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# Statistical Analysis of Communication

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This 23 page Bundle was uploaded by Michelle Jarrard on Wednesday April 9, 2014. The Bundle belongs to a course at University of California Santa Barbara taught by a professor in Fall. Since its upload, it has received 172 views.

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Date Created: 04/09/14

COMM 87 EXAM 1 STUDY GUIDE DEFINITIONS AND DESCRIPTIONS 1 10 11 12 13 Qualitative research non numerical interpretive research You are trying to understand a phenomenon by making careful observations ex Field studies Quantitative Research numerical research that requires measurement of variables Descriptive Statistics statistics that describe characteristics of data Inferential Statistics Statistics that use data from a sample to infer characteristics of a population Asking a portion sample of the population and using inferential statistics to make inferences about entire population Also called sampling statistics Variable the varying observable characteristics of a person object or event Measurement assignment of numbers to re ect characteristics of a variable Nominal Level of Measurement numbers are used to classify or categorize objects people or characteristics There is no ranking numbers are just assigned to distinguish categories from one another Ex Male 1 and Female 2 CATEGORICAL Ordinal Level of Measurement the data are ordered or ranked but the intervals between these observations are undefined and likely unequal Do know whether one category is bigger smaller than faster slower than other category Ex 1 2nd 3rd CATEGORICAL Interval Level of Measurement the intervals between ranks are meaningful and equal and the distance between values is known Has an arbitrary zero point where a O on the scale does not mean an absence of something Ex Degrees in Celsius or Fahrenheit Likert scales Ratio Level of Measurement the measurements are ranked intervals between the ranks are known and equal and there is an absolute zero point where a O on the scale means an absence of something Ex Temperature in Kelvin age time distance weight height Content Analysis analyzing the content of communication people39s conversations what people talk about amount of violence in children39s cartoons Used to describe population Survey constructed by translating research problems into items on questionnaires Objective may be either explanatory or descriptive Ex How often do children watch violent cartoons Do you become aggressive after watching Samples selected for survey research are random Population the total class of whatever is being observed Large group of people in which a researcher is interested 14 Sample portion of the population that is selected to represent that population 15 Random Sample chosen in such a way that data collected from those members of the sample are representative of all members of the population every member of population has an equal chance of being included in sample 16 Experiment The researcher manipulates the variable to study the effect of the manipulation Experiments involve a researcher taking an action and then examining the effect of that action on another variable Primarily aimed at discovering cause and effect relationships 17 Independent Variable the cause The variable that is manipulated by the researcher 18 Dependent Variable the phenomenon that is affected by the manipulation The effect 19 Random assignment the study participants who may or may not be a random sample from the population are assigned to groups or conditions in such a way that each participant has an equal chance of being in any group every member of the sample has an equal chance of either being in the control group or the experimental group 20 Validity the degree to which a measurement actually measures what it claims to measure 21 Reliability the degree to which a measurement is consistent You get the same result every time consistency over time 22 Frequency distribution distribution of numbers with a corresponding frequency of occurrences for each data point 23 Frequency polygon line graph 24 Histogram bar graph bars don39t touch 25 Pie chart percentages of responses falling into each category are graphed as wedges of a pie 26 Normal distribution frequency distribution that has a bell shaped normal curve frequency polygon 27 Positively Skewed Distribution distribution is skewed to the right the tail on the right side of the distribution is longest 28 Negatively Skewed Distribution distribution is skewed to the left the tail on the left side of the distribution is longest 29 Bimodal Distribution distribution with two modes 30 Mean average of all of the individual scores the sum of each of the individual scores divided by the total number of scores 31 Median the measure of central tendency which is the middlemost dcore in a distribution of data 32 Mode the most frequently occurring score in a distribution of data 33 Range the largest number in the distribution minus the smallest number in the distribution 34 Standard deviation measures how far away on average scores are from the mean of a set of data measures the standard or average variability in scores 35 Sum of Squares both the standard deviation and the variance are based on the sum of squares the sum of the squared deviations from the mean but standard deviation and variance need an average of the sum of squares 36 Variance the square of the standard deviation 37 Homogeneous Distribution leptokurtic distribution with a small standard deviation skinny distribution 38 Heterogeneous platykurtic distribution with a large standard deviation wide distribution 39 Sample Distribution distribution of the data from a sample 40 Population Distribution distribution from the data of an entire population 41 Sampling Distribution of Sample Means the data points for this distribution are sample means not individual raw scores represents sample means computed from an infinite number of random samples drawn from the same population 42 Sampling Distribution of Mean Differences Distribution of Differences represents differences between pairs of sample means that are computed from an infinite number of random samples drawn from the same population 43 Standard error of the mean another name for the standard deviation of the sampling distribution of sample means 44 Standard error of the difference another name for the standard deviation of the sampling distribution of sample mean differences distribution of differences 45 Zscores standardized raw scores of distributions 46 689599 rule 68 of scores fall within 1 standard deviation of the mean 95 of scores fall within 2 standard deviations of the mean and 99 of scores fall within 3 standard deviations of the mean on a normal distribution bell curve 47 Statistics measured characteristics of a SAMPLE 48 Parameter measured characteristics of a POPULATION 49 Sampling Error 50 Research or Alternative Hypothesis statement that the difference between means is not due to random chance sampling error difference in means is not attributable to chance sample means represent different populations 51 Null Hypothesis statement that difference is between means is due to chance sampling error there is no true difference between sample means any observable difference is due to chance 52 One sample ztests to compare one sample mean to the population mean 53 Two sample ztests to compare two means to each other one sample mean to a second sample mean no population mean 54 Categorical variables variables measured at the nominal and ordinal levels 55 Continuous Variables variables measured at the interval and ratio levels STATISTICS AND RESEARCH 1 What is the difference between qualitative and quantitative research a Qualitative research involves collecting information that cannot be subjected to numerical measurements whereas quantitative research focuses on gathering data that represents quantities and involves measuring data on a numerical scale 2 What is the difference between descriptive and inferential statistics a Descriptive statistics uses one or two numbers to organize and summarize a set of data in a form that is easy to comprehend whereas inferential statistics goes beyond simple description to make inferences about a population based on data gathered from a sample 3 What does the basic research plan consist of a The purpose research question or hypothesis the method content analysis survey or experiment results and discussion 4 Why are random sampling and random assignment so important a Random sampling and random assignment allow researchers to assume that the sample can be generalized to the larger population 5 What is a semantic differential scale a A scale with two opposing adjectives on both sides and people rank the degree to which they feel like one of the adjectives 6 What is a Likert Scale a An agree disagree scale and people rank the degree to which they agree or disagree with something MEASUREMENT 1 What is the relationship between validity and reliability a Validity is the degree to which a measurement actually measures what it claims to measure Reliability is the degree to which a measurement is consistent same result every time You can have reliability without validity but you cannot have validity without reliability If you don39t have a consistent measurement you are nowhere a measure that is not consistent is not a measurement of anything a measure scale needs to be reliable 2 What are ways to improve reliability and validity 3 To improve validity you can use multiple measures so that you have many ways of measuring the same variable To improve reliability you can use multiple judges whom you train to use the measurement in the same way so that they can use the same scale consistently DESCRIBING DISTRIBUTIONS 1 What are the important characteristics of a normal curve 3 A normal curve is bell shaped because more scores cluster in the middle It is perfectly symmetrical each side is a mirror image The mean median and mode all fall at the same central point 689599 rule 2 Compute measures of central tendency from a distribution of data a Mean median and mode 3 Which measure of central tendency is best for different kinds of distributions and data a Normal distribution mean can use all but mean gives us most info b Skewed distribution median because it is most in uenced by outliers c Nominal data mode d Ordinal data median and mode e Interval data mean median and mode f Ratio data mean median and mode 4 What is the relationship between standard deviation and variance 3 The standard deviation is the square root of the variance The variance is the standard deviation squared COMM 87 EXAM 2 STUDY GUIDE Definitions and Descriptions 1 10 11 Ttest tratio compares two means to see how they differ used when you have ONE independent variable with TWO levels and ONE dependent variable at the interval level of measurement Degrees of Freedom how many scores are free to vary in a group of scores in order to obtain the observed mean Ttable table given that has all the critical values for a t score at the 05 and 01 levels Tdistribution as the sample size increases and the t distributions come closer to the normal 2 distribution the critical values needed to reject the null hypothesis gets smaller a large sample t test is more powerful than a small sample t test Single factor ANOVA one way tests whether more than two sample means differ from one another used when you have ONE independent variable with MORE THAN TWO levels and ONE dependent variable measured at least at interval level of measurement Ftest Fratio ratio of different kinds of variance between groups variance within groups variance Between groups variance tells us how different the group means are from each other how much each group mean varies from the grand mean Within groups variance tells us how much the individual scores vary with each group error variance Factor independent variable Post Hoc Tests compare individual pairs of means while keeping Type 1 Error at 05 level will not compute by hand sig needs to be less than 05 if greater than 05 cannot reject the null hypothesis Fdistribution theoretical distributions created from the ratio of two variances for different degrees of freedom 12 Ftable table given that has all the critical values for a t score at the 05 and 01 levels 13 Sum of Squares Between difference between each group mean and grand mean 14 Sum of Squares within difference between each individual score and its own group mean 15 Mean Squares Between sum of squares between degrees of freedom between 16 Mean Squares Within sum of squares within degrees of freedom within 17 Multiple Factor ANOVA tests whether differences exist between more than two means in factorial designs use when you have MORE THAN ONE independent variable factor in which each factor has AT LEAST TWO levels and only ONE dependent variable measured at the ratio or interval level 18 Factorial Design type of experimental design in which subjects are randomly assigned to groups defined by two or more independent variables or factors 19 Main Effect effect or difference across levels for a single independent variable 20 Interaction Effect effect or difference across levels of two or more independent variables 2 1 Rules for Identifying Main and Interaction Effects a Main effects calculate marginal means b Interaction effects what combination of variables produces the biggest effect Look at cell means 22 OneSample Chi Square subjects from a single sample are distributed across categories determines whether there is a difference in the number of observations in each category with the theoretical values 23 MultipleSample Chi Square examines whether the distribution of observations across categories differs between two or more samples two dimensions or variables categories and samples are of interest 24 Observed frequencies frequency observed for each category 25 Theoretical frequency frequency one would theoretically expect to observe if there was no difference in preference for the two class styles 26 LogLinear Analysis examines whether the distribution of observations across categories differs between two or more samples can also test interaction effects used when you have THREE OR MORE nominal or ordinal variables and want to look for interactions Ttests 1 What is the relationship between sample size and the t distribution a The larger the sample size the more t distribution approaches a normal distribution the smaller the sample size the atter the t distribution 2 Under what conditions do you use a t test in research a One single independent variable i Two categorical levels nominal or ordinal b One single dependent variable measured at either interval or ratio levels of measurement 3 What are the null and research hypotheses for this type of analysis a Null Hypothesis Two tailed 11 112 One tailed 11 25 12 b Research Hypothesis Two tailed 11 at 12 One tailed 11 gtlt 12 4 Distinguish between the use of one and two tailed hypothesis tests 5 What is the relationship between the size of the difference between the sample means and the size of t a A larger difference between sample means a larger t b A smaller difference between sample means a smaller t 6 What is the relationship between the standard error of the difference and the size of t a A larger sample size a more normal distribution a smaller standard error of the difference a larger t b A smaller sample size a less normal distribution a larger standard error of the difference a smaller t 7 How do you calculate degrees of freedom for the t test df N 1 N2 2 SingleFactor ANOVA 1 What is the difference between single factor ANOVA and the t test a The t test has one independent variable with two levels and the single factor ANOVA has one independent variable with more than two levels 2 Under what conditions do you use multiple factor ANOVA in research a One independent variable with more than two levels b One dependent variable measured at least at the interval level of measurement 3 What are factors a Independent variables 4 What are the null and research hypotheses for this type of analysis a Null hypothesis 11 12 13 b Research hypothesis I11 3 I12 3 I13 5 What does it mean F is a ratio of variances 6 What is between groups variance a Tells us how different the group means are from each other how much each mean varies from grand mean 7 What is within groups variance a Tells us how much the individual scores vary within each group error variance 8 9 Be able to complete an ANOVA table when given the sum of squares SS sample size N number of groups or levels of the factor K and critical F State the conclusion regarding the null hypothesis statistically and interpret it in words a LOOK AT EXAMPLES What pieces of information do you need to find critical value in an F table a Degrees of freedom between and degrees of freedom within 10 Be able to interpret computer output of a single factor ANOVA a LOOK AT EXAMPLES 11 What is the purpose of a post hoc test a To compare individual pairs of means while keeping Type 1 Error at 05 if sig value is more than 05 cannot reject the null hypothesis Multiplefactor ANOVA 1 What is the advantage of a multiple factor ANOVA over a single factor ANOVA a You can test several hypotheses at the same time Under what conditions do you use multiple factor ANOVA in research a MORE THAN ONE independent variable with AT LEAST TWO levels each b ONLY ONE dependent variable measured at the interval or ratio level Be able to identify the numbers of factors the number of levels of each factor and the number of main and interaction effects in a factorial design a LOOK AT EXAMPLES What is a main effect a Effect of each independent variable by itself on the dependent variable have as many main effects as you have independent variables What is an interaction effect How do you iden tijjl one a Effect of each combination of independent variables on dependent variable 6 Be able to identify main and interaction effects from both tables and graphs a In graphs calculate marginal means to determine main effect b In graphs look at cell means to determine interaction effect 7 Be able to complete and ANOVA table when given the sum of squares SS degrees of freedom df and critical F State the conclusion regarding the null hypothesis for each type of effect each main and interaction effect statistically and interpret that conclusion in words a LOOK AT EXAMPLES 8 Be able to interpret computer output of multiple factor ANOVA a LOOK AT EXAMPLES 9 Identify when a MANOVA should be used in research a When you have more than one dependent variable i Example effect of diet and exercise on weight loss and blood pressure 1 Dependent variables blood pressure weight loss 2 Independent variables diet exercise 10 If discussed in lecture identify repeated measures designs and know their advantages and disadvantages a Used when same subjects are in more than one condition group Nonparametric Tests 1 What is the difference between parametric and nonparametric tests When do you use each type a Parametric tests deal with estimating characteristics of populations parameters measured at interval or ratio levels b Nonparametric tests statistical techniques involving nominal or ordinal level data which do not deal with estimates of population parameters 2 What type of data do chi square analyses use a Determine if there is a significant difference in the number or frequency of observations across categories of a nominal level variable frequencies or counts are used to examine group differences rather than means 3 What are the differences between a one sample chi square and a multiple sample chi square test When would you use each type in research a One sample chi square subjects from a single sample are distributed across categories determines whether there is a difference in the number of observations in each category compared with theoretical values i One categorical nominal or ordinal variable b Multiple sample chi square examines whether the distribution of observations across categories differs between two or more samples i Two categorical nominal or ordinal variables 4 Be able to conduct a chi square test and interpret the results when given the observed frequencies and the critical chi square value a LOOK AT EXAMPLES 5 Be able to interpret chi square output from SPSS a LOOK AT EXAMPLES 6 When is it necessary to use log linear analysis a When we have 3 or more nominal or ordinal variables and we want to look at interactions 7 What is the relationship between nonparametric tests and power a Nonparametric tests are less powerful than parametric tests because categorical variables give less information than continuous variables DETERMINING WHAT STATISTICAL TEST TO USE EXAM 2 1 List variables 2 Check levels of variables are they nominal ordinal interval or ratio 3 If variables are categorical statistical test will be nonparametric a If one categorical variable 9 SINGLE SAMPLE CHISQUARE b If two categorical variables 9 MULTIPLE SAMPLE CHISQUARE c If three categorical variables 9 LOGLINEAR ANALYSIS 4 If variables are continuous statistical test will be parametric a Look at DV s they will be continuous i If2 DV s 9 MANOVA ii If 1 DV 9look at IV s 1 2 IV s 9 MULTIPLE FACTOR ANOVA 2 1 IV 9 look at levels of IV a 2 Levels 9TWO SAMPLE TTEST b 3 Levels 9 SINGLE FACTOR ANOVA TWO SAMPLE TTEST One single independent variable 0 Two categorical levels nominal or ordinal One single dependent variable interval or ratio SINGLE FACTOR ANOVA One single independent variable 0 More than two levels 3 One independent variable interval or ratio MULTIPLE FACTOR ANOVA More than one independent variables 2 o At least two levels each One dependent variable interval or ratio MANOVA More than one dependent variable 2 SINGLE SAMPLE CHISQUARE One categorical variable with X number of levels MULTIPLE SAMPLE CHI SQUARE Two categorical variables with X number of levels LOGLINEAR ANALYSIS Three categorical variables with X number of levels COMM 87 EXAM 3 STUDY GUIDE DEFINITIONS AND DESCRIPTIONS Bivariate or simple Correlation relationship between two variables in terms of how these variables are related to or associated with one another how they covary 0 Purpose to test the extent to which variables are related to one another used to assess the relationship between two variables 0 Same sample must be measured on both variables 0 Both variables must be measured with at least interval data Pearson Product Moment Correlation Coefficient r statistic that represents the simple correlation between two variables measured at the interval or ratio level aka Pearson r Coefficient of determination r2 shared variance tells us the proportion of variance in one variable that can be accounted for or explained by variance in another variable Venn Diagram each variable is represented by a circle with the amount of variance the variables share with one another denoted by the degree to which the circles overlap Scatterplot Multiple Correlation R used to assess relationship between one variable with two or more variables at least 3 variables pg 2 11 Coefficient of Multiple Determination R2 represents the amount of variance in one variable that is explained by the variability in two or more other variables pg 2 11 Dummy coding used when you have one nominal variable and one intervalration variable codes categories of nominal variable eg Female 1 Male 2 then does a Pearson correlation Partial Correlation the unique relationship between two variables removing or partialling out the effects of any third variables from both the criterion and predictor variables Pg 2 12 0 I xYz correlation of X and Y controlling for Z Coefficient of Partial Determination I392XYZ shared variance of X and Y controlling for Z Pg 2 12 Spearman s Rho nonparametric correlation that compares ranks on variables rather than scores used when you have ordinal data Bivariate Linear Regression involves specifying a straight line or linear relationship between two variables such that one variable can be used to predict the second variable predicting one variable Y from a second variable X based on a regression equation Pg 195 Regression line line of best fit a line drawn through all the data points that best fits the data when points clustered near line strong correlation when points more spread out weak correlation Pg 195 Least squares when regression line is drawn in such a way that across all data points the sum of the average squared distance between each point and the line sum of squares is as small as possibl Pg 195 Regression Equation Y bX a pg 196 Predictor Variable known variable independent variable used to predict criterion variable better than chance Pg 196 Criterion Variable dependent variable Pg 196 Regression Coefficient b slope of the line refers to the degree to which the line is slanted upward positive or downward negative indicates how many units Y increases for every one unit increase in X pg 196 Constant a indicates where the line crosses or intercepts the y axis also called intercept Pg 196 Standard Error of the Estimate SEE used to obtain a measure of the magnitude of error involved in predicting Y from X in a particular regression equation standard or average measure of the variability of the actual observed values from values predicted by the regression line Pg 198 Multiple Regression predicts one criterion variable from more than one predictor variable used to see which combination of predictor variables make the best prediction of the criterion Pg 213 Multiple Regression Equation model Y b1X1 b2X2 a Partial Slope Partial Regression Coefficient b1 b2 etc specifies the relationship between a predictor variable and the criterion variable partialling out or holding constant the effects of all other predictor variables Pg 2 13 Standardized Regression Coefficient B directly compares the importance of each predictor variable to the regression model used because partial regression coefficients b might not be measured in the same units and cannot be directly compared to determine which variable are the best predictors B standardizes b so that they are measured in same units and we can compare them Pg 215216 Simultaneous Regression Standard Multiple Regression involves entering all predictor variables into the regression equation simultaneously not in any specific order to determine which predictor variable IV is most important compared standardized regression coefficients B39s Pg 216 o Unique contribution if a predictor variable is highly correlated with the criterion variable but is also highly correlated to other predictor variables its unique contribution might be low since it is redundant with other predictors Pg 216 o Conducting Standard Multiple Regression putting all predictor variables of interest into regression equation and assessing significant via Ftest If it is significant each partial regression coefficient 3 can be examined via ttest to determine which predictor variables contribute a unique amount of variance to criterion variable Pg 217 Sequential Hierarchical Regression involves entering the predictor variables into the regression equation one at a time or in sets in an order specified by the researcher reassessed every time a new predictor variables is added to determine if the addition results in a significant increase in the model39s ability to predict the criterion variable The order of entry of predictor variables should be guided by theoretical or logical considerations aka researcher To determine which predictor variable IV is most important compare R2 Change Pg 217 Stepwise Statistical Multiple Regression predictor variables are entered or removed one at a time into or from the regression equation and the change in regression models is assessed for significance Statistical criteria should guide the order of entry of predictor variables To determine which predictor variable IV is most important compare R2 Change R2 Change tested to determine whether the addition of a predictor variables results in a significant increase in prediction partial F test difference between the R2 value obtained with the second regression equation R22 and the R2 value obtained with the first regression equation R21 the part correlation squared for the variable Factor Component refer to the common underlying dimensions of a set of variables not IVs Factor Analysis used to determine if a large number of variables can be combined into fewer more basic underlying variables factors tells the researcher which variables clump together which ones tend to be correlated with each other and not with other variables Correlation Matrix shows correlation of every variable with every other variable Pearson r correlations first table when conducting Factor Analysis Factor Matrix Component Matrix shows correlations of every variable with every underlying factor that was extracted interpreted like Pearson r second table when conducting Factor Analysis Factor Loading correlation of each variable with each factor relative connection of each of the original variables to a factor variables have loadings on each factor but usually have high loadings on only one 0 Interpreted in same way as Pearson r 1 perfect negative correlation to 0 no correlation to 1 perfect positive correlation Primary Loading highest magnitude correlation between variable and factor Secondary Loading second highest magnitude correlation between variable and factor Factor Score Dimension Score computed by adding raw scores on the variables that load on each other can then be used as variables in subsequent analyses Causal Modeling 0 Path Analysis Researcher makes diagram with arrows connecting the variables arrows show the cause and effect connections between variables based on the researcher s theory 0 Path coefficient tells you how much change in the variable at the start of the arrow is associated with a change in the variable at the end of the arrow 0 Structural Equation Modeling latent variable modeling special extension of path analysis also involves a path diagram with arrows between variables and path coefficients for each arrow 0 Advantages gives an overall indication of the fit between the data and the theory can compute a kind of significance test for whether the data fit the theory uses latent variable variable that is not actually measured but stands for the true variable that the researcher would like to measure but can only approximate with real life measures CORRELATION 1 What is the range of values that a correlation coefficient can assume 10 1 2 How can you determine the direction and magnitude of a correlation a Direction look at signs of correlation coefficient i Positive direct as X 1a Y4 ii Negative inverse as X 1a Y 1 b Magnitude strength of relationship look at correlation coefficient the farther away coefficient is from O in direction the stronger the relationship 3 When testing a correlation coefficient for significance a What null and research hypotheses may be tested i Directional Research Ha pxy gt 0 Ha pxylt 0 Nmh mps p20 ii Non Directional Research Ha p at 0 relationship exists in population Null Ho p 0 relationship doesn39t exist in population b Given r and the critical value for r determine if you can reject the null hypothesis i If r is greater than the critical value for r REIECT the null hypothesis 9 means that there is a significant positive or negative difference between the two variables ii If r is less than the critical value for r FAIL TO REIECT the null hypothesis 9 means that there is no significant difference between the two variables 4 Be able to interpret computer output of a correlation state the outcome statistically and in words a Look at the sig value in the SPSS output b If sig is less than 05 REIECT the null hypothesis 9 means that there is a significant positive or negative relationship between the two variables at 99 or 95 confidence level c If sig is greater than 05 FAIL TO REIECT the null hypothesis 9means that there is no significant difference between the two variables 5 What does the coefficient of determination tell you a r2 shared variance tells us the proportion of variance in one variable that can be accounted for or explained by variance in another variable 6 When given r calculate the coefficient of determination and vice versa a Coefficient of determination r2 b r r2 7 When given multiple R calculate the coefficient of multiple determination a Coefficient of multiple determination R2 b R R2 8 In what kind of research situation do you use each type of correlation and how is each one symbolized a Simple correlation r two variables both with at least interval data b Multiple correlation R at least three variables assess relationship between one variable with two or more variables c Partial correlation s at least three variables assess correlation of one variable with another while removing any correlation coming from a third variable 9 What is meant by the statement CORRELATION DOES NOT EQUAL CAUSATION a Obtaining a significant correlation means simply that there is a relationship between two variables it does not mean that one variable causes the other variable 10 In a Venn Diagram identify the areas that represent the coefficient of determination the coefficient of multiple determination and the coefficient of partial determination a LOOK AT EXAMPLES BIVARIATE LINEAR REGRESSION 1 What is the purpose of Bivariate Linear Regression a To predict the values of one variable criterion variable from values of another variable predictor variable only two variables 2 What is the relationship between correlation and regression a Linear regression is just another way to view a simple correlation between variables Bivariate Correlation relationship between X and Y Bivariate Linear Regression predict Y from X Multiple Correlation relationship of Y with X and Z Multiple Regression predict Y from X and Z 3 Identify criterion and predictor variables when given a research scenario a Criterion Variable dependent variable trying to predict b Predictor Variable Independent variable known 4 Why is the Regression Line the Line of Best Fit a Because the line is drawn through all the points that best fits the data 5 What is the general regression equation Identify elements of the regression equation b a and what they mean a YbXa b b Regression Coefficient slope refers to the degree to which the line is slanted c a Constant where line crosses y axis 6 What information does the Standard Error of the Estimate SEE provide a Used to obtain a measure of the magnitude of error involved in predicting Y from X in a particular regression equation 7 When testing a regression equation for significance a What kinds of tests may be used i Pearson r determine whether the correlation between the two variables is significant If correlation is significant the equation is significant ASSESS THE CORRELATION COEFFICIENT FOR SIGNIFICANCE ii Ttest assess bivariate regression coefficient b for significance Compare t to critical t value iii Ftest assess regression equation for significance b Be able to interpret computer output of a bivariate regression analysis and state the outcome statistically and interpret it in words i LOOK AT SPSS 8 Predict the criterion variable when given a regression equation and values for the predictor variable a EXAMPLE Y 084X 5 X 3 Y O843 5 Y 752 MULTIPLE REGRESSION 1 In what research situations do you use multiple regression a When predicting one criterion variable DV from more than one predictor variables IVs at least 3 variables and to see which combination of predictor variables makes the best prediction of the criterion variable 2 Identify the criterion and predictor variables when given a research scenario a Criterion Variable dependent variable trying to predict b Predictor Variable independent variable known 3 What is the general multiple regression equation Identify the elements of the equation and what they mean a Y b1X1 bzX2 j a b b1 132 etc Partial Regression Coefficients partial slope specifies the relationship between a predictor variable and the criterion variable partialling out or holding constant the effects of all other predictor variables c a Constant Indicates where the line crosses or intercepts the y axis also called intercept 4 Why do we have partial regression coefficients in multiple regression What do they mean a Each predictor variable has its own slope which indicates how much Y changes for each one unit change in X1 X2 etc when the effects of all other predictor variables are held constant 5 What is the meaning of Multiple R Multiple R2 and R2 Change in multiple regression What do they tell us a Multiple R Multiple Regression predicts one criterion variable from more than one predictor variable b Multiple R2 shared variance amount of variance in criterion variables explained by combination of predictor variables c R2 Change tested to determine whether the addition of a predictor variables results in a significant increase in prediction partial F test difference between the R2 value obtained with the second regression equation R22 and the R2 value obtained with the first regression equation R21 the part correlation squared for the variable 6 When testing a multiple regression equation for significance what kind of tests is are used and what does this test tell you a Ftest do the predictor variables as a group predict the criterion variable better than chance b ttest is each individual predictor variable a significant predictor or the criterion variable 7 Be able to interpret computer output of a multiple regression analysis both standard and stepwise state the outcome statistically and interpret it in words a LOOK AT SPSS 8 How does one determine which variables should be kept in the equation and which should be deleted for both simultaneous and sequential types of regression a Simultaneous Standard Regression t test test each predictor variable s regression coefficient b and keep only predictor variables with significant t test b Sequential Stepwise Regression F Change look to see which predictors are significant and compare R2 Change to see which is the best predictor 9 Predict the criterion variable when given a regression equation and values for the predictor variables a EXAMPLE Y 084X1 O33X2 1OX3 5 X1 3 X2 1 X3 53 Y 0843 0331 1053 5 Y 6085 FACTOR ANALYSIS 1 What is the purpose of the factor analysis a To determine if a large number of variables can be combined into fewer more basic underlying variables called factors 2 What are the main uses of factor analysis in research a Understand the important dimensions of complex concepts b Build measurement scales find what variables should be used to measure each dimension of a concept 3 What is a factor in factor analysis a Common underlying dimensions of a set of variables not IVs predictor variables 4 Identify research scenarios requiring the use of factor analysis 5 Know how to label factors when given variables and factor loadings a Ex Weight Chest Size Pant Size Size b Ex GPA SAT scores Intelligence 6 Be able to interpret computer output of factor analysis including a The number of factors extracted i Look at ROTATED COMPONENT FACTOR MATRIX number of columns under component number of factors extracted b How to determine which variables load on which factors i Look at ROTATED COMPONENT FACTOR MATRIX if variable factor is close to 1 Le 90 80 variable loads highly on that factor c Primary and secondary loadings i Primary loadings highest magnitude of variable with factor ii Secondary loadings second highest magnitude of variable with factor d Identify the percentage of variance explained by the factors i Look at TOTAL VARIANCE EXPLAINED of Variance tells how important each factor is higher Variance more important Cumulative tells how well all factors describe the original Variables 7 Know the procedure for computing factor scores a After building measurement scale from factor analysis results compute factor score by adding raw scores on the variables that load each factor factor scores then used as variables in subsequent analyses MANOVA used when you have more than one dependent variable Three groups studied and each subject measured on four dependent variables MANOVA gives an overall F and significance level for the difference among the three groups in terms of how much they differ in combination of the four variables Reliability degree of consistency extent to which you would obtain the same result if you were to administer the same measure again to the same person under the same circumstances Testretest reliability using the measure with the same group of people twice Splithalf reliability evaluating reliability by correlating the responses of half the items with the other half ANCOVA researcher does an ordinary analysis of variance but only after first adjusting the variables to get rid of the effect of some unwanted additional variable df for correlation and bivariate regression equation df N 2 df for multiple regression equations df N K 1

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