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Digression - Hypotheses

Digression - Hypotheses. Many research designs involve statistical tests – involve accepting or rejecting a hypothesis Null (statistical) hypotheses assume no relationship between two or more variables. Statistics are used to test null hypotheses

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Digression - Hypotheses

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  1. Digression - Hypotheses • Many research designs involve statistical tests – involve accepting or rejecting a hypothesis • Null (statistical) hypotheses assume no relationship between two or more variables. • Statistics are used to test null hypotheses • E.g. We assume that there is no relationship between weight and fast food consumption until we find statistical evidence that there is 1 2 3

  2. Probability 1 • Probability is the odds that a certain event will occur • In research, we deal with the odds that patterns in data have emerged by chance vs. they are representative of a real relationship • Remember – inference is the key…samples and populations • Alpha (α) is the probability level (or significance level) set, in advance, by the researcher as the odds that something occurs by chance 2 3 4

  3. Probability • Alpha levels (cont.) • E.g. a = .05 means that there will be a 5% chance that significant findings are due to chance rather than a relationship in the data 1 2

  4. Probability 1 • Most statistical tests produce a p-value that is then compared to the a-level to accept or reject the null hypothesis • E.g. Researcher sets significance level at .05 a priori; test results show p = .02. • Researcher can then reject the null hypothesis and conclude the result was not due to chance but to there being a real relationship in the data • How about p = .051, when a-level = .05?

  5. Error 1 • Significance levels (e.g. a = .05) are set in order to avoid error • Type I error = rejection of the null hypothesis when it was actually true • Conclusion = relationship; there wasn’t one (false positive) (= a) • Type II error = acceptance of the null hypothesis when it was actually false • Conclusion = no relationship; there was one 2 3 4

  6. Error – Truth Table 1 4 2 3

  7. Back to Our Example • Conclusion: No relationship exists between weight and fast food consumption with this group of respondents 1

  8. Really? • Conclusion: We have found no evidence that a relationship exists between weight and fast food consumption with this group of subjects • Do you believe this? Can you critique it? Construct validity? External validity? • Thinking in this fashion will help you adopt a critical stance when reading research 1 2

  9. Another Example 1 • Now let’s see if a relationship exists between weight and the number of piercings a person has • What’s your guess (hypothesis) about how the results of this test will turn out? • It’s fine to guess, but remember that our null hypothesis is that no relationship exists, until the data shows otherwise

  10. Another Example (continued) • What can we conclude from this test? • Does this mean that  weight causes  piercings, or vice versa, or what? 1 2

  11. Correlations and causality • Correlations only describe the relationship, they do not prove cause and effect • Correlation is a necessary, but not sufficient condition for determining causality • There are Three Requirements to Infer a Causal Relationship 1

  12. Causality… • A statistically significant relationship between the variables • The causal variable occurred prior to the other variable • There are no other factors that could account for the cause • Correlation studies do not meet the last requirement and may not meet the second requirement (go back to internal validity – 497) 1

  13. Correlations and causality • If there is a relationship between weight and # piercings it could be because • weight  # piercings • weight  # piercings • weight  some other factor  # piercings • Which do you think is most likely here? 1 2 3 4

  14. Other Types of Correlations • Other measures of correlation between two variables: • Point-biserial correlation=use when you have a dichotomous variable • The formula for computing a PBC is actually just a mathematical simplification of the formula used to compute Pearson’s r, so to compute a PBC in SPSS, just compute r and the result is the same 1

  15. 1 Other Types of Correlations • Other measures of correlation between two variables: (cont.) • Spearman rho correlation; use with ordinal (rank) data • Computed in SPSS the same way as Pearson’s r…simply toggle the Spearman button on the Bivariate Correlations window

  16. Coefficient of Determination • Correlation Coefficient Squared • Percentage of the variability among scores on one variable that can be attributed to differences in the scores on the other variable • The coefficient of determination is useful because it gives the proportion of the variance of one variable that is predictable from the other variable • Next week we will discuss regression, which builds upon correlation and utilizes this coefficient of determination 1 2 3

  17. Correlation in excel 1 Use the function “correl” The “arguments” (components) of the function are the two arrays

  18. Applets (see applets page) 1 • http://www.stat.uiuc.edu/courses/stat100/java/GCApplet/GCAppletFrame.html • http:// www.stat.tamu.edu /~west/applets/clicktest.html • http://www.stat.tamu.edu/~west/applets/rplot.html 2

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