STANDARD DEVIATION.

Slides:

Advertisements

Similar presentations

Statistical Analysis WHY ?.

Advertisements

Topics

Introduction to Regression Analysis

REVIEW OF BASICS PART II Probability Distributions Confidence Intervals Statistical Significance.

Sample size computations Petter Mostad

Introduction to Inference Estimating with Confidence Chapter 6.1.

Mean for sample of n=10 n = 10: t = 1.361df = 9Critical value = Conclusion: accept the null hypothesis; no difference between this sample.

PSY 307 – Statistics for the Behavioral Sciences

Measures of Variability or Dispersion

Understanding Research Results. Effect Size Effect Size – strength of relationship & magnitude of effect Effect size r = √ (t2/(t2+df))

PSY 1950 Confidence and Power December, Requisite Quote “The picturing of data allows us to be sensitive not only to the multiple hypotheses that.

Hypothesis Testing. G/RG/R Null Hypothesis: The means of the populations from which the samples were drawn are the same. The samples come from the same.

Chapter 9 Hypothesis Testing.

Analysis of Variance Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing.

Chapter 4 SUMMARIZING SCORES WITH MEASURES OF VARIABILITY.

One Sample  M ean μ, Variance σ 2, Proportion π Two Samples  M eans, Variances, Proportions μ1 vs. μ2 σ12 vs. σ22 π1 vs. π Multiple.

Analysis & Interpretation: Individual Variables Independently Chapter 12.

Basic statistics 11/09/13.

Statistical Analysis Mean, Standard deviation, Standard deviation of the sample means, t-test.

Smith/Davis (c) 2005 Prentice Hall Chapter Six Summarizing and Comparing Data: Measures of Variation, Distribution of Means and the Standard Error of the.

+ Chapter 12: Inference for Regression Inference for Linear Regression.

Inferences about the slope of the regression line Section 13.2.

Large sample CI for μ Small sample CI for μ Large sample CI for p

Chapter 10: Basics of Confidence Intervals

Unit 8 Section 8-1 & : Steps in Hypothesis Testing- Traditional Method  Hypothesis Testing – a decision making process for evaluating a claim.

Sour Patch Distribution Chiquta Hicks 05/24/10 Period 8.

Understanding Your Data Set Statistics are used to describe data sets Gives us a metric in place of a graph What are some types of statistics used to describe.

Introduction to Inference: Confidence Intervals and Hypothesis Testing Presentation 8 First Part.

Introduction to Inference: Confidence Intervals and Hypothesis Testing Presentation 4 First Part.

1 CHAPTER 4 CHAPTER 4 WHAT IS A CONFIDENCE INTERVAL? WHAT IS A CONFIDENCE INTERVAL? confidence interval A confidence interval estimates a population parameter.

Copyright © 2011 Pearson Education, Inc. Putting Statistics to Work.

Lesson 14 - R Chapter 14 Review. Objectives Summarize the chapter Define the vocabulary used Complete all objectives Successfully answer any of the review.

1 Hypothesis Tests on the Mean H 0 :  =  0 H 1 :    0.

Measures of Central Tendency Mean, Median, Mode, and Range.

HOW LARGE OF A SAMPLE SHOULD YOU USE? The larger the sample size, the more likely: o It will be representative of the whole population o The conclusions.

Introduction to inference Estimating with confidence IPS chapter 6.1 © 2006 W.H. Freeman and Company.

Type I and Type II Errors. For type I and type II errors, we must know the null and alternate hypotheses. H 0 : µ = 40 The mean of the population is 40.

1 Probability and Statistics Confidence Intervals.

Chapter ?? 7 Statistical Issues in Research Planning and Evaluation C H A P T E R.

R&R Homework Statgraphics “Range Method”. DATA OperatorPartTrialMeasure B B B B B B326.5 B B B C

Analysis of Variance ANOVA - method used to test the equality of three or more population means Null Hypothesis - H 0 : μ 1 = μ 2 = μ 3 = μ k Alternative.

Hypothesis Testing and Statistical Significance

Critical Appraisal Course for Emergency Medicine Trainees Module 2 Statistics.

Chapter Six Summarizing and Comparing Data: Measures of Variation, Distribution of Means and the Standard Error of the Mean, and z Scores PowerPoint Presentation.

Lecture 9-I Data Analysis: Bivariate Analysis and Hypothesis Testing

Active Learning Lecture Slides

AP Biology Intro to Statistics

Effect Size 10/15.

Introduction to inference Estimating with confidence

Statistics for the Social Sciences

STAT 312 Chapter 7 - Statistical Intervals Based on a Single Sample

The Relationship between Confidence Intervals & Hypothesis Tests

Quantitative Methods PSY302 Quiz Chapter 9 Statistical Significance

When Data Comes in Pairs

AP Biology Intro to Statistics

Hypothesis Tests for a Population Mean in Practice

Bootstrap Confidence Intervals using Percentiles

LESSON 24: INFERENCES USING REGRESSION

Section 11.2 Day 2.

Using Statistics in Biology

Using Statistics in Biology

CHAPTER 6 Statistical Inference & Hypothesis Testing

Chapter 10: Basics of Confidence Intervals

STA 291 Spring 2008 Lecture 18 Dustin Lueker.

Standard Deviation & Standard Error

Objectives 6.1 Estimating with confidence Statistical confidence

Objectives 6.1 Estimating with confidence Statistical confidence

Presentation transcript:

STANDARD DEVIATION

NARROW range of measured data WIDE range of measured data STANDARD DEVIATION (symbol is σ sigma) measures VARIABILITY or SPREAD of MEASUREMENTS in a data set from repetition of trials within one experiment What is the standard deviation of each data set below? High or Low? Mean LOW standard deviation NARROW range of measured data Mean HIGH standard deviation WIDE range of measured data

3. SMALLEST standard deviation 2. INTERMEDIATE standard deviation 1. LARGEST standard deviation Put these in order from the highest standard deviation to lowest standard deviation. LARGEST standard deviation (most variability of measurements in a data set) 1. red INTERMEDIATE standard deviation (moderate variability of measurements in a data set) 2. green SMALLEST standard deviation (least variability of measurements in a data set) 3. blue

All three have the SAME standard deviation because they all have the same data variability (spread). 10 15 20 Each data set has a different mean. Put these in order from the lowest standard deviation to highest standard deviation. SAME standard deviation (least variability of measurements in a data set) blue green red

1. lowest standard deviation 4. highest standard deviation Put these in order from the lowest standard deviation to highest standard deviation. LOWEST standard deviation (least variability of measurements in a data set) 1. blue Low standard deviation (less variability of measurements in a data set) 2. green High standard deviation (more variability of measurements in a data set) 3. red HIGHEST standard deviation (most variability of measurements in a data set) 4. yellow

STANDARD ERROR of the MEANS (symbol SEM) measures PRECISION OF THE MEAN of a data set of means from multiple replications of an experiment (standard deviation of the means of replicated experiments) how much sampling variation there is if resample & re-estimate ±2 SEM means 95% of replications will contain the true mean smaller standard deviation (σ) decreases standard error larger sample size (n) decreases standard error

out here is like way weird!! AND YOU MUST REJECT THE NULL HYPOTHESIS CONFIDENCE INTERVALS a 95% confidence interval reflects a significance level of 0.05 (p-value < α-value of 0.05) confidence interval of 95% means that the means of multiple replications would be within this confidence interval 95% of the time Data found out here is like way weird!! AND YOU MUST REJECT THE NULL HYPOTHESIS