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Data Analysis Using Statistics • There are several reasons researchers use statistics in their research. – To describe – To identify relationships – To determine if there are differences – To identify other variables that may be impacting on the research To Describe • Descriptive statistics are used to provide an overview of the data • Typically, the population being studied is described statistically. This helps the reader of the research to see if the research can be generalized to other groups. Descriptive Statistics • The Mean – This is simply the average. • The Median – This is the halfway number. Half of the scores are above this number and half are below. When one or two extreme scores may skew the mean, the median is a better descriptor. • The Mode – This is the score found most often in the data. Descriptive Statistics • The Range – This is the “distance” between the highest score and the lowest score. • Maximum – The highest score in a range. • Minimum – The lowest score in a range. Descriptive Statistics • Standard Deviation – A number that tells how close together or how spread out the scores are. The smaller the number the more closely grouped the scores are. • Typically, we like to see closely grouped scores . Standard Deviation • Assume we have three groups of scores – Group 1 – 1,2,3,4,5,6,7,8,9,10 – Group 2 – 5,5,5,5,5,5,5,5,5,5 – Group 3 – 4,5,6,4,5,6,4,5,6,5 • The mean score for each of the three groups is 5.0, but the Standard Deviation is 3.0, 0, 0.8 respectively. Without looking at the raw scores the SD tell us there is great variation in scores for the first group, none in the second, and a little variation in the third. Standard Deviation • It is accepted practice to also report the Standard Deviation when you are reporting the Mean in a research report. • The Standard Deviation and the Variance (the Standard Deviation is the square root of the variance) are important in calculating statistical tests. Statistics Identify Relationships • In an earlier lesson we discussed the various types of correlations and how to interpret them. Correlational statistics are used to identify relationships between variables. – You might want to review this information. Statistics are Used to Identify Differences • Whenever we conduct research, we often want to know if the difference between two groups is a “real” difference or did it just happen by chance. • There are several statistics used to accomplish this. t-test • The t-test is used to determine if there are differences between two groups when the dependent variable is interval or ratio. – Test scores, job satisfaction scores, salary, academic achievement, gain scores, etc. t-test • There are two types of t-tests – Independent or a two-sample t-test – is used for comparing two separate groups of individuals. Is group A different than group B? – Paired t-test - is used for comparing the same group of individuals on two scores (such as a pretest score and a posttest score). t-test • The result of a t-test is a value for t, such as t=4.61 • Unlike correlations the value of t means nothing, it cannot be interpreted. – You must look at the P value (Probability) associated with the t-test. If the value of P is equal to or less than .05, we can conclude the two groups are not the same. In other words, our findings are statistically significant. Analysis of Variance (ANOVA) • ANOVA is used to determine if there are differences among three or more groups when the dependent variable is interval or ratio. – Test scores, job satisfaction scores, salary, academic achievement, gain scores, etc. ANOVA • The result of an ANOVA is reported as a value for F such as F=4.61. • Unlike correlations the value of F means nothing, it cannot be interpreted. – You must look at the P value (Probability) associated with the F-value. If the value of P is equal to or less than .05, we can conclude the three (or more) groups are not the same. In other words, our findings are statistically significant. ANOVA • One of the problems with ANOVA is when we have statistically significant results. The problem is which group is different (because we are dealing with three or more groups)? ANOVA doesn’t identify the difference. ANOVA • In order to determine where the differences are, we have to perform a procedure called post hoc analysis. This technique allows us to identify which groups are different from the other groups. • There are a variety of post hoc techniques that can be used. It all depends upon the characteristics of the data. Chi Square • Sometimes our dependent variable is categorical in nature. – Such as honor roll status; member or not; socioeconomic status; rural, suburban or urban; obese or not; etc. • We use the Chi Square test. This can be used with two groups, three groups, or more. Chi Square • The result of a chi square test is a value for c2, such as c2 =4.61 • Unlike correlations the value of c2 means nothing, it cannot be interpreted. – You must look at the P value (Probability) associated with the c2. If the value of P is equal to or less than .05, we can conclude the groups are not the same. In other words, our findings are statistically significant. A Problem • One of the deficiencies of research in agricultural and extension education is that it tends to be simplistic. We may think one variable is causing the effect and focus solely on that variable, when in fact several different variables may be combining to cause the effect. An Example • Attendance at the annual conference of the Association for Career and Technical Education has been steadily declining. Why? – Could it be the membership numbers have declined, so we should expect a decline in attendance? – Or has the rising registration cost resulted in declining attendance? – Or is the location of the conference? – Or is it something else? • One major factor could be the problem or it could be a combination of factors. The Solution • There is a statistical technique called Multiple Regression that examines a number of independent variables then identifies the ones causing the change in the dependent variable. • This procedure can even identify the contribution of each independent variable on the dependent variable. Multiple Regression • It can also tell us how much of the variance (difference) can be explained by the independent variables we have selected. There may be other variables at work that we have not yet identified. The Tools • How do we go about calculating all of these statistical tests? – In the old days these were hand calculated. It took several hours, even days. – Today we use a computer. Statistical Analysis • Excel has a statistical module. If you do a “standard” install of Excel, this module is not loaded. You have to do a custom install and select to load the statistical module. (installs as standard on 2007) • Excel can perform a number of the tests we have discussed. Statistical Analysis • The primary statistical tool used by researchers in agricultural and extension education is SPSS- (Statistical Package for Social Scientists) • This is an extremely powerful software program and it is easy to use. • This software is one of the installed applications on your Novell launcher in the computer labs. Statistical Analysis • There are several web sites where you can paste data and perform statistical analyses. – Webstats http://www.webstatsoftware.com/ – Vassarstats http://faculty.vassar.edu/lowry/VassarStats.html

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