The Importance of Numbers: What Large Skeletal Samples Can (and Cannot) Reveal About the Health Status of Earlier Human Population Phillip L. Walker Department.

Slides:



Advertisements
Similar presentations
Introduction to Hypothesis Testing
Advertisements

Introductory Mathematics & Statistics for Business
Statistical vs Clinical Significance
If you are viewing this slideshow within a browser window, select File/Save as… from the toolbar and save the slideshow to your computer, then open it.
Hypothesis Testing W&W, Chapter 9.
Power and sample size.
Inferential Statistics
How do we know when we know. Outline  What is Research  Measurement  Method Types  Statistical Reasoning  Issues in Human Factors.
Sample size estimation
Hypothesis Testing making decisions using sample data.
Review You run a t-test and get a result of t = 0.5. What is your conclusion? Reject the null hypothesis because t is bigger than expected by chance Reject.
Significance and probability Type I and II errors Practical Psychology 1 Week 10.
Statistical Issues in Research Planning and Evaluation
Statistical Decision Making
Statistical Techniques I EXST7005 Lets go Power and Types of Errors.
Analysis of frequency counts with Chi square
Nemours Biomedical Research Statistics March 19, 2009 Tim Bunnell, Ph.D. & Jobayer Hossain, Ph.D. Nemours Bioinformatics Core Facility.
Cal State Northridge  320 Ainsworth Sampling Distributions and Hypothesis Testing.
Chapter Sampling Distributions and Hypothesis Testing.
PSY 307 – Statistics for the Behavioral Sciences
Today Concepts underlying inferential statistics
Statistics for CS 312. Descriptive vs. inferential statistics Descriptive – used to describe an existing population Inferential – used to draw conclusions.
Hypothesis Testing Is It Significant?. Questions What is a statistical hypothesis? What is the null hypothesis? Why is it important for statistical tests?
Sample Size Determination Ziad Taib March 7, 2014.
Descriptive Statistics
Inferential Statistics
Introduction to Testing a Hypothesis Testing a treatment Descriptive statistics cannot determine if differences are due to chance. A sampling error occurs.
Chapter 12 Inferential Statistics Gay, Mills, and Airasian
Statistical hypothesis testing – Inferential statistics I.
Inferential Statistics
Sample size calculation
AM Recitation 2/10/11.
COLLECTING QUANTITATIVE DATA: Sampling and Data collection
Epidemiology The Basics Only… Adapted with permission from a class presentation developed by Dr. Charles Lynch – University of Iowa, Iowa City.
CHAPTER 16: Inference in Practice. Chapter 16 Concepts 2  Conditions for Inference in Practice  Cautions About Confidence Intervals  Cautions About.
Health and Disease in Populations 2001 Sources of variation (2) Jane Hutton (Paul Burton)
1 Statistical Inference. 2 The larger the sample size (n) the more confident you can be that your sample mean is a good representation of the population.
Introduction To Biological Research. Step-by-step analysis of biological data The statistical analysis of a biological experiment may be broken down into.
Education Research 250:205 Writing Chapter 3. Objectives Subjects Instrumentation Procedures Experimental Design Statistical Analysis  Displaying data.
Inferential Statistics 2 Maarten Buis January 11, 2006.
Instructor Resource Chapter 5 Copyright © Scott B. Patten, Permission granted for classroom use with Epidemiology for Canadian Students: Principles,
Psy B07 Chapter 4Slide 1 SAMPLING DISTRIBUTIONS AND HYPOTHESIS TESTING.
1 Lecture 19: Hypothesis Tests Devore, Ch Topics I.Statistical Hypotheses (pl!) –Null and Alternative Hypotheses –Testing statistics and rejection.
Research Process Parts of the research study Parts of the research study Aim: purpose of the study Aim: purpose of the study Target population: group whose.
Inference and Inferential Statistics Methods of Educational Research EDU 660.
Copyright © Cengage Learning. All rights reserved. 8 Introduction to Statistical Inferences.
Introduction to Inferential Statistics Statistical analyses are initially divided into: Descriptive Statistics or Inferential Statistics. Descriptive Statistics.
DIRECTIONAL HYPOTHESIS The 1-tailed test: –Instead of dividing alpha by 2, you are looking for unlikely outcomes on only 1 side of the distribution –No.
Educational Research Chapter 13 Inferential Statistics Gay, Mills, and Airasian 10 th Edition.
Chapter 20 Testing Hypothesis about proportions
©2010 John Wiley and Sons Chapter 2 Research Methods in Human-Computer Interaction Chapter 2- Experimental Research.
Introduction Suppose that a pharmaceutical company is concerned that the mean potency  of an antibiotic meet the minimum government potency standards.
IMPORTANCE OF STATISTICS MR.CHITHRAVEL.V ASST.PROFESSOR ACN.
© Copyright McGraw-Hill 2004
URBDP 591 I Lecture 4: Research Question Objectives How do we define a research question? What is a testable hypothesis? How do we test an hypothesis?
CHAPTER 5 CONSTRUCTING HYPOTHESeS. What is A Hypothesis? A proposition, condition, or principle which is assumed, perhaps without belief, in order to.
Statistical Techniques
P Values - part 2 Samples & Populations Robin Beaumont 2011 With much help from Professor Chris Wilds material University of Auckland.
Results: How to interpret and report statistical findings Today’s agenda: 1)A bit about statistical inference, as it is commonly described in scientific.
Introduction to statistics Definitions Why is statistics important?
Statistical Inference for the Mean Objectives: (Chapter 8&9, DeCoursey) -To understand the terms variance and standard error of a sample mean, Null Hypothesis,
Data Analysis. Qualitative vs. Quantitative Data collection methods can be roughly divided into two groups. It is essential to understand the difference.
Inferential Statistics Psych 231: Research Methods in Psychology.
Chapter 9 Introduction to the t Statistic
Section Testing a Proportion
Review You run a t-test and get a result of t = 0.5. What is your conclusion? Reject the null hypothesis because t is bigger than expected by chance Reject.
Understanding Results
Statistical significance using p-value
1 Chapter 8: Introduction to Hypothesis Testing. 2 Hypothesis Testing The general goal of a hypothesis test is to rule out chance (sampling error) as.
Statistical Test A test of significance is a formal procedure for comparing observed data with a claim (also called a hypothesis) whose truth we want to.
Presentation transcript:

The Importance of Numbers: What Large Skeletal Samples Can (and Cannot) Reveal About the Health Status of Earlier Human Population Phillip L. Walker Department of Anthropology University of California, Santa Barbara

The history of paleopathology: from small to large numbers Stage I: Case Studies –Dominated almost the end of the 20 th century –“Physician to the dead” approach –century took a descriptive, case study –Emphasis on determining the spatial temporal distribution of diseases. Stage II: Population Studies –Mainly during the last 50 years. –Emphasis on calculating the prevalence of common pathological conditions in cemetery collections – Bioarchaeological approach with an emphasis on cultural and ecological determinants of health status

Goals of Modern Paleopathology Describe the chronology and spatial distribution of health-related conditions in an earlier populations Determine the biocultural interactions that occur as a population responds to its environment, using disease as an index of the success or failure of adaptation Use the prevalence and pattern of disease to shed light on the adaptation of the population Investigate the processes involved in prehistoric the evolution of ancient diseases

What are the limitations of a population-based approach in paleopahtology? How large are the samples that we will need to detect population differences we might reasonably expect to see in the frequency of pathological conditions? How significant are sample biases introduced by age, sex, and preservation differences between samples? What problems are there with pooling samples from different sites to increase sample sizes?

Western Hemisphere and History of Health in Europe Project Sites 893 sites, total n= 142,952

Most archaeological skeletal collections are small!

Cemetery collections from archaeological sites: median =59, mode= 1

Number of skeletons required to detect a statistically significant difference in the proportion of people afflicted with a pathological condition

Cutting up the Pie Makes Things Worse! Testing bioarchaeological hypotheses typically requires subdividing site samples  Age  Sex  Social Status

Sex is a big part of the pie! % 39.8 of burials in the Western Hemisphere sample are younger than 15 years old and thus probably not subject to reliable sex determination.

The real world situation is worse.. Only 41% of the Western Hemisphere sample could be sexed to the level of “probable male” or “probable” female. This means that about 24 burials in a sample with the median size of 59 can be reliably sexed. Assuming a balanced sex ratio, this would mean that within-site sex comparisons would typically involve 12 males and 12 f es

Age Subadults: 59 x 0.38= 22 Adults: 59 x 0.62= 37

The effects of preservation biases can be significant!

How should frequencies of pathological lesions be measured?

The under-representation of pathological conditions in skeletal samples Many diseases such as tuberculosis only leave lesions on a small proportion of individuals Many lethal injuries leave no skeletal traces Poor preservation of ancient skeletal material means that often subtle signs of disease and traumatic injury will either be unobservable or uninterpretable

What can large samples tell us?

A Caveat: variation among contemporaneous populations within a region can be significant

Variations in the bathtub curve Wide differentials in the excess mortality occurring at the youngest and oldest ages Marked differences in the timing of the decline in juvenile mortality or the rise in adult mortality

Could we detect minor variations in the bathtub curve? The adolescent “accident hump” Apparent slowing down of the rate of increase of mortality among the oldest of the old

What are our chances of detecting the “Basic” human mortality pattern? The “bathtub curve” this is a species-wide theme in human mortality Basic features –Excess mortality at the youngest ages of the life span –Rapid decline to a lifetime low at around years of age –Accelerating, roughly exponential, rise in mortality at later ages

Conclusions Small sample sizes and preservation biases mean that paleodemographers will ever be able to reconstruct the fine details of any set of mortality rates. At best, we can hope to learn something about the overall level and age pattern of death in the distant past - and perhaps something about the gross differences in material conditions that led to variation in level and age pattern. Paleodemographers will probably never be able to reconstruct the "bumps and squiggles" in ancient mortality patters. Reconstructing the general shape and level of the bathtub curve will be challenging enough.

Statistical Power The probability of rejecting a false statistical null hypothesis. Performing power analysis and sample size estimation is an important aspect of experimental design, because without these calculations, sample size may be too high or too low. If sample size is too low, the experiment will lack the precision to provide reliable answers to the questions it is investigating. If sample size is too large, time and resources will be wasted, often for minimal gain.

Determining Sample Size What kind of statistical test is being performed. Some statistical tests are inherently more powerful than others. Sample size. In general, the larger the sample size, the larger the power. However, generally increasing sample size involves tangible costs, both in time, money, and effort. Consequently, it is important to make sample size "large enough," but not wastefully large. In paleopathological studies increasing sample size is typically impossible The size of experimental effects. If the null hypothesis is wrong by a substantial amount, power will be higher than if it is wrong by a small amount. The level of error in experimental measurements. Measurement error acts like "noise" that can bury the "signal" of real experimental effects. Consequently, anything that enhances the accuracy and consistency of measurement can increase

Regional Variation

Bioarchaeologically Interesting Differences Time: how does health status vary through time Space: What regional or intraregional differences are there Age: What is the relationship between age at death and the presence of pathological lesions indicative of specific diseases Sex: how does a person’s sex influence their health status Social Status: How do social stratification and gender roles influence health status.

alpha specifies the significance level of the test; the default is alpha (.05). power(#) is power of the test. Default is power(.90).

Age determination is a blunt sword…

A priori sample size estimation Based on the acceptable statistical significance of your outcome measure. Specify the smallest effect you want to detect of the Type I and Type II error rates

Error Types Type 1 error: The chance of accepting the research hypothesis when the null hypothesis is actually true ("false positive"). Type 2 error: The chance of accepting the null hypothesis when the research hypothesis is actually true ("false negative").

Age Related Changes in Bones Mass

Osteoperiostitis

Long Bones Affected

Temporal Variation