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# Comparing Means

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Brief, simple introduction to comparing means for students in SCED 421L

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### Comparing Means

1. 1. Comparing Means Dr. Roger Passman Northeastern Illinois University SCED 421L
2. 2. Scales of Measurement <ul><li>Nominal Scale </li></ul><ul><ul><li>Placing objects or individuals into categories that are qualitatively different. </li></ul></ul><ul><ul><ul><li>Age </li></ul></ul></ul><ul><ul><ul><li>Gender </li></ul></ul></ul><ul><ul><ul><li>Race </li></ul></ul></ul><ul><ul><ul><li>Grade range </li></ul></ul></ul><ul><ul><ul><li>Class membership </li></ul></ul></ul><ul><ul><li>Nominal scale NAMES things </li></ul></ul>
3. 3. Scales of Measurement <ul><li>Ordinal Scale </li></ul><ul><ul><li>Ranks objects or individuals with respect to how much or how little of an attribute under consideration the object or individual possesses. </li></ul></ul><ul><ul><ul><li>Rank order </li></ul></ul></ul><ul><ul><ul><li>Likert scale data </li></ul></ul></ul><ul><ul><ul><li>The interval between A & B and B & C is unknown, unequal or unmeasurable. </li></ul></ul></ul><ul><ul><li>Non-parametric data </li></ul></ul>
4. 4. Scales of Measurement <ul><li>Interval Scale (sometimes referred to as Scale Data) </li></ul><ul><ul><li>Not only orders objects or events according to the amount of the attribute they represent but also has an arbitrary origin and establishes equal intervals between units of measure. </li></ul></ul><ul><ul><ul><li>The measured distance between A & B is equal to the distance between B & C or C & D and so on. </li></ul></ul></ul><ul><ul><li>Parametric Data </li></ul></ul>
5. 5. Validity & Reliability <ul><li>Validity </li></ul><ul><ul><li>The extent to which the scale in fact measures that which is intended to measure. </li></ul></ul><ul><li>Reliability </li></ul><ul><ul><li>The extent to which the measure yields consistent results each time it is used </li></ul></ul>
6. 6. Inferential Statistics <ul><li>The science of making reasonable decisions with limited information </li></ul><ul><ul><li>Use what is learned through sample data to make generalized predictions for larger populations </li></ul></ul><ul><ul><li>Generalizations are understood to be fallible but reasonable due to a concept known as sampling error. </li></ul></ul><ul><ul><li>Decisions are based on tests of significance. </li></ul></ul>
7. 7. The Null Hypothesis <ul><li>The null hypothesis (H 0 )states that there is NO relationship between the variables; that any observed relationship is only a function of chance </li></ul><ul><ul><li>Researchers choose between two potential explanations </li></ul></ul><ul><ul><ul><li>Null hypothesis—observed difference is merely due to chance </li></ul></ul></ul><ul><ul><ul><li>Research hypothesis—observed difference is due to research intervention </li></ul></ul></ul>
8. 8. The t -Test <ul><li>Among the most widely used tests of significance to test the null hypothesis </li></ul><ul><ul><li>Often used when sample size is under 30 </li></ul></ul><ul><ul><li>Compares two means for significance </li></ul></ul><ul><ul><ul><li>Significance is chart dependent </li></ul></ul></ul>
9. 9. The t -Test Table of Values
10. 10. T -Test Sample
11. 11. Analysis of Variance (ANOVA) <ul><li>ANOVA computes the F -ratio which employs the variance of a group means as a measure of observed differences among groups. </li></ul><ul><ul><li>The general rationale of ANOVA is that the total variance of all subjects can be subdivided into two sources </li></ul></ul><ul><ul><ul><li>Variance between groups </li></ul></ul></ul><ul><ul><ul><li>Variance within groups </li></ul></ul></ul><ul><ul><li>The F- ratio is the calculation of the variance between groups/variance within groups </li></ul></ul><ul><ul><ul><li>As the variance between groups increases the F -ratio increases </li></ul></ul></ul><ul><ul><ul><li>As the variance within groups increases the F -ratio decreases </li></ul></ul></ul><ul><ul><ul><li>The F- ratio is influenced by the number of subjects </li></ul></ul></ul>
12. 12. A sample ANOVA
13. 13. What you NEED to Know <ul><li>Tests of significance allow one to accept or reject the null hypothesis ( H 0 ) </li></ul><ul><ul><li>Either the results can be attributed to random chance, or </li></ul></ul><ul><ul><li>The results can be attributed to experimental intervention </li></ul></ul><ul><li>Tests of significance do not guarantee that the interpretation is correct or even appropriate </li></ul><ul><ul><li>Provide a probability value for one’s interpretative assumptions </li></ul></ul><ul><ul><li>Leave open the possibility of inappropriate interpretation </li></ul></ul>