# The Time Course of Grief Reactions to Spousal Loss: Evidence From a National Probability Sample

Save this PDF as:

Size: px
Start display at page:

Download "The Time Course of Grief Reactions to Spousal Loss: Evidence From a National Probability Sample"

## Transcription

6 GRIEF REACTIONS TO SPOUSAL LOSS 481 Table 1 Characteristics of the Widowed Sample Total (n 768) Men (n 149) Women (n 619) Characteristic M SD M SD M SD Average age (years) Average age when widowed (years) Education (number of years) Spouse s age at death (years) Total number of children % currently married Race White (%) Black (%) Other (%) Religion Protestant (%) Catholic (%) Jewish (%) Other/none (%) Time since death (years) Died suddenly (%) Number of years married included because it could plausibly be associated with both time since widowhood and the grief response, thereby leading to a bias in the relationship between the two. These adjusted means (also knows as least squares means) represent the predicted level of a given outcome for each time interval for individuals at the mean on the control variables, and they were computed using the LS- MEANS option in the general linear model (GLM) procedure available in SAS software (SAS Institute, 004). As we illustrate in the graphs presented below, although many of the process variables showed a negative exponential pattern with time, some showed what appeared to be a linear trend, and some showed no relationship with time. In our modeling of the functional form, we allowed for all three possibilities. The simplest or null model, shown in Figure 1(i), was one in which, after adjusting for the control variables (x i ) listed above, there was no relationship between time since widowhood (t) and a given process measure, labeled y. In formal terms, y a 0 t c i x i ε. (1) Each control variable (x i ) was mean centered, that is, the sample mean was subtracted from each person s score (resulting in a mean of 0 for all control variables). With the controls coded in this way, the intercept a is the mean of y, and the relationship between time (t) and y net of the controls is constrained to be 0. Each c i represents the unique linear relationship between control variable i and y. Finally, ε is a random variable that represents all other remaining influences on y. It is assumed that these (a) average to zero, (b) are uncorrelated with the other variables in the model, and (c) have the same variability over time and the covariates. Note that time t in this and the other two regression models discussed below is the original, continuous time scale, not the categorized version of time since widowhood used to estimate the adjusted means discussed above. The second or linear model, shown in Figure 1(ii), specified that after adjusting for the control variables, there was a linear relationship between time since widowhood and y, as follows: y a b t c i x i ε. () The intercept a is the value of y for a typical person who has just been widowed. The slope b is the expected difference in each recovery measure y associated with a one-year difference in time since widowhood. Here, each c i represents the unique linear relationship between control variable i and y, adjusting for time. As in the null model, ε is a random variable related to the unmeasured Figure 1. Characteristic forms of the null, linear, and negative exponential models.

7 48 CARNELLEY, WORTMAN, BOLGER, AND BURKE Table Goodness-of-Fit and Improvement-in-Fit Measures for Null, Linear, and Negative Exponential Models: Measures of Continued Involvement and Emotional Resolution Measure RMSE R adj R adj p Frequency of thoughts and memories Null model Linear model Negative exponential model Frequency of conversations Null model.5.14 Linear model Negative exponential model Positive affect Null model Linear model Negative exponential model Negative affect Null model Linear model Negative exponential model Frequency of anniversary reactions Null model Linear model Negative exponential model Length of anniversary reactions Null model Linear model Negative exponential model Intensity of anniversary reactions Null model Linear model Negative exponential model Note. RMSE root-mean-square error. influences on y, conforming to the same set of assumptions laid out above. The third or negative exponential model, illustrated in Figure 1(iii), specified that after adjusting for the control variables (x i ), there was a negative exponential relationship between time since widowhood (t) and y such that adjustment was relatively rapid at first but gradually slowed until an asymptote was reached. The model was as follows: y f d e s t c i x i ε, (3) in which y is the measure of recovery, f is the final or asymptotic level of y, d is the distance between the initial level and the final level of y, e is a mathematical constant representing the base of the natural logarithm, and t is time in years since widowhood. The final parameter, s, is known as the decay constant. It is a positive number related to the rate of adjustment, with larger numbers representing more rapid adjustment. In this specification, f d is the equivalent of a and a in the previous models, that is, a. Again, each c i represents the unique linear relationship between control variable i and y. Once again, ε corresponds to all other random, unmeasured influences on y. The same assumptions described for the null model also apply to this residual term in the negative exponential model. The estimation of all three models was accomplished using the NLIN procedure available with SAS software (SAS Institute, 004), although the null and linear models could have equivalently been estimated with several other SAS procedures (e.g., REG or GLM) or any software capable of least squares linear regression. To determine which of the three models was most appropriate for each measure, we computed adjusted goodness-of-fit indices for each model for each measure (shown in Tables and 3). Like many other methods for computing regression estimates, the NLIN procedure uses least squares estimation to arrive at these estimates (SAS Institute, 004). That is, the estimates produced are those that minimize the sum of squared residuals. Note that because the linear and negative exponential models are not nested models, they cannot be directly compared in terms of their fit. They can, however, be compared in terms of how much each improves the fit compared with the null model. A simple change in R statistic would not suffice for this purpose, though, because it does not take the relative degrees of freedom of the two models into account, namely, that one degree of freedom is lost when fitting the linear model, whereas two degrees of freedom are lost when fitting the negative exponential model. To account for the different degrees of freedom of the linear and negative expo- Unlike some other regression programs, the NLIN procedure requires the user to provide starting values for the parameter estimates. These starting values can be estimated from descriptive data and plots. An additional feature of NLIN is the ability to set bounds on the parameter estimates. In all negative exponential regression analyses presented here, f and f d from Equation 3 were constrained to be between 0 and 100, and s was constrained to be 0 or larger.

9 484 CARNELLEY, WORTMAN, BOLGER, AND BURKE Figure. Functional relationships between years since widowhood and measures of continuing involvement and emotional resolution, adjusted for sex, race, education, age of respondent; age of spouse and number of children at time of widowhood; whether the death was expected or not; whether the death was due to murder, accident, or suicide; and whether the respondent became remarried. Points indicate least squares means for 5-year intervals, and error bars represent standard errors of those means. improvement in fit, we show results for both in the tables. We also indicate the rate of change of each measure as a function of time. For those variables showing a linear relationship, this corresponds to b in Equation and represents the number of units on the dependent variable corresponding to a one-year difference in time since widowhood, adjusting for the control variables listed above. For example, knowing that the linear rate of change in frequency of thoughts about the deceased spouse is.89 units per year means that we would expect respondents widowed 10 years apart to differ on this variable by 8.9 units. For those variables showing a negative exponential relationship, the value listed in the table corresponds to s in Equation 3, although no such easy calculation of adjustment level is possible here because the rate of change depends on time itself. To determine how respondents were doing

10 GRIEF REACTIONS TO SPOUSAL LOSS 485 Figure 3. Functional relationships between years since widowhood and measures of meaning finding, adjusted for sex, race, education, age of respondent; age of spouse and number of children at time of widowhood; whether the death was expected or not; whether the death was due to murder, accident, or suicide; and whether the respondent became remarried. Points indicate least squares means for 5-year intervals, and error bars represent standard errors of those means. after a specified number of years, it is necessary to calculate the predicted levels of y using Equation 3. Tables 4 6 provide several additional pieces of information about the models we estimated. First, they provide the initial value or intercept predicted for each model. For all three models, this has the same interpretation, namely, the predicted level of the dependent variable for people at the point of widowhood, adjusting for the control variables. Second, for measures in which the negative exponential model provided the best fit, these tables provide what we call the 90% asymptotic level. This value represents the level of adjustment corresponding to 90% of the distance between the initial value and the asymptotic value. Finally, for those variables

11 486 CARNELLEY, WORTMAN, BOLGER, AND BURKE Figure 4. Functional relationship between years since widowhood and measures of personal growth, adjusted for sex, race, education, age of respondent; age of spouse and number of children at time of widowhood; whether the death was expected or not; whether the death was due to murder, accident, or suicide; and whether the respondent became remarried. Points indicate least squares means for 5-year intervals, and error bars represent standard errors of those means. in which there was a negative exponential relationship between time since widowhood and adjustment, we used Equation 3 to estimate the number of years it would take to reach 5%, 50%, 75%, and 90% of the distance to the asymptotes. These values provide a view of adjustment as a function of time for the negative exponential models that is easier to interpret than the s parameter of Equation 3. In those cases in which the relationship between the dependent variable and time since widowhood is linear, identifying a specific long-term recovery level is not possible because the rate of recovery does not change over time. Thus, for those variables in which the model was linear, we left the 5%, 50%, 75%, and 90% columns blank. A Note on the Figures Figures 4 show the best fitting model for each measure of recovery as well as the least squares means estimated for each 5-year interval since widowhood (described earlier). Although the total sample contained respondents widowed as little as a few months to as long as 64 years prior to the survey, small cell sizes Table 4 Linear and Negative Exponential Regressions Relating Indicators of Continuing Involvement and Emotional Resolution to the Duration of Time Since Widowhood Dependent variable & form of relationship Level of dependent variable Number of years to % of asymptotic level Speed of change SE Initial SE 90% asymptotic SE 5% 50% 75% 90% Frequency of memories Linear.89* *.0 Negative exponential * * a Frequency of conversations Negative exponential.06* * 3.4.8* Positive affect b Null 0 60.* 1.3 Negative affect b Negative exponential.18* * * Frequency of anniversary reactions Negative exponential.04* * * Duration of anniversary reactions c Null * 1. Intensity of anniversary reactions c Negative exponential.3* * * Note. For linear results, rates are in units per year. All analyses adjust for sex, race, education, age of respondent, age of spouse, and number of children at time of widowhood; whether the death was expected or not; whether the death was due to murder, accident, or suicide; and whether the respondent became remarried. a Projected value is beyond the range of the data. b Total n 697. c Total n 484. p.10. * p.05.

12 GRIEF REACTIONS TO SPOUSAL LOSS 487 Table 5 Linear and Negative Exponential Regressions Relating Indicators of Meaning Finding to the Duration of Time Since Widowhood Level of dependent variable Number of years to % of asymptotic level Dependent variable & form of relationship Speed of change SE Initial SE 90% asymptotic SE 5% 50% 75% 90% View death as meant to be Linear.60* *.7 Negative exponential.0* * * b b View death as something that just happens Linear.65* *.3 Negative Exponential.03* * * b Currently searching for meaning? a Negative exponential.1* * 6.5.* If searched, found meaning? a Null 0 5.9* 1.7 View death as senseless and unfair Linear.50* *.6 Negative exponential * * View of spouse as better off now Null * 1.5 Note. For linear results, rates are in units per year. All analyses adjust for sex, race, education, age of respondent, age of spouse, and number of children at time of widowhood; whether the death was expected or not; whether the death was due to murder, accident, or suicide; and whether the respondent became remarried. a Total n 313. b Projected value is beyond the range of the data. * p.05. limited the interpretability of the least squares means analysis to widows of 35 years or less. For this reason, Figures 4 depict only the first 35 years since widowhood, although all analyses made use of the entire widowed sample. Also, each of these figures has two ordinate axes, one showing the scale of the dependent measure and one showing the actual verbal labels the respondents were given. Continuing Involvement and Emotional Resolution We first present results for measures of continuing involvement with the lost loved one, such as the frequency of memories and conversations about one s spouse, and measures of emotional resolution, such as positive and negative feelings from thinking and talking about the loss and the frequency, duration, and intensity of feeling upset with reminders of the loss. Table summarizes the goodness-of-fit results, whereas Table 4 summarizes the fitted models. For frequency of thoughts and memories about the deceased spouse, both the linear and negative exponential models showed equal improvement in fit over the null model. For simplicity, we chose to graph only the negative exponential results ( R adj.0477, p.001), as shown in Figure (i). These results show a moderate decline in thoughts and memories as a function of time since widowhood. Respondents who were recently widowed reported having thoughts and memories of their loved one approximately two to three times per week (corresponding to 80.5 units). The 90% asymptotic value (34.5 units) corresponds to thoughts or memories about once per month, and the number of years widowed corresponding to this value is 71.3 years. This value is beyond the observed range of our data (0 64 years postwidowhood). Table 6 Linear and Negative Exponential Regressions Relating Perceptions of Personal Growth to the Duration of Time Since Widowhood Dependent variable & form of relationship Level of dependent variable Speed of change SE Initial SE Number of years to % of asymptotic level 90% asymptotic SE 5% 50% 75% 90% Increased self-confidence Linear.34* *.4 Negative exponential * * Stronger person as a result Null * 1.3 Note. Rates are in units per year. All analyses adjust for sex, race, education, age of respondent, age of spouse, and number of children at time of widowhood; whether the death was expected or not; whether the death was due to murder, accident, or suicide; and whether the respondent became remarried. * p.05.

17 49 CARNELLEY, WORTMAN, BOLGER, AND BURKE effects of losing a spouse or child in a motor vehicle crash. Journal of Personality and Social Psychology, 5, Lessler, J. T., & Kalsbeek, W. D. (199). Nonsampling errors in surveys. New York: Wiley. Lieberman, M. (1996). Doors close, doors open: Windows, grieving and growing. New York: Putnam. Lopata, H. Z. (1973). Self-identity in marriage and widowhood. Sociological Quarterly, 14, Marris, P. (1958). Widows and their families. London: Routledge & Kegan Paul. McGuigan, F. J. (1994). Biological psychology: A cybernetic science. Upper Saddle River, NJ: Prentice-Hall. Miller, E. D., & Omarzu, J. (1998). New directions in loss research. In J. Harvey (Ed.), Perspectives on loss: A sourcebook (pp. 3 0). Washington, DC: Taylor & Francis. Nolen-Hoeksema, S., Parker, L. E., & Larson, J. (1994). Ruminative coping with depressed mood following loss. Journal of Personality and Social Psychology, 67, Parkes, C. M., & Weiss, R. S. (1983). Recovery from bereavement. New York: Basic Books. Rando, T. A. (1993). Treatment of complicated mourning. Champaign, IL: Research Press. Rawlings, J. O., Pantula, S. G., & Dickey, D. A. (1998). Applied regression analysis: A research tool (nd ed.). New York: Springer-Verlag. SAS Institute. (004). SAS/STAT 9.1 user s guide. Cary, NC: Author. Schaefer, J. A., & Moos, R. H. (001). Bereavement experiences and personal growth. In M. S. Stroebe, R. O. Hansson, W. Stroebe, & H. Schut (Eds.), Handbook of bereavement research: Consequences, coping, and care (pp ). Washington, DC: American Psychological Association. Shaver, P. R., & Tancredy, C. M. (001). Emotion, attachment, and bereavement: A conceptual commentary. In M. S. Stroebe, R. O. Hansson, W. Stroebe, & H. Schut (Eds.), Handbook of bereavement research: Consequences, coping, and care (pp ). Washington, DC: American Psychological Association. Singer, J. D., & Willett, J. B. (003). Applied longitudinal data analysis: Modeling change and event occurrence. New York: Oxford University Press. Stephenson, J. S. (1985). Death, grief, and mourning. New York: Free Press. Stroebe, M. S., Hansson, R. O., Stroebe, W., & Schut, H. (001a). Future directions for bereavement research. In M. S. Stroebe, R. O. Hansson, W. Stroebe, & H. Schut (Eds.), Handbook of bereavement research: Consequences, coping, and care (pp ). Washington, DC: American Psychological Association. Stroebe, M. S., Hansson, R. O., Stroebe, W., & Schut, H. (Eds.). (001b). Handbook of bereavement research: Consequences, coping, and care. Washington, DC: American Psychological Association. Stroebe, M. S., Hansson, R. O., Stroebe, W., & Schut, H. (001c). Introduction: Concepts and issues in contemporary research on bereavement. In M. S. Stroebe, R. O. Hansson, W. Stroebe, & H. Schut (Eds.), Handbook of bereavement research: Consequences, coping, and care (pp. 3 ). Washington, DC: American Psychological Association. Stroebe, M. S., & Stroebe, W. (1989). Who participates in bereavement research? A review and empirical study. Omega: Journal of Death and Dying, 0, 1 9. Stroebe, M. S., & Stroebe, W. (1991). Does grief work work? Journal of Consulting and Clinical Psychology, 59, Stroebe, W., & Schut, H. (001). Models of coping with bereavement: A review. In M. S. Stroebe, R. O. Hansson, W. Stroebe, & H. Schut (Eds.), Handbook of bereavement research: Consequences, coping, and care (pp ). Washington, DC: American Psychological Association. Stroebe, W., & Stroebe, M. S. (1987). Bereavement and health: The psychological and physical consequences of partner loss. New York: Cambridge University Press. Thomas, L. E., DiGiulio, R. C., & Sheehan, N. W. (1988). Identity loss and psychological crisis in widowhood: A re-evaluation. International Journal of Aging and Human Development, 6, Umberson, D., Wortman, C. B., & Kessler, R. (199). Widowhood and depression: Explaining gender differences in vulnerability. Journal of Health and Social Behavior, 33, United States Bureau of the Census. (1985). Statistical abstracts of the U.S., Washington, DC: Government Printing Office. Weiss, R. S. (1988). Loss and recovery. Journal of Social Issues, 44, Weiss, R. S. (001). Grief, bonds, and relationships. In M. S. Stroebe, R. O. Hansson, W. Stroebe, & H. Schut (Eds.), Handbook of bereavement research: Consequences, coping, and care (pp. 47 6). Washington, DC: American Psychological Association. Worden, J. W. (00). Grief counseling and grief therapy (3rd ed.). New York: Springer Publishing Company. Wortman, C. B., & Silver, R. C. (1990). Successful mastery of bereavement and widowhood: A lifecourse perspective. In P. B. Baltes & M. M. Baltes (Eds.), Successful aging: Perspectives from the behavioral sciences (pp. 5 64). New York: Cambridge University Press. Zisook, S., Devaul, R. A., & Click, M. A. (198). Measuring symptoms of grief and bereavement. American Journal of Psychiatry, 139, Received September 8, 005 Revision received January 18, 006 Accepted January 30, 006

### FROM FREUD TO NIEMEYER. How our understanding of bereavement response has changed over the last three decades

FROM FREUD TO NIEMEYER How our understanding of bereavement response has changed over the last three decades May 2012 Dr Helen Greally AIMS OF DISCUSSION Offer a brief overview of the major theories of

### Below is a diagram showing the Models of Grief that have been developed by a range of theorists since the 1940 s. The 1964, 1972) Restitution

Models of grief Below is a diagram showing the Models of Grief that have been developed by a range of theorists since the 1940 s. Models of grief Theorist Stage or Phase Lindemann Shock & Acute Mourning

### 1/27/2013. PSY 512: Advanced Statistics for Psychological and Behavioral Research 2

PSY 512: Advanced Statistics for Psychological and Behavioral Research 2 Introduce moderated multiple regression Continuous predictor continuous predictor Continuous predictor categorical predictor Understand

### How to Get More Value from Your Survey Data

Technical report How to Get More Value from Your Survey Data Discover four advanced analysis techniques that make survey research more effective Table of contents Introduction..............................................................2

### Module 3: Correlation and Covariance

Using Statistical Data to Make Decisions Module 3: Correlation and Covariance Tom Ilvento Dr. Mugdim Pašiƒ University of Delaware Sarajevo Graduate School of Business O ften our interest in data analysis

### Theories around loss & bereavement

Theories around loss & bereavement 25 & 26 May 2016 Shirley Thompson 1 Objectives: Define bereavement terms Identify myths associated with grief Identify theories related to grief Describe normal grief

### GRIEVING PET DEATH: NORMATIVE, GENDER, AND ATTACHMENT ISSUES

OMEGA, Vol. 47(4) 385-393, 2003 GRIEVING PET DEATH: NORMATIVE, GENDER, AND ATTACHMENT ISSUES THOMAS A. WROBEL AMANDA L. DYE University of Michigan Flint ABSTRACT Grief over the loss of a pet was investigated

### Number, Timing, and Duration of Marriages and Divorces: 2009

Number, Timing, and Duration of Marriages and Divorces: 2009 Household Economic Studies Issued May 2011 P70-125 INTRODUCTION Marriage and divorce are central to the study of living arrangements and family

### 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,

### 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

### 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

### The Grieving Process. Lydia Snyder Fourth year Medical Student

The Grieving Process Lydia Snyder Fourth year Medical Student What is Grief? The normal process of reacting to a loss Loss of loved one Sense of one s own nearing death Loss of familiar home environment

### Reference document. Understanding and living through grief

Reference document Understanding and living through grief Table of content Introduction 2 Definition 2 Myths 2 Stages and symptoms 2 Differentiate grief from depression 3 How to overcome grief 3 When grief

### Engineering Problem Solving and Excel. EGN 1006 Introduction to Engineering

Engineering Problem Solving and Excel EGN 1006 Introduction to Engineering Mathematical Solution Procedures Commonly Used in Engineering Analysis Data Analysis Techniques (Statistics) Curve Fitting techniques

### Multivariate Logistic Regression

1 Multivariate Logistic Regression As in univariate logistic regression, let π(x) represent the probability of an event that depends on p covariates or independent variables. Then, using an inv.logit formulation

### Critical Incidents. Information for schools from Derbyshire Educational Psychology Service

Critical Incidents Information for schools from Derbyshire Educational Psychology Service Introduction to Critical Incidents A critical incident (CI) is any event that is unexpected, acute, stressful and

### Introduction to Longitudinal Data Analysis

Introduction to Longitudinal Data Analysis Longitudinal Data Analysis Workshop Section 1 University of Georgia: Institute for Interdisciplinary Research in Education and Human Development Section 1: Introduction

### 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

### 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

### Family Factors that Affect The Resolution of Grief In Older Persoru;

Family Factors that Affect The Resolution of Grief In Older Persoru; Kathleen Triche, D.S.W. D.S.W., Wurzweiler School of Social Work, Yeshiva University, 1994 Coordinator, Geriatric Psychiatric Outpatient

### WHERE HAS HE GONE? GRIEF AND LOSS IN DEMENTIA. Di Moncrieff Dr Thomas Dellmann

WHERE HAS HE GONE? GRIEF AND LOSS IN DEMENTIA Di Moncrieff Dr Thomas Dellmann The dark clouds of disease can cover up the essence of the person. 1 in 10 people would avoid spending time with a person with

### Unthinkable... Facing Grief After a Child s Death

Unthinkable... Facing Grief After a Child s Death www.austins.co.uk Unthinkable... Facing Grief After a Child s Death Jan and Bob could not believe what they were hearing. Their nine-year-old son, Ryan,

### 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

### Depression in Older Persons

Depression in Older Persons How common is depression in later life? Depression affects more than 6.5 million of the 35 million Americans aged 65 or older. Most people in this stage of life with depression

### Business Valuation Review

Business Valuation Review Regression Analysis in Valuation Engagements By: George B. Hawkins, ASA, CFA Introduction Business valuation is as much as art as it is science. Sage advice, however, quantitative

### DEALING WITH GRIEF THE PHASES OF GRIEF

Page 1 of 7 DEALING WITH GRIEF Topics On This Page Phases of Grief Help Through Grief Symptoms Of Grief Feelings During Grief How Grief Changes Our Lives Myths About Grief THE PHASES OF GRIEF From My Son...My

### This chapter will demonstrate how to perform multiple linear regression with IBM SPSS

CHAPTER 7B Multiple Regression: Statistical Methods Using IBM SPSS This chapter will demonstrate how to perform multiple linear regression with IBM SPSS first using the standard method and then using the

### MINITAB ASSISTANT WHITE PAPER

MINITAB ASSISTANT WHITE PAPER This paper explains the research conducted by Minitab statisticians to develop the methods and data checks used in the Assistant in Minitab 17 Statistical Software. One-Way

### The Effect of Questionnaire Cover Design in Mail Surveys

The Effect of Questionnaire Cover Design in Mail Surveys Philip Gendall It has been suggested that the response rate for a self administered questionnaire will be enhanced if the cover of the questionnaire

### PSYCHOLOGY AND PROJECT MANAGEMENT

PSYCHOLOGY AND PROJECT MANAGEMENT Human aspects of the project management Ver 1.0 2 360 Degree Approach of IT Infrastructure Projects PSYCHOLOGY AND PROJECT MANAGEMENT Abstract Project Management usually

### PEER REVIEW HISTORY ARTICLE DETAILS VERSION 1 - REVIEW. Elizabeth Comino Centre fo Primary Health Care and Equity 12-Aug-2015

PEER REVIEW HISTORY BMJ Open publishes all reviews undertaken for accepted manuscripts. Reviewers are asked to complete a checklist review form (http://bmjopen.bmj.com/site/about/resources/checklist.pdf)

### Remarriage in the United States

Remarriage in the United States Poster presented at the annual meeting of the American Sociological Association, Montreal, August 10-14, 2006 Rose M. Kreider U.S. Census Bureau rose.kreider@census.gov

### Chapter 7: Simple linear regression Learning Objectives

Chapter 7: Simple linear regression Learning Objectives Reading: Section 7.1 of OpenIntro Statistics Video: Correlation vs. causation, YouTube (2:19) Video: Intro to Linear Regression, YouTube (5:18) -

### DESCRIPTIVE STATISTICS AND EXPLORATORY DATA ANALYSIS

DESCRIPTIVE STATISTICS AND EXPLORATORY DATA ANALYSIS SEEMA JAGGI Indian Agricultural Statistics Research Institute Library Avenue, New Delhi - 110 012 seema@iasri.res.in 1. Descriptive Statistics Statistics

### Research Methods 1 Handouts, Graham Hole,COGS - version 1.0, September 2000: Page 1:

Research Methods 1 Handouts, Graham Hole,COGS - version 1.0, September 000: Page 1: DESCRIPTIVE STATISTICS - FREQUENCY DISTRIBUTIONS AND AVERAGES: Inferential and Descriptive Statistics: There are four

### Objectives. Traumatic, Unexpected Death. Grief Conferences Jill Wilke, MS, RN, CPLC

Grief Conferences Lead Educator Resolve Through Sharing This slide presentation is a copyright of Gundersen Lutheran Medical Founda on, Inc., 2014 All Rights Reserved Objectives Describe two processes

### INVESTIGATING THE EFFECTIVENESS OF POSITIVE PSYCHOLOGY TRAINING ON INCREASED HARDINESS AND PSYCHOLOGICAL WELL-BEING

INVESTIGATING THE EFFECTIVENESS OF POSITIVE PSYCHOLOGY TRAINING ON INCREASED HARDINESS AND PSYCHOLOGICAL WELL-BEING *Zahra Gholami Ghareh Shiran 1, Ghodsi Ahghar 2, Afshin Ahramiyan 3, Afsaneh Boostan

### AN INDICATION OF THE EFFECT OF NONINTERVIEW ADJUSTMENT AND POST -STRATIFICATION ON ESTIMATES FROM A SAMPLE SURVEY

AN INDICATION OF THE EFFECT OF NONINTERVIEW AND POST -STRATIFICATION ON ESTIMATES FROM A SAMPLE SURVEY Martha J. Banks, University of Chicago This paper is based on research done at the Center for Health

### Bill Burton Albert Einstein College of Medicine william.burton@einstein.yu.edu April 28, 2014 EERS: Managing the Tension Between Rigor and Resources 1

Bill Burton Albert Einstein College of Medicine william.burton@einstein.yu.edu April 28, 2014 EERS: Managing the Tension Between Rigor and Resources 1 Calculate counts, means, and standard deviations Produce

### DATA ANALYSIS AND REPORT. Melissa Lehmann Work Solutions. Abstract

PO Box 12499 A Beckett Melbourne VIC 8006 t 03 9224 8800 f 03 9224 8801 DATA ANALYSIS AND REPORT Melissa Lehmann Work Solutions Abstract The role of work and work-life balance in contributing to stress

### 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

### How to get more value from your survey data

IBM SPSS Statistics How to get more value from your survey data Discover four advanced analysis techniques that make survey research more effective Contents: 1 Introduction 2 Descriptive survey research

### 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:

### Main Effects and Interactions

Main Effects & Interactions page 1 Main Effects and Interactions So far, we ve talked about studies in which there is just one independent variable, such as violence of television program. You might randomly

### Defining Death. Defining Death. In the past several decades, defining death has become more complex

4/30/2009 1 4/30/2009 2 Defining Death In the past several decades, defining death has become more complex Defining Death In the past several decades, defining death has become more complex Brain death

### 4. Simple regression. QBUS6840 Predictive Analytics. https://www.otexts.org/fpp/4

4. Simple regression QBUS6840 Predictive Analytics https://www.otexts.org/fpp/4 Outline The simple linear model Least squares estimation Forecasting with regression Non-linear functional forms Regression

### Chapter 6: The Information Function 129. CHAPTER 7 Test Calibration

Chapter 6: The Information Function 129 CHAPTER 7 Test Calibration 130 Chapter 7: Test Calibration CHAPTER 7 Test Calibration For didactic purposes, all of the preceding chapters have assumed that the

### Grief is a normal response to

Grief is a normal response to loss. It can be the loss of a home, job, marriage or a loved one. Often the most painful loss is the death of a person you love, whether from a long illness or from an accident

### MISSING DATA TECHNIQUES WITH SAS. IDRE Statistical Consulting Group

MISSING DATA TECHNIQUES WITH SAS IDRE Statistical Consulting Group ROAD MAP FOR TODAY To discuss: 1. Commonly used techniques for handling missing data, focusing on multiple imputation 2. Issues that could

### Survey, Statistics and Psychometrics Core Research Facility University of Nebraska-Lincoln. Log-Rank Test for More Than Two Groups

Survey, Statistics and Psychometrics Core Research Facility University of Nebraska-Lincoln Log-Rank Test for More Than Two Groups Prepared by Harlan Sayles (SRAM) Revised by Julia Soulakova (Statistics)

### Marital Status and Suicide in the National Longitudinal Mortality Study

Marital Status and Suicide in the National Longitudinal Mortality Study Augustine J. Kposowa, Ph.D. University of California Riverside Journal of Epidemiology & Community Health March, 2000 Volume 54,

### Exercise 1.12 (Pg. 22-23)

Individuals: The objects that are described by a set of data. They may be people, animals, things, etc. (Also referred to as Cases or Records) Variables: The characteristics recorded about each individual.

### You can give bereavement care. Module 6

You can give bereavement care Module 6 Learning objectives Describe loss, grief, mourning, bereavement Explore theories of loss Outline the 9 cell tool Describe cultural practices around death Discuss

### ORIGINAL ATTACHMENT THREE-CATEGORY MEASURE

ORIGINAL ATTACHMENT THREE-CATEGORY MEASURE Reference: Hazan, C., & Shaver, P. R. (1987). Romantic love conceptualized as an attachment process. Journal of Personality and Social Psychology, 52, 511-524.

### Quality of Life The Priorities of Older People with a Cognitive Impairment

Living in a Nursing Home Quality of Life The Priorities of Older People with a Cognitive Impairment Compiled by Suzanne Cahill PhD and Ana Diaz in association with Dementia Services Information and Development

### ANNEX 2: Assessment of the 7 points agreed by WATCH as meriting attention (cover paper, paragraph 9, bullet points) by Andy Darnton, HSE

ANNEX 2: Assessment of the 7 points agreed by WATCH as meriting attention (cover paper, paragraph 9, bullet points) by Andy Darnton, HSE The 7 issues to be addressed outlined in paragraph 9 of the cover

### The Effects of Moderate Aerobic Exercise on Memory Retention and Recall

The Effects of Moderate Aerobic Exercise on Memory Retention and Recall Lab 603 Group 1 Kailey Fritz, Emily Drakas, Naureen Rashid, Terry Schmitt, Graham King Medical Sciences Center University of Wisconsin-Madison

### Grief, Depression, and the DSM-5 By Rochelle Perper, Ph.D.

1 Grief, Depression, and the DSM-5 By Rochelle Perper, Ph.D. The relationship between grief and depression following bereavement has been debated in the literature as well as in the general public media.

### 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

### Belief Formation in the Returns to Schooling

Working paper Belief Formation in the Returns to ing Jim Berry Lucas Coffman March 212 Belief Formation in the Returns to ing March 31, 212 Jim Berry Cornell University Lucas Coffman Ohio State U. & Yale

### Overview Classes. 12-3 Logistic regression (5) 19-3 Building and applying logistic regression (6) 26-3 Generalizations of logistic regression (7)

Overview Classes 12-3 Logistic regression (5) 19-3 Building and applying logistic regression (6) 26-3 Generalizations of logistic regression (7) 2-4 Loglinear models (8) 5-4 15-17 hrs; 5B02 Building and

### Analyzing and interpreting data Evaluation resources from Wilder Research

Wilder Research Analyzing and interpreting data Evaluation resources from Wilder Research Once data are collected, the next step is to analyze the data. A plan for analyzing your data should be developed

### Chapter 6 Partial Correlation

Chapter 6 Partial Correlation Chapter Overview Partial correlation is a statistical technique for computing the Pearson correlation between a predictor and a criterion variable while controlling for (removing)

### , then the form of the model is given by: which comprises a deterministic component involving the three regression coefficients (

Multiple regression Introduction Multiple regression is a logical extension of the principles of simple linear regression to situations in which there are several predictor variables. For instance if we

### Post Traumatic Stress Disorder & Substance Misuse

Post Traumatic Stress Disorder & Substance Misuse Produced and Presented by Dr Derek Lee Consultant Chartered Clinical Psychologist Famous Sufferers. Samuel Pepys following the Great Fire of London:..much

### 4.1 Exploratory Analysis: Once the data is collected and entered, the first question is: "What do the data look like?"

Data Analysis Plan The appropriate methods of data analysis are determined by your data types and variables of interest, the actual distribution of the variables, and the number of cases. Different analyses

### Age to Age Factor Selection under Changing Development Chris G. Gross, ACAS, MAAA

Age to Age Factor Selection under Changing Development Chris G. Gross, ACAS, MAAA Introduction A common question faced by many actuaries when selecting loss development factors is whether to base the selected

### 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

### Development and Standardization

Development and Standardization 2 Development of the DECA-P2 Items Item development for the Devereux Early Childhood Assessment for Preschoolers, Second Edition (DECA-P2) began with a review of the items

### How to Use a Monte Carlo Study to Decide on Sample Size and Determine Power

STRUCTURAL EQUATION MODELING, 9(4), 599 620 Copyright 2002, Lawrence Erlbaum Associates, Inc. TEACHER S CORNER How to Use a Monte Carlo Study to Decide on Sample Size and Determine Power Linda K. Muthén

### Answer: C. The strength of a correlation does not change if units change by a linear transformation such as: Fahrenheit = 32 + (5/9) * Centigrade

Statistics Quiz Correlation and Regression -- ANSWERS 1. Temperature and air pollution are known to be correlated. We collect data from two laboratories, in Boston and Montreal. Boston makes their measurements

### Ask the Expert. by Howard Gruetzner, M.Ed., LPC. Education and Family Support Specialist. Alzheimer s Association - North Central Texas Chapter

Ask the Expert by Howard Gruetzner, M.Ed., LPC Education and Family Support Specialist Alzheimer s Association - North Central Texas Chapter What should families understand about the guilt that often accompanies

### CHAPTER 13 SIMPLE LINEAR REGRESSION. Opening Example. Simple Regression. Linear Regression

Opening Example CHAPTER 13 SIMPLE LINEAR REGREION SIMPLE LINEAR REGREION! Simple Regression! Linear Regression Simple Regression Definition A regression model is a mathematical equation that descries the

### 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

### SATISFACTION WITH LIFE SCALE

SATISFACTION WITH LIFE SCALE Reference: Diener, E., Emmons, R. A., Larsen, R. J., & Griffin, S. (1985). The Satisfaction with Life Scale. Journal of Personality Assessment, 49, 71-75. Description of Measure:

### An analysis of the 2003 HEFCE national student survey pilot data.

An analysis of the 2003 HEFCE national student survey pilot data. by Harvey Goldstein Institute of Education, University of London h.goldstein@ioe.ac.uk Abstract The summary report produced from the first

### X X X a) perfect linear correlation b) no correlation c) positive correlation (r = 1) (r = 0) (0 < r < 1)

CORRELATION AND REGRESSION / 47 CHAPTER EIGHT CORRELATION AND REGRESSION Correlation and regression are statistical methods that are commonly used in the medical literature to compare two or more variables.

### Getting Correct Results from PROC REG

Getting Correct Results from PROC REG Nathaniel Derby, Statis Pro Data Analytics, Seattle, WA ABSTRACT PROC REG, SAS s implementation of linear regression, is often used to fit a line without checking

### SOCIETY OF ACTUARIES THE AMERICAN ACADEMY OF ACTUARIES RETIREMENT PLAN PREFERENCES SURVEY REPORT OF FINDINGS. January 2004

SOCIETY OF ACTUARIES THE AMERICAN ACADEMY OF ACTUARIES RETIREMENT PLAN PREFERENCES SURVEY REPORT OF FINDINGS January 2004 Mathew Greenwald & Associates, Inc. TABLE OF CONTENTS INTRODUCTION... 1 SETTING

### International Statistical Institute, 56th Session, 2007: Phil Everson

Teaching Regression using American Football Scores Everson, Phil Swarthmore College Department of Mathematics and Statistics 5 College Avenue Swarthmore, PA198, USA E-mail: peverso1@swarthmore.edu 1. Introduction

### Module 5: Multiple Regression Analysis

Using Statistical Data Using to Make Statistical Decisions: Data Multiple to Make Regression Decisions Analysis Page 1 Module 5: Multiple Regression Analysis Tom Ilvento, University of Delaware, College

### A Study of the Therapeutic Journey of Children who have been Bereaved. Executive Summary

A Study of the Therapeutic Journey of Children who have been Bereaved Executive Summary Research Team Ms. Mairéad Dowling, School of Nursing, Dublin City University Dr. Gemma Kiernan, School of Nursing,

### 3:3 LEC - NONLINEAR REGRESSION

3:3 LEC - NONLINEAR REGRESSION Not all relationships between predictor and criterion variables are strictly linear. For a linear relationship, a unit change on X produces exactly the same amount of change

### Research Variables. Measurement. Scales of Measurement. Chapter 4: Data & the Nature of Measurement

Chapter 4: Data & the Nature of Graziano, Raulin. Research Methods, a Process of Inquiry Presented by Dustin Adams Research Variables Variable Any characteristic that can take more than one form or value.

### GUIDANCE FOR CAREGIVERS: CHILDREN OR TEENS WHO HAD A LOVED ONE DIE IN THE EARTHQUAKE

GUIDANCE FOR CAREGIVERS: CHILDREN OR TEENS WHO HAD A LOVED ONE DIE IN THE EARTHQUAKE Introduction to trauma The earthquake was a terrifying disaster for adults, children, families, and communities. The

### 1 Theory: The General Linear Model

QMIN GLM Theory - 1.1 1 Theory: The General Linear Model 1.1 Introduction Before digital computers, statistics textbooks spoke of three procedures regression, the analysis of variance (ANOVA), and the

T O P I C 1 2 Techniques and tools for data analysis Preview Introduction In chapter 3 of Statistics In A Day different combinations of numbers and types of variables are presented. We go through these

### Getting the Most from Demographics: Things to Consider for Powerful Market Analysis

Getting the Most from Demographics: Things to Consider for Powerful Market Analysis Charles J. Schwartz Principal, Intelligent Analytical Services Demographic analysis has become a fact of life in market

### PASS Sample Size Software

Chapter 250 Introduction The Chi-square test is often used to test whether sets of frequencies or proportions follow certain patterns. The two most common instances are tests of goodness of fit using multinomial

### 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

### 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

### F. Farrokhyar, MPhil, PhD, PDoc

Learning objectives Descriptive Statistics F. Farrokhyar, MPhil, PhD, PDoc To recognize different types of variables To learn how to appropriately explore your data How to display data using graphs How

### 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

### AP Physics 1 and 2 Lab Investigations

AP Physics 1 and 2 Lab Investigations Student Guide to Data Analysis New York, NY. College Board, Advanced Placement, Advanced Placement Program, AP, AP Central, and the acorn logo are registered trademarks

### Chapter 11: Two Variable Regression Analysis

Department of Mathematics Izmir University of Economics Week 14-15 2014-2015 In this chapter, we will focus on linear models and extend our analysis to relationships between variables, the definitions

### 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

### Regression III: Dummy Variable Regression

Regression III: Dummy Variable Regression Tom Ilvento FREC 408 Linear Regression Assumptions about the error term Mean of Probability Distribution of the Error term is zero Probability Distribution of

### Organizing Your Approach to a Data Analysis

Biost/Stat 578 B: Data Analysis Emerson, September 29, 2003 Handout #1 Organizing Your Approach to a Data Analysis The general theme should be to maximize thinking about the data analysis and to minimize

### The Many Emotions of Grief

The Many Emotions of Grief While it is important to understand grief and know how it can affect us, we must also acknowledge that: The focus of grief is not on our ability to understand, but on our ability

### 4. Describing Bivariate Data

4. Describing Bivariate Data A. Introduction to Bivariate Data B. Values of the Pearson Correlation C. Properties of Pearson's r D. Computing Pearson's r E. Variance Sum Law II F. Exercises A dataset with