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Basic Quantitative Data Analysis
Chapters 7 and 12

Additional Education Flashcards




Statistics PURPOSES:
o Description (descriptive statistics)
• Describe data that has been collected
• Used to reveal the the distribution of the data in each variable
• Commonly used descriptive statistics measures of central tendency, and standard deviations
o Prediction (inferential statistics)
are a set of tools (methods) used to organize and analyze data (but just because you have statistics, does not mean research is high quality)
(Statistics) Distributions
o Graphic representation of data
o Line formed by connecting data points is called a frequency distribution. This line can take many shapes.
o Single most important shape is that of the bell-shaped curve – characterizes the distribution as “normal.”
o As a frequency distribution approaches a normal curve, generalizations about the data set from which the distribution was derived can be made with greater clarity
o Important to remember that not all frequency distributions approach a normal curve. Some are skewed, but don’t focus on that.
o When a frequency distribution is skewed, the characteristics inherent to a normal curve no longer apply
o Mean, Median, and Mode – KNOW
Rules of Thumb for Measures of Central Tendency
Use….. If……
o Mean to describe the middle of a set of data that does not have outliers. An outlier is a data value that is much higher or lower than the other data values in the set.
o Median is the middle value in the set when the numbers are arranged in order. For a set containing an even number of data items, the median is the mean of the two middle data values. Use the median to describe the middle of a set of data that does have an outlier.
o Mode is the data item that occurs the most times. It is possible for a set of data to have no mode, one mode, or more than one mode. Use the mode when choosing the most popular item.
Standard deviation
o Is a statistic that tells you how tightly all the various examples are clustered around the mean in a set of data.
o When the examples are pretty tightly bunched together and the bell-shaped curve is steep, the standard deviation is small.
o When the examples are spread apart and the bell curve is relatively flat, there is a relatively large standard deviation
Normal Distribution and 68-95-99.7 Rule
• If the mean is 100, expect 50 below the mean, and 50 above the mean
• Standard deviation is 15 above or below 100.
• 100 is the “peak.” Half above 100, half below 100.
• 68% will be between 15 below and 15 above – or between 85 – 115 (one standard deviation away)
• 95% will be between two standard deviations away.
• 99.7% will be between three standard deviations away.
Inferential Statistics
• Used to draw conclusions and make predictions based on the descriptions of data.
• These predictions are related to probability
Probability Language
• Probability is the chance that a phenomenon has of occurring randomly.
• Shown as p (the "p" level or level of significance).
• The smaller the level of significance (e.g., p<.001), the greater confidence in rejecting the null hypothesis.
• In other words, p<.001, suggests that there is a 1/1000 chance that the statistical finding reported would occur by chance
• As a general rule P<.05 is the minimum standard in the field
Statistical Tests for Analyzing Differences
-t tests
T-Tests (reported as t value) -
A statistical test used to determine if the scores of two groups differ on a single variable. A Paired t-test could be used to determine if the scores of the same participants in a study differ under different conditions. It is often used in pre-post designs. See the Adventure Learning Study ****
ANOVA (Analysis of Variance) (reported as F value) -
A method of statistical analysis used to determine differences among the means of two or more groups on a variable.
ANCOVA (Analysis of Co-Variance) (reported as F value) -
A method used to test differences in the means of dependent variables for two groups, controlling for the effects of selected variables that may co-vary with the dependent variable. In other words, if the researcher has evidence of an existing difference between 2 or more groups that might influence the dependent variable, then ANCOVA should be selected to statistically adjust for the difference.
Non Parametric Test for Analyzing Differences - Chi Square
Chi-Square (X2)– Non parametric (without the assumption of normal distribution) method to test the difference between an actual sample and another hypothetical or previously established distribution.
Multivariate Analyses
o Statistical procedures to simultaneously analyze the effects of multiple dependent variables on an independent variable
o Examples include: MANOVA, MANCOVA, Multiple Regression Analysis
o Results are reported in terms of correlations between variables
o Correlation denotes positive or negative association between variables in a study.
o Two variables are positively associated when larger values of one tend to be accompanied by larger values of the other. EX: Do homework, scores go up
o The variables are negatively associated when larger values of one tend to be accompanied by smaller values of the other EX: If you do homework, and scores go down
Correlation Coefficient
o The correlation coefficient is used to indicate the relationship of two random variables. It provides a measure of the strength and direction of the correlation varying from -1 to +1.
o .8 correlation, stronger than .3, since it is closer to 1.
o Positive values (the positive sign is understood) indicate that the two variables are positively correlated. Negative values indicate that the two variables are negatively correlated.
o Values close to +1 or -1 reveal the two variables are highly related.
Statistical Significance
Within quantitative research relationships between variables can be significant without being meaningful
Effect Size
is a way of showing the strength of association between variables. Effect sizes complement inferential statistics such as p values.
o An effect size of d = 1.0 for a reading program means that the reading program increased the reading score of the average student to one standard deviation above the mean. A negative effect size of d = -1 means that the reading score of the average student in the program decreased by one standard deviation below the mean.
o Generally, an Effect size of .2 is considered small; .5 moderate, and .8 large.
o For example, Adventure Learning, small effect size, and was not reported
o Big push in research
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