KIN 4310 1st Edition Lecture 5 Outline of Last Lecture I Key Concept II Definition III Frequency Distributions IV Frequency Distributions continued V Making a Frequency Table VI Frequency Distribution Ages of Best Actresses VII Reasons for Constructing Frequency Distributions VIII Key Concept IX Definitions X Skewness XI Histogram XII Interpreting Histograms XIII Frequency Polygon XIV Dot Plot XV Stemplot Stem and Leaf XVI Pareto Chart XVII Pie Chart XVIII Scatter Plot These notes represent a detailed interpretation of the professor s lecture GradeBuddy is best used as a supplement to your own notes not as a substitute XIX Box Plot XX Time Series Graph XXI Other Graphs Outline of Current Lecture I Misuse of Statistics II Definitions III Misleading Graphs IV Pictographs V Misleading Questions VI Experimental Research VII Independent and Dependent Variables VIII Correlation IX Correlation vs Experiment Research X Definition XI Definition XII Exploring the Data XIII Properties of the Linear Correlation Coefficient r XIV Scatter Plots of Paired Data XV Homoscedasticity Homogeneity of Variance XVI Requirements for r XVII Correlation Coefficient XVIII Coefficient of Determination r squared XIX Common Errors involving Correlation XX Correlation Between Gender and Strength XXI Examples Current Lecture for future assignments that don t specify significant digits the more sig figs the better I Misuses of Statistics a Refusals b Correlation Causality i Correlation is not causation c Self Interest Study d Precise Numbers e Partial Pictures f Deliberate Distortions g Bad Samples h Small Samples i Misleading Graphs j Pictographs k Distorted Percentages l Loaded Questions m Order of Questions II Definitions a Voluntary response sample i Self selection ii Respondents decide whether to be included iii Valid conclusions can be made only about the specific group of people who agree to participate iv True of nearly all human studies v Self selection can have profound effect on conclusion because they re voluntary III Misleading Graphs a To correctly interpret a graph we should analyze the numerical information given the graph instead of being mislead by its general shape b The units on the graph should start at zero c If not then the bars do not represent the quantity anymore d They re inflating the difference IV Pictographs a Double the length width and height of a cube and the volume increases by a factor of eight b Often misleading because you inflate the difference V Misleading Questions a 97 yes i Should the President have the line item veto to eliminate waste ii This one is loaded b 57 yes i Should the President have the line item veto or not VI Experimental Research a Experimental research aims to find causal mechanisms and determine predictability b There is always at least one independent and one dependent variable c Relationships may be i Bivariate ii Multivariate d This is a way to find a causal link VII Independent and Dependent Variables a Independent variable is the variable on which the dependent variable depends and in an experiment it is the variable that is manipulated by the investigator b Dependent variable is the outcome that is contingent upon the independent variable c Examples i Independent variable dependent variable ii Training performance iii Hair length confidence iv Obesity hypertension VIII Correlation TQ a A correlation is a relationship between two variables b A correlation equation can be generated for predicting the value of one variable given the value of the other variable c This is appropriate for sample data that come in pairs d If you know two things are correlated you can use that to make a correlation with something else IX Correlation vs Experimental Research a Correlational research i Investigates a linear relationship between two variable ii Variables must be continuous iii Data can be presented graphically scatter plot iv Neither variable is truly the independent or dependent variable v Called a bivariate relationship vi There is no causation X Definition a A correlation exists between two variables when one of them is related to the other in some way b A positive correlation indicated that when one variable increases the other variable increases c A negative correlation indicates that when one variable increases the other variable decreases XI Definition a Linear correlation coefficient r i A numerical measure of the strength of the relationship between two variable representing quantitative data ii Gives us 2 features of correlation 1 Direction is it positive or negative 2 Strength iii r can be either positive or negative iv Minimum is 1 v Maximum is 1 XII Exploring the Data a Relationships between two variables can often be seen by constructing a scatterplot XIII Properties of the Linear Correlation Coefficient r a The value of r does not change if all values of either variable are converted to a different scale i r will be the same if you change from inches to centimeters b The value of r is not affected by the choice of x and y Interchange all x and yvalues and the values of r will not change c r measure strength and direction of a linear relationship XIV Scatter Plots of Paired Data a Must do scatter plot first because if you get an organized nonlinear pattern you should not calculate r because it will not have a meaning XV Homoscedasticity Homogeneity of Variance a Homoscedasticity means variance b The chart violates it c The chart is heterostaticity and if you see this don t solve for r XVI Requirements for r a The sample of paired x y data is a random sample of independent quantitative data b Visual examination of the scatterplot must confirm that the points approximate a straight line pattern i Unequal variability ii If you see a circle a bell shape or heterostaticity then don t calculate r c The outliers must be removed if they are known to be errors The effects of any other outliers should be considered by calculating r with and without the outliers included XVII Correlation coefficient XVIII Coefficient of Determination r squared a Explained variation b The value of r squared is the proportion of the variation in y that is explained by the linear relationship between x and y c r squared is between 0 and 1 d Read the part about this in chapter 5 XIX Common Errors Involving Correlation a Causation It is wrong to conclude that correlation implies causality b Averages Averages suppress individual variation and may inflate the correlation