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 deviationso Prediction (inferential statistics)
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 datao 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 clarityo 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 applyo Mean, Median, and Mode – KNOW
Rules of Thumb for Measures of Central TendencyUse….. 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.
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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-ANOVA-ANCOVA
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 variableo Examples include: MANOVA, MANCOVA, Multiple Regression Analysiso Results are reported in terms of correlations between variables
Correlation
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 upo 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 reportedo Big push in research