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PSYB01 - Chapter 12 notes.doc

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University of Toronto Scarborough
Anna Nagy

Chapter 12 - Understanding research results: description and correlation • Stats are used for describing data and making inferences on sample data Scales of Measurement: a review • Levels of a variable can be decribed by 4 scales o Nominal: no numerical, quantitative properties o Ordinal: rank order o Interval: quantitative properties, no absolute 0 o Ratio: quantitative properties, has an absolute 0 Analyzing the results if research investigation • Depending on the way the variables are studied there are 3 basic ways of describing the results o Comparing group percentages o Correlating scores of individuals on two variables o Comparing group means Comparing group percentages • Example: studying if which females or males like traveling more o Lets say out of 50 females and 50 males • 80% of females like to travel • 60% of males like to travel o Need to focus on % because of variable of liking travel or disliking travel is nominal Correlating individual scores • Used when you do not have distinct subject groups • Individuals are measured on 2 variables o Each variable has a range of numerical values • Example: do people who sit near the front receive higher grades? Comparing group means • Example: studying effect of exposure to an aggressive adult on children's play o On average how many aggressive acts did the children perform during play in both groups? • Aggression is a ratio scale variable because there is a true zero and equal intervals Frequency distributions • When analyzing results it is useful to start by making a frequency distribution of the data • Frequency Distribution: indicates the number of individuals that receive each possible score on a variable o Useful to look at this in terms of %s • Example: how many students in a class received a specific score on an exam Graphing frequency Distributions • Pie Charts: divide a whole circle or pie into slices that represent relative percentages o Useful when representing nominal scale information • Bar graphs: use a separate and distinct bar for each piece of information o X-axis is the independent variable o y-axis is the dependent variable • Frequency polygons: use a line to represent frequencies o Useful when representing interval or ratio scales o Can have more then one line to represent more then one group • Histograms: uses bars to display a frequency distribution for a quantitative variable o Scale values are continuous and show increasing amounts on a variable such as age, blood pressure or stress o Bars are drawn next to each other since values are continuous • Looking at frequency distributions allows you to directly observe how your participants responded o Can look at what scores are most frequent and the shape of the distribution of scores o Find "outliers" or unusual, unexpected scores Descriptive statistics • Descriptive statistics allow researchers to make precise statements about the data o Two statistics are needed to describe the data o One number can be used to describe the central tendency or how participants scored overall while another number describes the variability or how widely the distribution of scores is spread • These 2 numbers summarize the information contained in a frequency distribution Central tendency • Central tendency: a central tendency statistic tells us what the sample as a whole or on the average is like o Three measures of central tendency: • Mean: the average  Abbreviated as "M"  Indicator of central tendency only when scores are measured on an interval or ratio scale • Median: the score that divides the group in half  Abbreviated as "Mdn"  Indicator of central tendency only when scores are measured on an ordinal scale  Also useful with interval and ratio scale variables • Mode: the most frequent score  Only measure of central tendency that is appropriate if a nominal scale is used o The median or mode can be a better indicator of central tendency than the mean if a few unusual scores bias the mean Variability • A measure of variability is a number that characterizes the amount of spread in a distribution of scores o Standard deviation • Symbolized as "s" or "SD" • Indicates the average deviation of scores from the mean • Standard deviation is first derived by first calculating the variance; symbolized as s²  Standard deviation is the square root of the variance • Only appropriate for interval and ratio scale variables o Range: the difference between the highest score and the lowest score Graphing relationships • You can graph relationships between variables by using a bar graph or a line graph o Bar graphs are used when the values on the x-axis are nominal categories o Line graphs are used the values on the x-axis are numeric o If the distance between the points on the measurement scale is exaggerated, it makes the results appear more dramatic than they really are Correlation coefficients: describing the strength of relationships • Important to know whether a relationship between variables is weak or strong • Correlation Coefficient: a statistic that describes how strongly variables are related to one another o Pearson product-moment correlation coefficient • Used when both variables have interval or ratio scale properties • Called the Pearson r • Values can range from 0.00 to ± 1.00 • Provides information on the strength and the direction of the relationship o Perfect relationships are rarely if ever observed o If the relationships are not perfect you can
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