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UH KIN 4310 - Misuse of Statistics and Correlation

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KIN 4310 1st Edition Lecture 5Outline of Last Lecture I. Key ConceptII. DefinitionIII. Frequency DistributionsIV. Frequency Distributions continuedV. Making a Frequency TableVI. Frequency Distribution Ages of Best ActressesVII. Reasons for Constructing Frequency DistributionsVIII. Key ConceptIX. DefinitionsX. SkewnessXI. HistogramXII. Interpreting HistogramsXIII. Frequency PolygonXIV. Dot PlotXV. Stemplot (Stem and Leaf)XVI. Pareto ChartXVII. Pie ChartXVIII. Scatter PlotThese 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 PlotXX. Time Series GraphXXI. Other GraphsOutline of Current Lecture I. Misuse of StatisticsII. DefinitionsIII. Misleading GraphsIV. PictographsV. Misleading QuestionsVI. Experimental ResearchVII. Independent and Dependent VariablesVIII. CorrelationIX. Correlation vs. Experiment ResearchX. DefinitionXI. DefinitionXII. Exploring the DataXIII. Properties of the Linear Correlation Coefficient rXIV. Scatter Plots of Paired DataXV. Homoscedasticity (Homogeneity of Variance)XVI. Requirements for rXVII. Correlation CoefficientXVIII. Coefficient of Determination, r squaredXIX. Common Errors involving CorrelationXX. Correlation Between Gender and StrengthXXI. ExamplesCurrent Lecture*for future assignments that don’t specify significant digits, the more sig figs, the betterI. Misuses of Statisticsa. Refusalsb. Correlation & Causalityi. Correlation is not causationc. Self Interest Studyd. Precise Numberse. Partial Picturesf. Deliberate Distortionsg. Bad Samplesh. Small Samplesi. Misleading Graphsj. Pictographsk. Distorted Percentagesl. Loaded Questionsm. Order of QuestionsII. Definitionsa. Voluntary response samplei. Self-selectionii. Respondents decide whether to be includediii. Valid conclusions can be made only about the specific group of people who agree to participate iv. True of nearly all human studiesv. Self selection can have profound effect on conclusion because they’re voluntaryIII. Misleading Graphsa. To correctly interpret a graph, we should analyze the numerical information giventhe graph instead of being mislead by its general shapeb. The units on the graph should start at zeroc. If not, then the bars do not represent the quantity anymored. They’re inflating the differenceIV. Pictographsa. Double the length, width, and height of a cube, and the volume increases by a factor of eightb. Often misleading because you inflate the differenceV. Misleading Questionsa. 97% yes:i. “Should the President have the line item veto to eliminate waste?”ii. This one is loadedb. 57% yes:i. “Should the President have the line item veto, or not?”VI. Experimental Researcha. Experimental research aims to find causal mechanisms and determine predictability b. There is always at least one independent and one dependent variablec. Relationships may be i. Bivariate ii. Multivariated. This is a way to find a causal linkVII. Independent and Dependent Variablesa. Independent variable is the variable on which the dependent variable depends, and in an experiment, it is the variable that is manipulated by the investigatorb. Dependent variable is the outcome that is contingent upon the independent variablec. Examplesi. Independent variable  dependent variableii. Training  performanceiii. Hair length  confidenceiv. Obesity  hypertensionVIII. Correlation (TQ)a. A correlation is a relationship between two variablesb. A correlation equation can be generated for predicting the value of one variable given the value of the other variablec. This is appropriate for sample data that come in pairsd. If you know two things are correlated, you can use that to make a correlation with something elseIX. Correlation vs. Experimental Researcha. Correlational researchi. Investigates a linear relationship between two variableii. Variables must be continuous iii. Data can be presented graphically (scatter plot)iv. Neither variable is truly the independent or dependent variablev. Called a bivariate relationshipvi. There is no causationX. Definitiona. A correlation exists between two variables when one of them is related to the other in some wayb. A positive correlation indicated that when one variable increases, the other variable increasesc. A negative correlation indicates that when one variable increases, the other variable decreasesXI. Definitiona. Linear correlation coefficient, ri. A numerical measure of the strength of the relationship between two variable representing quantitative dataii. Gives us 2 features of correlation1. Direction (is it positive or negative)2. Strengthiii. r can be either positive or negative iv. Minimum is -1v. Maximum is +1XII. Exploring the Dataa. Relationships between two variables can often be seen by constructing a scatterplotXIII. Properties of the Linear Correlation Coefficient ra. The value of r does not change if all values of either variable are converted to a different scalei. r will be the same if you change from inches to centimetersb. The value of r is not affected by the choice of x and y. Interchange all x- and y-values and the values of r will not changec. r measure strength and direction of a linear relationshipXIV. Scatter Plots of Paired Dataa. Must do scatter plot first because if you get an organized nonlinear pattern, you should not calculate r because it will not have a meaningXV. Homoscedasticity (Homogeneity of Variance)a. Homoscedasticity means varianceb. The chart violates it c. The chart is heterostaticity and if you see this, don’t solve for rXVI. Requirements for ra. The sample of paired (x,y) data is a random sample of independent quantitative datab. Visual examination of the scatterplot must confirm that the points approximate astraight-line patterni. Unequal variabilityii. If you see a circle, a bell-shape, or heterostaticity then don’t calculate rc. 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 outliersincludedXVII. Correlation coefficientXVIII. Coefficient of Determination, r squareda. Explained variationb. The value of r squared is the proportion of the variation in y that is explained by the linear relationship between x and yc. r squared is between 0 and 1d. Read the part about this in chapter 5XIX. Common Errors Involving Correlationa. Causation: It is wrong to conclude


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