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MSE 600 Descriptive Statistics Chapter 10 in 6 th Edition (may be another chapter in 7 th edition)

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Quantitative Data Numbers of something…. (nominal - categorical Importance of something (ordinal - rankings) Relative of one thing to another (interval) Amount or degree of something (ratio) In sampling (inferential statistics) primarily collect data about the members of the sample within the group to represent a Group Interval and Ratio data most often Group data We can describe characteristics about it

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A set of scores represent each person in the group Frequency table Distribution of the group’s scores Frequency polygon X-Y axes X axis – the score Y axis – the number of times that each score occurs

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Example of a Frequency Polygon

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Frequency Polygons – shape of distribution Normal Skewed to the left (mean to the left of mode) to the right (mean to right of mode)

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Measures of Central Tendency Mean Median Mode Mode – most frequently occurring score useful for nominal data Median – 50 th percentile useful if extreme scores Mean – average commonly used in stats affected by extreme scores

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The Normal Curve Normal Curve – Bell Curve – Normal Distribution of Scores

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Example of the Mode, Median and Mean in a Distribution Mode = 62 Median 64.5 Mean = 66.7 Range = 93 (98 -5) St Dev = 17.1

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Calculation of the Standard Deviation of a Distribution Σ Σσ√Χ¯ √ Raw ScoreMeanX – X(X – X) 2 855431961 805426676 705416256 6054636 555411 5054-416 4554-981 4054-14196 3054-24576 2554-29841 Variance (SD 2 ) = Σ(X – X) 2 n = 3640 10 = 364 a Standard deviation (SD) = Σ(X – X) 2 n

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Summary of Commonly Used Statistical Techniques Two or more groups are compared: Descriptive Statistics Inferential Statistics Frequency polygons Averages Spreads Effect size t-test for means ANOVA Confidential interval Scatterplot Correlation coefficient (r) Percentages Bar graphs Pie charts Crossbreak (contingency) tables Chi square QuantitativeCategorical

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Percentiles Standardized test scores often accompanied by percentiles. Percentiles are a comparison with the whole group – a norming function – normalizing Related to the normal curve in terms of comparing one person’s score with another – using standard deviations.

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Probabilities Under the Normal Curve

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Percentages Under the Normal Curve

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Examples of Standard Scores

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Correlations A measure of the association between two quantitative variables Value of a correlation range from -1 to +1 Typically a 2 place decimal Positive value – the 2 variables change in similar directions Negative value – the 2 values change in opposite directions Zero value – no relationship between the 2 variables

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Correlation DOES NOT imply causation During the day, the more windows that are open is associated with more light and heat. Windows do not cause light or heat

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Examples of Scatterplots

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Interpretation of Correlation when Testing Research Hypotheses Magnitude of rInterpretation.00 to.40Of little practical importance except in unusual circumstances; perhaps of theoretical value. a.41 to.60Large enough to be of practical as well as theoretical use..61 to.80Very important, but rarely obtained in educational research..81 to abovePossibly an error in calculation; if not, a very sizable relationship.

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