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# CAS 301 - Week 7 Notes CAS 301

Cal State Fullerton

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This 8 page Class Notes was uploaded by Caru on Tuesday October 4, 2016. The Class Notes belongs to CAS 301 at California State University - Fullerton taught by Sarana Roberts in Fall 2016. Since its upload, it has received 8 views. For similar materials see Inquiry & Methodology in Child Development in Child and Adolescent Studies at California State University - Fullerton.

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Date Created: 10/04/16

CAS 301 - Week 7 Chapter 12 ● Describing Results ○ Comparing Group Percentages ■ Suppose you want to know whether males and females differ in their interest in travel ■ Poll 50 females and 50 males by asking whether they like or dislike to travel ■ 40 females(80%) and 30 males(60%) say they like to travel ■ A relationship between gender and travel variables appears to exist ■ Then perform a statistical analysis to determine whether there is a statistically significant difference between the males and females ○ Correlating Individual Scores ■ Used when you do not have distinct groups of subjects ■ Individuals are measured on two variables, and each variable has a range of numerical values ■ Ex. relationship between location in a classroom and grades in the class: Do people who sit near the front receive higher grades? ○ Comparing Group Means ■ Much research is designed to compare the mean responses of participants in two or more groups ■ Ex. study the effect of exposure to an aggressive adult ● Children in one group will observe an adult “model” aggressive behavior” while the control group does not ● Observers record the number of times the child behaves aggressively during play ● Mean number of aggressive acts by children in the two conditions will be compared to determine which group was more aggressive ● Frequency Distributions ○ Frequency distribution - indicates the number of individuals who receive each possible score on a variable ○ Graphing Frequency Distributions ■ Pie Charts ● Pie charts - divide a whole circle, or “pie,” into “slices” that represent relative percentages ● Number of pieces of information to graph = number of slices ● Useful when representing nominal scale information ● Most commonly used to depict simple descriptions of categories for a single variable ● Useful in applied research reports and articles written for the general public ● ■ Bar Graphs ● Bar graphs - use a separate and distinct bar for each piece of information ● ● X-axis(horizontal) indicates the possible responses ● y-axis(vertical) shows the number of people who chose each response ■ Frequency Polygons ● Frequency polygon - use a line to represent the distribution of frequencies of scores ● Most useful when the data represent interval or ratio scales ● ■ Histograms ● Histogram - uses bars to display a frequency distribution for a quantitative variable ● What can you discover by examining frequency distributions? ○ Can directly observe how your participants responded ○ Can see what scores are most frequent ○ Can look at the shape of the distribution of scores ○ Can tell whether there are any outliers(scores that are unusual, unexpected, or very different from the scores of other participants) ○ Can compare the distribution of scores in the groups ● Descriptive Statistics ○ Descriptive statistics - allow researchers to make precise statements about the data ■ Two statistics are needed to describe the data: ● Central tendency ● variability ■ Summarize the information contained in a frequency distribution ○ Central Tendency ■ Central tendency - tells us what the sample as whole, or on the average, is like; has three measures : mean, median, and mode ■ Mean - a set of scores is obtained by adding all the scores and dividing by the number of scores ● symbolized by x̅ (x-bar) ● abbreviated by M ● Appropriate indicator of central tendency only when scores are measured on an interval or ratio scale, because the actual values of the numbers are used in calculating the statistic ■ Median - the score that divides the group in half (with 50% scoring below and 50% scoring above the median) ● Abbreviated as Mdn in scientific reports ● Appropriate when scores are on an ordinal scale because it takes into account only the rank order of the scores ● Also useful with interval and ratio scale variables ■ Mode - the most frequent score ● The only appropriate measure if a nominal scale is used ● Does not use the actual values on the scale, but simply indicates the most frequently occurring value ■ The median or mode can be a better indicator of central tendency than the mean if a few unusual scores bias the mean ○ Variability ■ Variability - how widely the distribution of scores is spread ● Standard deviation - indicates the average deviation of scores from the mean ○ Symbolized as SD in scientific reports ○ Derived by first calculating the variance( ○ SD is small when most people have similar scores close to the mean ○ SD is larger as more people have scores that lie farther from the mean value ○ SD = square root of variance ○ Usually uses the actual value of the scores ○ Appropriate for only interval and ratio scale variables ● Range - the difference between the highest score and the lowest score ● Graphing Relationships ○ Common way to graph relationships between variables is to use a bar graph or line graph ○ X-axis = independent variable ○ Y-axis = dependent variable ○ Bar graphs are used when the values on the x-axis are nominal categories ○ Line graphs are used when the values on the x-axis are numeric ■ Line is used to connect the data points to represent the relationship between the variables ○ The scale for a bar graph allows a common manipulation of the distance between points on the scale to make results appear more dramatic than they really are ● Correlation Coefficients: Describing the Strength of Relationships ○ Correlation coefficient - a statistic that describes how strongly variables are related to one another ○ Pearson product-moment correlation coefficient - used when both variables have interval or ratio scale properties ■ Provides info about the strength of the relationship and the direction of the relationship ■ Scale of 0.00 to +/- 1.00 ■ Sign of the coefficient tells us the direction of the relationship ■ 0.00 = no relationship ○ Pearson r Correlation Coefficient ■ To calculate a correlation coefficient, we need to obtain pairs of observations from each subject -> each individual has two scores ■ Ask: Do the variables go together in a systematic fashion? ■ Scatterplots ● Scatterplots - each pair of scores is plotted as a single point in a diagram ● ○ Important Considerations ■ A = the constant ■ B = a weighting adjustment factor that is multiplied by X(the slope of the line) ○ Criterion variable - the variable/score that is predicted based upon an individual’s score on another variable (the predictor variable) ○ Predictor variable - a variable that is used to make a prediction of an individual’s score on another variable (the criterion variable) ● Multiple Correlation/Regression ○ Multiple correlation - used to combine a number of predictor variables to increase the accuracy of prediction of a given criterion or outcome variable; the correlation between a combined set of predictor variables and a single criterion variable ○ Symbolized as R ○ Taking all of the predictor variables into account usually permits greater accuracy of prediction ○ Usually higher than the correlation between any one of the predictor variables and the criterion or outcome variable ○ Formula: Y = a + b1X1 + b2X2 + … + bnXn ■ Y = criterion variable ■ X1 to Xn = predictor variables ■ A = constant ■ b1 to bn = weights that are multiplied by scores on the predictor variables ○ Used to study basic research topics ● The Third-Variable Problem ○ Problem in any nonexperimental research when some uncontrolled third variable may be responsible for the relationship between the two variables of interest ○ Partial correlation - provides a way of statistically controlling third variables; correlation between the two variables of interest, with the influence of the third variable removed from, or “partialed out of” ○ Partial correlation and original correlation can be compared to see if the third variable did have an effect ● Structural Equation Modeling ○ Structural equation modeling(SEM) - refers to the complex set of techniques to examine models that specify a set of relationships among variables using quantitative nonexperimental methods ○ A model is an expected pattern of relationships among a set of variables ○ The proposed model is based on a theory of how the variables are causally related to one another ○ After data have been collected, statistical methods can be applied to examine how closely the proposed model actually “fits” the obtained data ○ Researchers typically present path diagrams to visually represent the models being tested -> diagrams show the theoretical causal paths among the variables(path coefficients) ■ Path coefficients indicate the strength of a relationship on a -1.00 to 1.00 scale ○

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