Lecture 1 - Review and preliminary concepts Flashcards
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Define Individual Differences
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People are unique and so have different abilities, motivations, coping styles, etc. These individual differences mean that not all people will behave the same way in the same situation.
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Define Research Error
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Researchers sometimes make errors in coding data, technical problems can occur with equipment, etc. These factors can influence scores on the dependent variable.
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Define Chance Factors
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Although we try to control the environment to ensure that each participant is tested under the same circumstances there are some events over which researchers have no control (e.g., rain, boiler broken on a freezing day). Such chance factors may also influence participants’ scores on the dependent variable.
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Define Experimental Error
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(e. g)
- Individual Differences
- Chance Factors
- Research Error
These factors are collectively known as experimental error and we assume that experimental error is similar within each of the individual groups. That is, we assume that individual differences, researcher error and chance factors will occur to about the same extent in each of the groups. Such an assumption means that we can further assume that the within group variation is about the same across all groups. Therefore, within-group variation consists of experimental error:
Within-group variation = experimental error
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Give some examples as to what could cause within-group variation.
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- Individual Differences
- Chance Factors
- Research Error
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Give some examples as to what could cause between-group variation.
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1. Treatment/Intervention/Condition effects: If the treatment (or our intervention) has an impact on the dependent measure then the means of the groups would be expected to differ. In fact, almost all studies test hypotheses that would predict differences between group means. In this case we expect that the intervention providing patients with the most information (i.e., B+E+S) will lead to less distress and therefore better adjustment in these patients than patients receiving other interventions.
2. Experimental error: However, even if the treatment had no impact at all on the individual scores we still wouldn’t expect exactly the same means across the different groups. Why? Because of the experimental error mentioned previously. That is, experimental error (chance factors, individual differences, researcher error) would all be expected to cause some fluctuations among group means. Therefore, between-group variation consists of:
Between group variation = treatment effects + experimental error
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In Statistics, what is the F-ratio?
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The statistical test we will use to determine whether our treatment intervention is effective is a ratio of the between-groups variability to the within-group variability.
F = Between-groups variation
(treatment effects + experimental error) / Within-groups variation (experimental error)
If there are no treatment effects then it would be expected that the F-ratio would equal one since both between and within group variability would consist only of experimental error, as in:
F = (Between-groups variation
(0 + experimental error) / Within-groups variation (experimental error)) = 1
However, if there ARE treatment effects than the ratio would be expected to be larger than one since the treatment effects component would increase the between-group variability, making the numerator in the equation (treatment effects + experimental error) larger than the denominator (experimental error only).
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In an ANOVA test, how do we usually start the statistical hypothesis?
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Whenever we conduct an experiment we first propose a set of statistical hypotheses. The first hypothesis is always the null hypothesis that specifies that differences do not exist in population means. The null hypothesis is usually written out in ANOVA as:
Ho: μ1 = μ2 = μ3 …
or sometimes as
Ho: all μ’s are equal
The Greek symbol ‘μ’ refers to the population mean and is pronounced “mu”.
The alternative hypothesis refers to the presence of differences in population means and is usually written out as:
HA: not all μ’s are equal
The null and alternative hypotheses refer to population means (i.e., μ rather than YA1) because although we carry out our studies on samples we are usually interested in
generalising our sample results to the population that exists out there. For example, if I carry out a study on infertile couples I do so because I want to say something about all infertile couples and not just those that happen to have been randomly selected for my study. Note that the alternative hypothesis does not specify where the group differences will occur (e.g., μ1 > μ2 or μ3 < μ2) only that some difference will occur amongst the group means. Our task when we obtain the F-ratio is to decide whether we will retain or reject the null hypothesis of no difference between population means.
(reading):
Chapter 1: Why is my evil lecturer forcing me to learn statistics?
Chapter 12: Comparing several means: ANOVA (GLM 1, esp. p. 529 to 537)
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