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Published byJanel Bryan Modified over 7 years ago
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Chapter 12 Understanding Research Results: Description and Correlation
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Scales of Measurement Scales of measurement: A review
Levels of nominal scale variables No numerical, quantitative properties Levels are different categories or groups
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Scales of Measurement (con’t)
Scales of measurement: A review Variables with ordinal scale levels involve minimal quantitative distinctions Rank order the levels from lowest to highest
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Scales of Measurement (con’t)
Scales of measurement: A review Interval scale variables – quantitative properties Intervals between the levels are equal in size No absolute zero
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Scales of Measurement (con’t)
Scales of measurement: A review Ratio scale variables - detailed quantitative properties Equal intervals Absolute zero
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Analyzing the Results of Research Investigations
Scales of measurement have important implications Three basic ways of describing the results Comparing group percentages Correlating scores of individuals on two variables Comparing group means
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Analyzing the Results of Research Investigations (con’t)
For all types of data, it is important to understand the results by carefully describing the data collected Frequency distributions Graphing frequency distributions Directly observe how participants responded Examine which scores were the most frequent Examine the shape of the distribution of scores Identify outliers Compare the distributions of different groups
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Analyzing the Results of Research Investigations (con’t)
Graphing frequency distributions (con’t) Pie charts – very useful for nominal scale information
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Analyzing the Results of Research Investigations (con’t)
Bar graphs use a separate and distinct bar for each piece of information
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Analyzing the Results of Research Investigations (con’t)
Frequency polygons – a line is used to represent frequencies Most useful when data are interval or ratio scales
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Descriptive Statistics
Descriptive statistics allow researchers to make precise statements about the data Two statistics are needed to describe the data Central tendency Variability
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Descriptive Statistics (con’t)
Central tendency Mean M in scientific reports Mathematical average Appropriate for interval or ratio scale data Median Divides the group in half Appropriate for ordinal scale data Mode Most frequent score Appropriate for nominal scale data
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Descriptive Statistics (con’t)
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Descriptive Statistics (con’t)
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Descriptive Statistics (con’t)
Variability - the amount of spread in the distribution of scores Standard deviation = s or SD in reports Variance = s2 Range
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Graphing Relationships (con’t)
Levels of IV are shown on horizontal x-axis DV values are shown on the vertical y-axis y-axis x-axis
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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 Interval or ratio scale data r Values range from 0.00 to and 0.00 to –1.00
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Correlation Coefficients: Describing the Strength of Relationships (con’t)
Correlation coefficients (con’t) Sign of the value indicates direction Value indicates the strength
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Correlation Coefficients: Describing the Strength of Relationships (con’t)
Correlation coefficient – the nearer a correlation is to 1.00 (plus or minus), the stronger the relationship
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Scatterplots reveal the pattern of the relationship
Correlation Coefficients: Describing the Strength of Relationships (con’t) Scatterplots reveal the pattern of the relationship
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Correlation Coefficients: Describing the Strength of Relationships (con’t)
Important considerations Restriction of range Curvilinear relationship
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Effect Size Effect size is a general term that refers to the strength of the association between variables A scale of values that is consistent across all types of studies Values range from 0.00 to 1.00
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Effect size (con’t) Pearson r is one indicator of effect size
Small effects near r = .15 Medium effects near r = .30 Large effects above r = .40 Squared value of the coefficient r2 - transforms the value of r to a percentage Percent of shared variance between the two variables
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Statistical Significance
Decision about the statistical significance of the results Will the results hold up if the experiment is repeated several times? Topic discussed in Chapter 13.
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Regression Equations Regression equations are calculations used to predict a score on one variable using a known score on another variable Y = Score we wish to predict (criterion variable) X = Score that is known (predictor variable)
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Multiple Correlation Multiple correlation is uses (symbolized R) is the correlation between a combined set of predictor variables and a single criterion variable Permits greater accuracy of predictor than if any single predictor is used alone (never a perfect predictor) R2 = effect size
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Partial Correlation and the Third-Variable Problem
Partial correlation is a way of statistically controlling third variables Correlation between the two variables of interest, with the influence of the third variable “partialed out of” the original correlation
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Structural Models Structural models of relationships among variables using the nonexperimental method An expected pattern of relationships Based on a theory of how the variables are causally related to one another Approach called structural equation modeling Older but related tool is called path analysis
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Structural Models (con’t)
Arrows depict paths that relate the variables in the model Coefficients similar to the weights derived in regression equations (indicating the strength of the relationship)
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The End
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