comparison to treatment B which is only 50% effective; a legitimate question would be if the observed difference is really due to effect treatment and not because patients who received treatment A were for example less ill than those receiving treatment B? In other words, were both groups of patients comparable from the start by being selected from the same or from different populations with different degrees of illness?

22 Postulating the Null hypothesis In order to answer this question, statisticians have postulated a theoretical hypothesis to start with: The null hypothesis We start any study by the null hypothesis postulating that there is no difference between the compared treatments. Then we conduct our study and analyze the results; which can either retain or disprove this theory by showing that treatments are truly different. At this point, we can reject the null hypothesis and accept the alternative hypothesis that there is a true difference between treatments; which has just been proved : The alternative hypothesis Both hypotheses: the first suggested to begin with and the second that may be proved by the end of the study are the 2 faces of one coin and hence, cannot co-exist.

23 When to reject the null hypothesis? Returning to our example of the 95 newly born babies, and under the null hypothesis, all children have comparable weights and the recorded differences are just variations of comparable weights belonging to the same population Differences are expressed in Z scores and the higher is the Z score, the less probable it can be consider as being just a variation of this particular distribution. The probability of having such an extreme variation of a 5 Kg-child (=Z=4) is minimal and hence, can raise questions about the null hypothesis: being member of the same population. In general, if the observed difference is sufficiently large and hence, less probable to be considered as part of the variation, we can consider rejecting the null hypothesis, accepting the alternative hypothesis and concluding upon the existence of a true difference gm. 3650gm gm. 15% 2.5% 5000gm. <0.0001

24 When to maintain the null hypothesis? On the other hand, if the difference is (small), we will continue to maintain our theoretical null hypothesis. However, in such a case, we cannot conclude that the observed difference does not exist because the null hypothesis itself is only a hypothetical suggestion. In fact, the aim of the study was to find sufficient evidence supporting the alternative hypothesis. In absence of sufficient evidence, we will maintain the theoretical null hypothesis that was neither rejected nor proved, but has only been maintained for further studies. The usual closing remark, and not a conclusion, is that we could not put into evidence the targeted difference and further studies may be needed to reevaluate the evidence to support this difference (i.e. to support the alternative hypothesis). (Large difference) Reject null hypothesis & accept alternative hypothesis Conclude to a difference. Under the null hypothesis (Small difference) Maintain the null hypothesis X

25 We have to define a critical limit for rejection We can reject the null hypothesis when the analysis shows a sufficiently large difference that has a SMALL PROBABILITY of being just a variation of the same population. Consequently, it can be considered as being a true difference ; which is coming from a different population. A literal description that merits a numerical expression. Most of the researchers have agreed that the null hypothesis can be rejected whenever the probability of being a variation is as small as 5%. This probability is called primary risk of error?! It means that although we know that there is a small 5% probability that this difference is just an extreme variation of the population, yet we declared it as being coming from a different population. In other words, our conclusion carries a small risk of being wrong and that this difference is still a variation of the first population, even if it is an extreme one.

26 Primary risk of error (α) >2300 <4100 We maintain the null hypothesis The majority of birth weights (95%) are expected to be between gm. and, by deduction, only 5% of babies are expected to lie outside this range. The probability of having a baby weighting >4100 gm. (or <2300 gm.) is as small as 5% and hence, this baby can be considered as being born from another population e.g. from a diabetic mother This conclusion still carries the small 5 % risk of being wrong ; i.e. that the weight of this baby is just an extreme variation of non-diabetic mothers. This small, but still present, risk of being wrong (risk of rejecting the null hypothesis where as the null hypothesis is true) is the primary risk of error.

27 Distribution of the primary risk of error: the unilateral versus the bilateral design A) Whenever we are comparing a treatment to placebo, our only concern is to prove that treatment is better than placebo & never the reverse. Null hypothesis (H0): no difference + Placebo is better Alternative hypothesis (H1): treatment is better than placebo. The primary risk of error of the study (5%) is involved in a single conclusion: treatment is better than placebo, while this is untrue. B) On the other hand, a bilateral design involves testing the superiority of either treatments: A or B. H0: no difference between treatments A and B. H1: involves 2 situations 1) treatment A is better than treatment B 2) treatment B is better than treatment A In order to keep a primary risk of error of 5% for the whole study, (α) which is the risk to conclude upon a difference that does not exist; is equally split between the 2 possibilities: treatment A is better, while this is untrue (2.5%) and treatment B is better than treatment A, while this is untrue(2.5%).

28 An example (even if it is not the perfect one!) The null hypothesis is rejected whenever the difference (d) is large enough that the probability of being a normal variation is as small as 5%. Returning to the 95 new born babies and suppose that we want know if a newly coming baby does belong to a diabetic mother and hence, we are only interested to prove that he is significantly larger than the rest of the group. This is a unilateral design, H0= no difference in weights + baby weight is significantly smaller. H1 = the baby is significantly larger than the others and, the whole of α is dedicated to this single and only investigated possibility. On the other hand, and if the design was bilateral, we would be interested to know if the weight of the baby is significantly different (whether larger or smaller) from the others; this is the alternative hypothesis and α is no more dedicated to 1 possibility but it is equally split (50:50) between the 2 possibilities; each being α/2. The null hypothesis is that the baby weight is comparable to the rest of the group.

29 The null hypothesis will be rejected whenever the calculated Z score enters the critical area of our primary risk of error. In a unilateral study, we are only concerned if the difference is in favor of 1 treatment and hence, the whole 5% of α is on 1 side or one tail of the curve. In a bilateral design, the risk of error is equally split into 2 smaller risks of 2.5% each. In consequence, the limit of the larger (5%) critical area of rejection of the unilateral study is nearer to the mean than any of the 2 smaller (2.5%) areas of the bilateral design. In consequence, a smaller Z score (difference) is needed to enter the critical area of rejecting the null hypothesis and declaring statistical significance in a unilateral study; compared to a bilateral design.

30 In a unilateral design: the null hypothesis will be rejected whenever the calculated Z score enters the critical area of α gm % In a unilateral study, we are only concerned if the child is significantly larger than the rest of the group and hence, the whole 5% of α is on 1 side (one tail) of the curve. The child weight would be considered as being significantly larger if its corresponding Z score reaches the limit of α. Consulting the Z table, the Z value of point α=5% = 1.65 and by deduction (Z = x- m/sd; x = Z x SD + m = 1.65x = 3950); a child weighting only 3950 gm. would be considered as being significantly larger than the rest of the population; with a primary risk of error of 5%. In a unilateral design, the critical limit to reject the null hypothesis is Z > % %

31 In a bilateral design: the null hypothesis will be rejected whenever the calculated Z score enters the critical area of α/ % In a Bilateral study, we are equally concerned if the child is significantly larger or smaller than the rest of the group and hence, the 5% of α will be equally split between both tails of the curve (50:50). In comparison, a child weight would be considered as being significantly larger if its corresponding Z score reaches the limit of α/2 ; which by default has to be further away from the mean compared to whole α in a unilateral design In consequence, a larger Z (difference) is needed to touch a now more distal critical limit. The Z table, shows a larger Z (1.96) for the smaller α/2, of course. In consequence, a child has to be as large as 4100 gm. to be declared as being significantly different from the population, compared to only 3950 gm., in the case if the design was unilateral. In a bilateral design, the critical limit to reject the null hypothesis is a Z > % %

32 2B- Choose the WRONG answer A randomized controlled unilateral study was conducted to compare the analgesic effect of drug (X) to placebo. The analgesic gave significantly longer duration of pain relief ( hours), compared to placebo (2 + 1 hours) ; P = 0.05 (Student s test, one-tail). 1) A unilateral study means that the researchers were only concerned to show the superiority of the analgesic over placebo, but not the reverse. 2) A one-tail statistics implies that a smaller difference between compared analgesic effects is needed to declare statistical significance, compared to a bilateral design. 3) The statistical significance of the difference achieved will not change if the design was bilateral.

33 Testing hypothesis: the comparison of 2 means A standard feeding additive (A) is known to increase the weight of low birth weight babies by a mean value of 170g and a SD of 65g. A new feeding additive (B) is given to a sample of 32 low birth weight babies and the mean weight gain observed was 203g and a SD of 67.4 g. The question now is if additive (B) has provided significantly more weight gain to those babies, compared to the standard additive (A)? The null hypothesis Ho: The mean weight gain obtained by the new additive (B) is just a normal variation of the weight gain obtained by additive (A). The alternative hypothesis H1: the difference between the mean weight gain obtained by (A) and that obtained by (B) are sufficiently is sufficiently large to reject the null hypothesis, at the primary risk of error of 5%.

34 Testing hypothesis: the equation Maintain H Sample mean (203 gm.)

35 The secondary risk of error (β) Suppose that we repeat the study and we obtained the same weight gain difference but with only 5 newborns. With such a small sample. we have to expect a larger SEM and hence, a smaller z value. z value = ( ) / (65/ 5) = Being below the critical value of even a unilateral design, this second researcher will be obliged to retain the null hypothesis, despite the fact that a true difference was shown by the first researcher. This example demonstrates the secondary risk of error: the risk of not concluding upon a difference in the study despite that such a difference exists (or can exist) in the reality. The secondary risk of error (risk of secondary species or (β) or type II error) is usually behind the so called negative trials. Most importantly, and unlike the first researcher, our second researcher "cannot conclude and his usual statement will be: we could not put into evidence a significant difference between A and B; that is probably due to the lack of power.

36 3B- Choose the best answer A) The primary risk of error: 1) It is the risk to conclude upon a difference in the study that does not exist in the reality. 2) It is the risk not to conclude upon a difference in the study despite that this difference does exist in the reality. 3) Both definitions are wrong B) The secondary risk of error: 1) It is the risk to conclude upon a difference in the study that does not really exist. 2) It is the risk not to conclude upon a difference in the study despite that this difference does exist in the reality. 3) Bothe definitions are wrong C) The power of the study: 1) It is the ability of the study to accurately conclude upon a statistically significant difference. 2) It is the ability of the study not to miss a statistically significant difference. 3) Both definitions are wrong

37 Statistical significance & degree of significance

38 P value First, and before conducting any research, we have to designate the acceptable limit of (α), which is usually 5%. This is the limit that if reached, we can consider that the tested treatment is not just a variation of the classic one but a truly superior treatment. Concordantly, in the example of food additives, a new additive will be considered superior when the associated weight gain > 193 gm. Secondly, the researcher conducts his study and analyze his results using the appropriate statistical test now to calculate this probability for the new additive to be just a variation of the classic additive; this calculated probability is the P value. If the P value is at least equal or smaller than the designated (α), we can reject the null hypothesis and accept the alternative hypothesis. On the other hand, if this calculated probability is larger than (α), we maintain the null hypothesis and the test results are termed as being statistically insignificant α P

39 Relation between α and P In other words, we have 2 probabilities: one that we pre design before the experiment and another one that we calculate (using the appropriate statistical test) at the end of the experiment. The pre designed probability indicates the limit for rejecting the null hypothesis that we fix before the experiment. The calculated probability indicates the position of our results in relation to this limit, after the experiment. The null hypothesis will only be rejected If the calculated probability is at least equal or smaller than the pre designed limit; otherwise, it will be maintained. The pre designed probability is called the primary risk of error or (α) and the calculated probability is the well-known P value.

40 What is the P value? Unlike a common belief, the P value is not the probability for the null hypothesis to be untrue because the P value is calculated on the assumption that the null hypothesis is true. It cannot, therefore, be a direct measure of the probability that the null hypothesis is false. A proper definition of P is the probability of obtaining the observed or more extreme results, under the null hypothesis (i.e. while the null hypothesis is still true). The value of P is an index of the reliability of our results. In terms of percentage, the smaller is the P value, the higher it is in terms of significance; i.e. the more we can believe that the observed relation between variables in the sample is a reliable indicator of the relation between the respective variables in the population.

Additional sources Compilation of sources: http://lrs.ed.uiuc.edu/tseportal/datacollectionmethodologies/jin-tselink/tselink.htm

Additional sources Compilation of sources: http://lrs.ed.uiuc.edu/tseportal/datacollectionmethodologies/jin-tselink/tselink.htm Mgt 540 Research Methods Data Analysis 1 Additional sources Compilation of sources: http://lrs.ed.uiuc.edu/tseportal/datacollectionmethodologies/jin-tselink/tselink.htm http://web.utk.edu/~dap/random/order/start.htm

More information

II. DISTRIBUTIONS distribution normal distribution. standard scores

II. DISTRIBUTIONS distribution normal distribution. standard scores Appendix D Basic Measurement And Statistics The following information was developed by Steven Rothke, PhD, Department of Psychology, Rehabilitation Institute of Chicago (RIC) and expanded by Mary F. Schmidt,

More information

Study Guide for the Final Exam

Study Guide for the Final Exam Study Guide for the Final Exam When studying, remember that the computational portion of the exam will only involve new material (covered after the second midterm), that material from Exam 1 will make

More information

Statistical tests for SPSS

Statistical tests for SPSS Statistical tests for SPSS Paolo Coletti A.Y. 2010/11 Free University of Bolzano Bozen Premise This book is a very quick, rough and fast description of statistical tests and their usage. It is explicitly

More information

A POPULATION MEAN, CONFIDENCE INTERVALS AND HYPOTHESIS TESTING

A POPULATION MEAN, CONFIDENCE INTERVALS AND HYPOTHESIS TESTING CHAPTER 5. A POPULATION MEAN, CONFIDENCE INTERVALS AND HYPOTHESIS TESTING 5.1 Concepts When a number of animals or plots are exposed to a certain treatment, we usually estimate the effect of the treatment

More information

DATA INTERPRETATION AND STATISTICS

DATA INTERPRETATION AND STATISTICS PholC60 September 001 DATA INTERPRETATION AND STATISTICS Books A easy and systematic introductory text is Essentials of Medical Statistics by Betty Kirkwood, published by Blackwell at about 14. DESCRIPTIVE

More information

11. Analysis of Case-control Studies Logistic Regression

11. Analysis of Case-control Studies Logistic Regression Research methods II 113 11. Analysis of Case-control Studies Logistic Regression This chapter builds upon and further develops the concepts and strategies described in Ch.6 of Mother and Child Health:

More information

" Y. Notation and Equations for Regression Lecture 11/4. Notation:

 Y. Notation and Equations for Regression Lecture 11/4. Notation: Notation: Notation and Equations for Regression Lecture 11/4 m: The number of predictor variables in a regression Xi: One of multiple predictor variables. The subscript i represents any number from 1 through

More information

Descriptive Statistics

Descriptive Statistics Descriptive Statistics Primer Descriptive statistics Central tendency Variation Relative position Relationships Calculating descriptive statistics Descriptive Statistics Purpose to describe or summarize

More information

UNIVERSITY OF NAIROBI

UNIVERSITY OF NAIROBI UNIVERSITY OF NAIROBI MASTERS IN PROJECT PLANNING AND MANAGEMENT NAME: SARU CAROLYNN ELIZABETH REGISTRATION NO: L50/61646/2013 COURSE CODE: LDP 603 COURSE TITLE: RESEARCH METHODS LECTURER: GAKUU CHRISTOPHER

More information

Introduction to. Hypothesis Testing CHAPTER LEARNING OBJECTIVES. 1 Identify the four steps of hypothesis testing.

Introduction to. Hypothesis Testing CHAPTER LEARNING OBJECTIVES. 1 Identify the four steps of hypothesis testing. Introduction to Hypothesis Testing CHAPTER 8 LEARNING OBJECTIVES After reading this chapter, you should be able to: 1 Identify the four steps of hypothesis testing. 2 Define null hypothesis, alternative

More information

Simple Linear Regression Inference

Simple Linear Regression Inference Simple Linear Regression Inference 1 Inference requirements The Normality assumption of the stochastic term e is needed for inference even if it is not a OLS requirement. Therefore we have: Interpretation

More information

Introduction to Statistics and Quantitative Research Methods

Introduction to Statistics and Quantitative Research Methods Introduction to Statistics and Quantitative Research Methods Purpose of Presentation To aid in the understanding of basic statistics, including terminology, common terms, and common statistical methods.

More information

Introduction to Quantitative Methods

Introduction to Quantitative Methods Introduction to Quantitative Methods October 15, 2009 Contents 1 Definition of Key Terms 2 2 Descriptive Statistics 3 2.1 Frequency Tables......................... 4 2.2 Measures of Central Tendencies.................

More information

10. Analysis of Longitudinal Studies Repeat-measures analysis

10. Analysis of Longitudinal Studies Repeat-measures analysis Research Methods II 99 10. Analysis of Longitudinal Studies Repeat-measures analysis This chapter builds on the concepts and methods described in Chapters 7 and 8 of Mother and Child Health: Research methods.

More information

Projects Involving Statistics (& SPSS)

Projects Involving Statistics (& SPSS) Projects Involving Statistics (& SPSS) Academic Skills Advice Starting a project which involves using statistics can feel confusing as there seems to be many different things you can do (charts, graphs,

More information

COMPARISONS OF CUSTOMER LOYALTY: PUBLIC & PRIVATE INSURANCE COMPANIES.

COMPARISONS OF CUSTOMER LOYALTY: PUBLIC & PRIVATE INSURANCE COMPANIES. 277 CHAPTER VI COMPARISONS OF CUSTOMER LOYALTY: PUBLIC & PRIVATE INSURANCE COMPANIES. This chapter contains a full discussion of customer loyalty comparisons between private and public insurance companies

More information

Introduction to Hypothesis Testing

Introduction to Hypothesis Testing I. Terms, Concepts. Introduction to Hypothesis Testing A. In general, we do not know the true value of population parameters - they must be estimated. However, we do have hypotheses about what the true

More information

RECRUITERS PRIORITIES IN PLACING MBA FRESHER: AN EMPIRICAL ANALYSIS

RECRUITERS PRIORITIES IN PLACING MBA FRESHER: AN EMPIRICAL ANALYSIS RECRUITERS PRIORITIES IN PLACING MBA FRESHER: AN EMPIRICAL ANALYSIS Miss Sangeeta Mohanty Assistant Professor, Academy of Business Administration, Angaragadia, Balasore, Orissa, India ABSTRACT Recruitment

More information

Chi Square Tests. Chapter 10. 10.1 Introduction

Chi Square Tests. Chapter 10. 10.1 Introduction Contents 10 Chi Square Tests 703 10.1 Introduction............................ 703 10.2 The Chi Square Distribution.................. 704 10.3 Goodness of Fit Test....................... 709 10.4 Chi Square

More information

QUANTITATIVE METHODS BIOLOGY FINAL HONOUR SCHOOL NON-PARAMETRIC TESTS

QUANTITATIVE METHODS BIOLOGY FINAL HONOUR SCHOOL NON-PARAMETRIC TESTS QUANTITATIVE METHODS BIOLOGY FINAL HONOUR SCHOOL NON-PARAMETRIC TESTS This booklet contains lecture notes for the nonparametric work in the QM course. This booklet may be online at http://users.ox.ac.uk/~grafen/qmnotes/index.html.

More information

2. Simple Linear Regression

2. Simple Linear Regression Research methods - II 3 2. Simple Linear Regression Simple linear regression is a technique in parametric statistics that is commonly used for analyzing mean response of a variable Y which changes according

More information

HYPOTHESIS TESTING WITH SPSS:

HYPOTHESIS TESTING WITH SPSS: HYPOTHESIS TESTING WITH SPSS: A NON-STATISTICIAN S GUIDE & TUTORIAL by Dr. Jim Mirabella SPSS 14.0 screenshots reprinted with permission from SPSS Inc. Published June 2006 Copyright Dr. Jim Mirabella CHAPTER

More information

Sample Size and Power in Clinical Trials

Sample Size and Power in Clinical Trials Sample Size and Power in Clinical Trials Version 1.0 May 011 1. Power of a Test. Factors affecting Power 3. Required Sample Size RELATED ISSUES 1. Effect Size. Test Statistics 3. Variation 4. Significance

More information

Statistics Review PSY379

Statistics Review PSY379 Statistics Review PSY379 Basic concepts Measurement scales Populations vs. samples Continuous vs. discrete variable Independent vs. dependent variable Descriptive vs. inferential stats Common analyses

More information

Chapter 13 Introduction to Linear Regression and Correlation Analysis

Chapter 13 Introduction to Linear Regression and Correlation Analysis Chapter 3 Student Lecture Notes 3- Chapter 3 Introduction to Linear Regression and Correlation Analsis Fall 2006 Fundamentals of Business Statistics Chapter Goals To understand the methods for displaing

More information

Statistics in Medicine Research Lecture Series CSMC Fall 2014

Statistics in Medicine Research Lecture Series CSMC Fall 2014 Catherine Bresee, MS Senior Biostatistician Biostatistics & Bioinformatics Research Institute Statistics in Medicine Research Lecture Series CSMC Fall 2014 Overview Review concept of statistical power

More information

STATISTICS 8, FINAL EXAM. Last six digits of Student ID#: Circle your Discussion Section: 1 2 3 4

STATISTICS 8, FINAL EXAM. Last six digits of Student ID#: Circle your Discussion Section: 1 2 3 4 STATISTICS 8, FINAL EXAM NAME: KEY Seat Number: Last six digits of Student ID#: Circle your Discussion Section: 1 2 3 4 Make sure you have 8 pages. You will be provided with a table as well, as a separate

More information

Recall this chart that showed how most of our course would be organized:

Recall this chart that showed how most of our course would be organized: Chapter 4 One-Way ANOVA Recall this chart that showed how most of our course would be organized: Explanatory Variable(s) Response Variable Methods Categorical Categorical Contingency Tables Categorical

More information

Multivariate Analysis of Ecological Data

Multivariate Analysis of Ecological Data Multivariate Analysis of Ecological Data MICHAEL GREENACRE Professor of Statistics at the Pompeu Fabra University in Barcelona, Spain RAUL PRIMICERIO Associate Professor of Ecology, Evolutionary Biology

More information

Using Excel for inferential statistics

Using Excel for inferential statistics FACT SHEET Using Excel for inferential statistics Introduction When you collect data, you expect a certain amount of variation, just caused by chance. A wide variety of statistical tests can be applied

More information

Chapter 7 Section 7.1: Inference for the Mean of a Population

Chapter 7 Section 7.1: Inference for the Mean of a Population Chapter 7 Section 7.1: Inference for the Mean of a Population Now let s look at a similar situation Take an SRS of size n Normal Population : N(, ). Both and are unknown parameters. Unlike what we used

More information

SCHOOL OF HEALTH AND HUMAN SCIENCES DON T FORGET TO RECODE YOUR MISSING VALUES

SCHOOL OF HEALTH AND HUMAN SCIENCES DON T FORGET TO RECODE YOUR MISSING VALUES SCHOOL OF HEALTH AND HUMAN SCIENCES Using SPSS Topics addressed today: 1. Differences between groups 2. Graphing Use the s4data.sav file for the first part of this session. DON T FORGET TO RECODE YOUR

More information

One-Way Analysis of Variance (ANOVA) Example Problem

One-Way Analysis of Variance (ANOVA) Example Problem One-Way Analysis of Variance (ANOVA) Example Problem Introduction Analysis of Variance (ANOVA) is a hypothesis-testing technique used to test the equality of two or more population (or treatment) means

More information

Elementary Statistics Sample Exam #3

Elementary Statistics Sample Exam #3 Elementary Statistics Sample Exam #3 Instructions. No books or telephones. Only the supplied calculators are allowed. The exam is worth 100 points. 1. A chi square goodness of fit test is considered to

More information

Research Methods & Experimental Design

Research Methods & Experimental Design Research Methods & Experimental Design 16.422 Human Supervisory Control April 2004 Research Methods Qualitative vs. quantitative Understanding the relationship between objectives (research question) and

More information

Business Statistics. Successful completion of Introductory and/or Intermediate Algebra courses is recommended before taking Business Statistics.

Business Statistics. Successful completion of Introductory and/or Intermediate Algebra courses is recommended before taking Business Statistics. Business Course Text Bowerman, Bruce L., Richard T. O'Connell, J. B. Orris, and Dawn C. Porter. Essentials of Business, 2nd edition, McGraw-Hill/Irwin, 2008, ISBN: 978-0-07-331988-9. Required Computing

More information

2013 MBA Jump Start Program. Statistics Module Part 3

2013 MBA Jump Start Program. Statistics Module Part 3 2013 MBA Jump Start Program Module 1: Statistics Thomas Gilbert Part 3 Statistics Module Part 3 Hypothesis Testing (Inference) Regressions 2 1 Making an Investment Decision A researcher in your firm just

More information

Bivariate Statistics Session 2: Measuring Associations Chi-Square Test

Bivariate Statistics Session 2: Measuring Associations Chi-Square Test Bivariate Statistics Session 2: Measuring Associations Chi-Square Test Features Of The Chi-Square Statistic The chi-square test is non-parametric. That is, it makes no assumptions about the distribution

More information

MULTIPLE REGRESSION AND ISSUES IN REGRESSION ANALYSIS

MULTIPLE REGRESSION AND ISSUES IN REGRESSION ANALYSIS MULTIPLE REGRESSION AND ISSUES IN REGRESSION ANALYSIS MSR = Mean Regression Sum of Squares MSE = Mean Squared Error RSS = Regression Sum of Squares SSE = Sum of Squared Errors/Residuals α = Level of Significance

More information

Tutorial 5: Hypothesis Testing

Tutorial 5: Hypothesis Testing Tutorial 5: Hypothesis Testing Rob Nicholls nicholls@mrc-lmb.cam.ac.uk MRC LMB Statistics Course 2014 Contents 1 Introduction................................ 1 2 Testing distributional assumptions....................

More information

Simple Regression Theory II 2010 Samuel L. Baker

Simple Regression Theory II 2010 Samuel L. Baker SIMPLE REGRESSION THEORY II 1 Simple Regression Theory II 2010 Samuel L. Baker Assessing how good the regression equation is likely to be Assignment 1A gets into drawing inferences about how close the

More information

Testing Group Differences using T-tests, ANOVA, and Nonparametric Measures

Testing Group Differences using T-tests, ANOVA, and Nonparametric Measures Testing Group Differences using T-tests, ANOVA, and Nonparametric Measures Jamie DeCoster Department of Psychology University of Alabama 348 Gordon Palmer Hall Box 870348 Tuscaloosa, AL 35487-0348 Phone:

More information

Introduction. Hypothesis Testing. Hypothesis Testing. Significance Testing

Introduction. Hypothesis Testing. Hypothesis Testing. Significance Testing Introduction Hypothesis Testing Mark Lunt Arthritis Research UK Centre for Ecellence in Epidemiology University of Manchester 13/10/2015 We saw last week that we can never know the population parameters

More information

Data Analysis Tools. Tools for Summarizing Data

Data Analysis Tools. Tools for Summarizing Data Data Analysis Tools This section of the notes is meant to introduce you to many of the tools that are provided by Excel under the Tools/Data Analysis menu item. If your computer does not have that tool

More information

Class 19: Two Way Tables, Conditional Distributions, Chi-Square (Text: Sections 2.5; 9.1)

Class 19: Two Way Tables, Conditional Distributions, Chi-Square (Text: Sections 2.5; 9.1) Spring 204 Class 9: Two Way Tables, Conditional Distributions, Chi-Square (Text: Sections 2.5; 9.) Big Picture: More than Two Samples In Chapter 7: We looked at quantitative variables and compared the

More information

Parametric and Nonparametric: Demystifying the Terms

Parametric and Nonparametric: Demystifying the Terms Parametric and Nonparametric: Demystifying the Terms By Tanya Hoskin, a statistician in the Mayo Clinic Department of Health Sciences Research who provides consultations through the Mayo Clinic CTSA BERD

More information

Section Format Day Begin End Building Rm# Instructor. 001 Lecture Tue 6:45 PM 8:40 PM Silver 401 Ballerini

Section Format Day Begin End Building Rm# Instructor. 001 Lecture Tue 6:45 PM 8:40 PM Silver 401 Ballerini NEW YORK UNIVERSITY ROBERT F. WAGNER GRADUATE SCHOOL OF PUBLIC SERVICE Course Syllabus Spring 2016 Statistical Methods for Public, Nonprofit, and Health Management Section Format Day Begin End Building

More information

Experimental Designs (revisited)

Experimental Designs (revisited) Introduction to ANOVA Copyright 2000, 2011, J. Toby Mordkoff Probably, the best way to start thinking about ANOVA is in terms of factors with levels. (I say this because this is how they are described

More information

Statistical Functions in Excel

Statistical Functions in Excel Statistical Functions in Excel There are many statistical functions in Excel. Moreover, there are other functions that are not specified as statistical functions that are helpful in some statistical analyses.

More information

Come scegliere un test statistico

Come scegliere un test statistico Come scegliere un test statistico Estratto dal Capitolo 37 of Intuitive Biostatistics (ISBN 0-19-508607-4) by Harvey Motulsky. Copyright 1995 by Oxfd University Press Inc. (disponibile in Iinternet) Table

More information

Linear Models in STATA and ANOVA

Linear Models in STATA and ANOVA Session 4 Linear Models in STATA and ANOVA Page Strengths of Linear Relationships 4-2 A Note on Non-Linear Relationships 4-4 Multiple Linear Regression 4-5 Removal of Variables 4-8 Independent Samples

More information

MEASURES OF VARIATION

MEASURES OF VARIATION NORMAL DISTRIBTIONS MEASURES OF VARIATION In statistics, it is important to measure the spread of data. A simple way to measure spread is to find the range. But statisticians want to know if the data are

More information

Course Text. Required Computing Software. Course Description. Course Objectives. StraighterLine. Business Statistics

Course Text. Required Computing Software. Course Description. Course Objectives. StraighterLine. Business Statistics Course Text Business Statistics Lind, Douglas A., Marchal, William A. and Samuel A. Wathen. Basic Statistics for Business and Economics, 7th edition, McGraw-Hill/Irwin, 2010, ISBN: 9780077384470 [This

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. STT315 Practice Ch 5-7 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 1) The length of time a traffic signal stays green (nicknamed

More information

Analysing Questionnaires using Minitab (for SPSS queries contact -) Graham.Currell@uwe.ac.uk

Analysing Questionnaires using Minitab (for SPSS queries contact -) Graham.Currell@uwe.ac.uk Analysing Questionnaires using Minitab (for SPSS queries contact -) Graham.Currell@uwe.ac.uk Structure As a starting point it is useful to consider a basic questionnaire as containing three main sections:

More information

Parametric and non-parametric statistical methods for the life sciences - Session I

Parametric and non-parametric statistical methods for the life sciences - Session I Why nonparametric methods What test to use? Rank Tests Parametric and non-parametric statistical methods for the life sciences - Session I Liesbeth Bruckers Geert Molenberghs Interuniversity Institute

More information

One-Way Analysis of Variance

One-Way Analysis of Variance One-Way Analysis of Variance Note: Much of the math here is tedious but straightforward. We ll skim over it in class but you should be sure to ask questions if you don t understand it. I. Overview A. We

More information

Analysis of Data. Organizing Data Files in SPSS. Descriptive Statistics

Analysis of Data. Organizing Data Files in SPSS. Descriptive Statistics Analysis of Data Claudia J. Stanny PSY 67 Research Design Organizing Data Files in SPSS All data for one subject entered on the same line Identification data Between-subjects manipulations: variable to

More information

Normality Testing in Excel

Normality Testing in Excel Normality Testing in Excel By Mark Harmon Copyright 2011 Mark Harmon No part of this publication may be reproduced or distributed without the express permission of the author. mark@excelmasterseries.com

More information

MONT 107N Understanding Randomness Solutions For Final Examination May 11, 2010

MONT 107N Understanding Randomness Solutions For Final Examination May 11, 2010 MONT 07N Understanding Randomness Solutions For Final Examination May, 00 Short Answer (a) (0) How are the EV and SE for the sum of n draws with replacement from a box computed? Solution: The EV is n times

More information

Introduction to Statistics with GraphPad Prism (5.01) Version 1.1

Introduction to Statistics with GraphPad Prism (5.01) Version 1.1 Babraham Bioinformatics Introduction to Statistics with GraphPad Prism (5.01) Version 1.1 Introduction to Statistics with GraphPad Prism 2 Licence This manual is 2010-11, Anne Segonds-Pichon. This manual

More information

Directions for using SPSS

Directions for using SPSS Directions for using SPSS Table of Contents Connecting and Working with Files 1. Accessing SPSS... 2 2. Transferring Files to N:\drive or your computer... 3 3. Importing Data from Another File Format...

More information

There are three kinds of people in the world those who are good at math and those who are not. PSY 511: Advanced Statistics for Psychological and Behavioral Research 1 Positive Views The record of a month

More information

Unit 31 A Hypothesis Test about Correlation and Slope in a Simple Linear Regression

Unit 31 A Hypothesis Test about Correlation and Slope in a Simple Linear Regression Unit 31 A Hypothesis Test about Correlation and Slope in a Simple Linear Regression Objectives: To perform a hypothesis test concerning the slope of a least squares line To recognize that testing for a

More information

Testing Hypotheses About Proportions

Testing Hypotheses About Proportions Chapter 11 Testing Hypotheses About Proportions Hypothesis testing method: uses data from a sample to judge whether or not a statement about a population may be true. Steps in Any Hypothesis Test 1. Determine

More information

t Tests in Excel The Excel Statistical Master By Mark Harmon Copyright 2011 Mark Harmon

t Tests in Excel The Excel Statistical Master By Mark Harmon Copyright 2011 Mark Harmon t-tests in Excel By Mark Harmon Copyright 2011 Mark Harmon No part of this publication may be reproduced or distributed without the express permission of the author. mark@excelmasterseries.com www.excelmasterseries.com

More information

NCSS Statistical Software Principal Components Regression. In ordinary least squares, the regression coefficients are estimated using the formula ( )

NCSS Statistical Software Principal Components Regression. In ordinary least squares, the regression coefficients are estimated using the formula ( ) Chapter 340 Principal Components Regression Introduction is a technique for analyzing multiple regression data that suffer from multicollinearity. When multicollinearity occurs, least squares estimates

More information

WISE Power Tutorial All Exercises

WISE Power Tutorial All Exercises ame Date Class WISE Power Tutorial All Exercises Power: The B.E.A.. Mnemonic Four interrelated features of power can be summarized using BEA B Beta Error (Power = 1 Beta Error): Beta error (or Type II

More information

research/scientific includes the following: statistical hypotheses: you have a null and alternative you accept one and reject the other

research/scientific includes the following: statistical hypotheses: you have a null and alternative you accept one and reject the other 1 Hypothesis Testing Richard S. Balkin, Ph.D., LPC-S, NCC 2 Overview When we have questions about the effect of a treatment or intervention or wish to compare groups, we use hypothesis testing Parametric

More information

Chapter 9. Two-Sample Tests. Effect Sizes and Power Paired t Test Calculation

Chapter 9. Two-Sample Tests. Effect Sizes and Power Paired t Test Calculation Chapter 9 Two-Sample Tests Paired t Test (Correlated Groups t Test) Effect Sizes and Power Paired t Test Calculation Summary Independent t Test Chapter 9 Homework Power and Two-Sample Tests: Paired Versus

More information

Chapter 7. One-way ANOVA

Chapter 7. One-way ANOVA Chapter 7 One-way ANOVA One-way ANOVA examines equality of population means for a quantitative outcome and a single categorical explanatory variable with any number of levels. The t-test of Chapter 6 looks

More information

One-Way Analysis of Variance: A Guide to Testing Differences Between Multiple Groups

One-Way Analysis of Variance: A Guide to Testing Differences Between Multiple Groups One-Way Analysis of Variance: A Guide to Testing Differences Between Multiple Groups In analysis of variance, the main research question is whether the sample means are from different populations. The

More information

6: Introduction to Hypothesis Testing

6: Introduction to Hypothesis Testing 6: Introduction to Hypothesis Testing Significance testing is used to help make a judgment about a claim by addressing the question, Can the observed difference be attributed to chance? We break up significance

More information

Outline. Topic 4 - Analysis of Variance Approach to Regression. Partitioning Sums of Squares. Total Sum of Squares. Partitioning sums of squares

Outline. Topic 4 - Analysis of Variance Approach to Regression. Partitioning Sums of Squares. Total Sum of Squares. Partitioning sums of squares Topic 4 - Analysis of Variance Approach to Regression Outline Partitioning sums of squares Degrees of freedom Expected mean squares General linear test - Fall 2013 R 2 and the coefficient of correlation

More information

STA-201-TE. 5. Measures of relationship: correlation (5%) Correlation coefficient; Pearson r; correlation and causation; proportion of common variance

STA-201-TE. 5. Measures of relationship: correlation (5%) Correlation coefficient; Pearson r; correlation and causation; proportion of common variance 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 information

Research Methodology: Tools

Research Methodology: Tools MSc Business Administration Research Methodology: Tools Applied Data Analysis (with SPSS) Lecture 11: Nonparametric Methods May 2014 Prof. Dr. Jürg Schwarz Lic. phil. Heidi Bruderer Enzler Contents Slide

More information

Section 14 Simple Linear Regression: Introduction to Least Squares Regression

Section 14 Simple Linear Regression: Introduction to Least Squares Regression Slide 1 Section 14 Simple Linear Regression: Introduction to Least Squares Regression There are several different measures of statistical association used for understanding the quantitative relationship

More information

HYPOTHESIS TESTING (ONE SAMPLE) - CHAPTER 7 1. used confidence intervals to answer questions such as...

HYPOTHESIS TESTING (ONE SAMPLE) - CHAPTER 7 1. used confidence intervals to answer questions such as... HYPOTHESIS TESTING (ONE SAMPLE) - CHAPTER 7 1 PREVIOUSLY used confidence intervals to answer questions such as... You know that 0.25% of women have red/green color blindness. You conduct a study of men

More information

Basic Concepts in Research and Data Analysis

Basic Concepts in Research and Data Analysis Basic Concepts in Research and Data Analysis Introduction: A Common Language for Researchers...2 Steps to Follow When Conducting Research...3 The Research Question... 3 The Hypothesis... 4 Defining the

More information

http://www.jstor.org This content downloaded on Tue, 19 Feb 2013 17:28:43 PM All use subject to JSTOR Terms and Conditions

http://www.jstor.org This content downloaded on Tue, 19 Feb 2013 17:28:43 PM All use subject to JSTOR Terms and Conditions A Significance Test for Time Series Analysis Author(s): W. Allen Wallis and Geoffrey H. Moore Reviewed work(s): Source: Journal of the American Statistical Association, Vol. 36, No. 215 (Sep., 1941), pp.

More information

DATA ANALYSIS. QEM Network HBCU-UP Fundamentals of Education Research Workshop Gerunda B. Hughes, Ph.D. Howard University

DATA ANALYSIS. QEM Network HBCU-UP Fundamentals of Education Research Workshop Gerunda B. Hughes, Ph.D. Howard University DATA ANALYSIS QEM Network HBCU-UP Fundamentals of Education Research Workshop Gerunda B. Hughes, Ph.D. Howard University Quantitative Research What is Statistics? Statistics (as a subject) is the science

More information

Name: Date: Use the following to answer questions 3-4:

Name: Date: Use the following to answer questions 3-4: Name: Date: 1. Determine whether each of the following statements is true or false. A) The margin of error for a 95% confidence interval for the mean increases as the sample size increases. B) The margin

More information

Part 2: Analysis of Relationship Between Two Variables

Part 2: Analysis of Relationship Between Two Variables Part 2: Analysis of Relationship Between Two Variables Linear Regression Linear correlation Significance Tests Multiple regression Linear Regression Y = a X + b Dependent Variable Independent Variable

More information

Case Study in Data Analysis Does a drug prevent cardiomegaly in heart failure?

Case Study in Data Analysis Does a drug prevent cardiomegaly in heart failure? Case Study in Data Analysis Does a drug prevent cardiomegaly in heart failure? Harvey Motulsky hmotulsky@graphpad.com This is the first case in what I expect will be a series of case studies. While I mention

More information

Comparing Two Groups. Standard Error of ȳ 1 ȳ 2. Setting. Two Independent Samples

Comparing Two Groups. Standard Error of ȳ 1 ȳ 2. Setting. Two Independent Samples Comparing Two Groups Chapter 7 describes two ways to compare two populations on the basis of independent samples: a confidence interval for the difference in population means and a hypothesis test. The

More information

1) The table lists the smoking habits of a group of college students. Answer: 0.218

1) The table lists the smoking habits of a group of college students. Answer: 0.218 FINAL EXAM REVIEW Name ) The table lists the smoking habits of a group of college students. Sex Non-smoker Regular Smoker Heavy Smoker Total Man 5 52 5 92 Woman 8 2 2 220 Total 22 2 If a student is chosen

More information

Chicago Booth BUSINESS STATISTICS 41000 Final Exam Fall 2011

Chicago Booth BUSINESS STATISTICS 41000 Final Exam Fall 2011 Chicago Booth BUSINESS STATISTICS 41000 Final Exam Fall 2011 Name: Section: I pledge my honor that I have not violated the Honor Code Signature: This exam has 34 pages. You have 3 hours to complete this

More information

"Statistical methods are objective methods by which group trends are abstracted from observations on many separate individuals." 1

Statistical methods are objective methods by which group trends are abstracted from observations on many separate individuals. 1 BASIC STATISTICAL THEORY / 3 CHAPTER ONE BASIC STATISTICAL THEORY "Statistical methods are objective methods by which group trends are abstracted from observations on many separate individuals." 1 Medicine

More information

Simple linear regression

Simple linear regression Simple linear regression Introduction Simple linear regression is a statistical method for obtaining a formula to predict values of one variable from another where there is a causal relationship between

More information

1. The parameters to be estimated in the simple linear regression model Y=α+βx+ε ε~n(0,σ) are: a) α, β, σ b) α, β, ε c) a, b, s d) ε, 0, σ

1. The parameters to be estimated in the simple linear regression model Y=α+βx+ε ε~n(0,σ) are: a) α, β, σ b) α, β, ε c) a, b, s d) ε, 0, σ STA 3024 Practice Problems Exam 2 NOTE: These are just Practice Problems. This is NOT meant to look just like the test, and it is NOT the only thing that you should study. Make sure you know all the material

More information

Nonparametric Two-Sample Tests. Nonparametric Tests. Sign Test

Nonparametric Two-Sample Tests. Nonparametric Tests. Sign Test Nonparametric Two-Sample Tests Sign test Mann-Whitney U-test (a.k.a. Wilcoxon two-sample test) Kolmogorov-Smirnov Test Wilcoxon Signed-Rank Test Tukey-Duckworth Test 1 Nonparametric Tests Recall, nonparametric

More information

Chapter Seven. Multiple regression An introduction to multiple regression Performing a multiple regression on SPSS

Chapter Seven. Multiple regression An introduction to multiple regression Performing a multiple regression on SPSS Chapter Seven Multiple regression An introduction to multiple regression Performing a multiple regression on SPSS Section : An introduction to multiple regression WHAT IS MULTIPLE REGRESSION? Multiple

More information

Simple Predictive Analytics Curtis Seare

Simple Predictive Analytics Curtis Seare Using Excel to Solve Business Problems: Simple Predictive Analytics Curtis Seare Copyright: Vault Analytics July 2010 Contents Section I: Background Information Why use Predictive Analytics? How to use

More information

Levels of measurement in psychological research:

Levels of measurement in psychological research: Research Skills: Levels of Measurement. Graham Hole, February 2011 Page 1 Levels of measurement in psychological research: Psychology is a science. As such it generally involves objective measurement of

More information

HYPOTHESIS TESTING (ONE SAMPLE) - CHAPTER 7 1. used confidence intervals to answer questions such as...

HYPOTHESIS TESTING (ONE SAMPLE) - CHAPTER 7 1. used confidence intervals to answer questions such as... HYPOTHESIS TESTING (ONE SAMPLE) - CHAPTER 7 1 PREVIOUSLY used confidence intervals to answer questions such as... You know that 0.25% of women have red/green color blindness. You conduct a study of men

More information

Regression Analysis: A Complete Example

Regression Analysis: A Complete Example Regression Analysis: A Complete Example This section works out an example that includes all the topics we have discussed so far in this chapter. A complete example of regression analysis. PhotoDisc, Inc./Getty

More information

Two-Sample T-Tests Assuming Equal Variance (Enter Means)

Two-Sample T-Tests Assuming Equal Variance (Enter Means) Chapter 4 Two-Sample T-Tests Assuming Equal Variance (Enter Means) Introduction This procedure provides sample size and power calculations for one- or two-sided two-sample t-tests when the variances of

More information

ANALYSING LIKERT SCALE/TYPE DATA, ORDINAL LOGISTIC REGRESSION EXAMPLE IN R.

ANALYSING LIKERT SCALE/TYPE DATA, ORDINAL LOGISTIC REGRESSION EXAMPLE IN R. ANALYSING LIKERT SCALE/TYPE DATA, ORDINAL LOGISTIC REGRESSION EXAMPLE IN R. 1. Motivation. Likert items are used to measure respondents attitudes to a particular question or statement. One must recall

More information