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Where is the location of null hypothesis in research articles?
typically you have to infer the null hypothesis from the purpose statement
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What is the goal of inferential statistics?
to test whether the results achieve "statistical significance". A statistically significant result is one that is very unlikely to be due to chance variations or sampling error.
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What are the two alternatives that hypothesis testing offers us?
- conclude that the difference b/w the test groups is large enough that it is unlikely to be due to chance alone. Reject the null hypothesis and conclude that the groups really do differ.
- Conclude that the difference b/w the groups could be explained just by chance. Fail to reject the null hypothesis, at least for now
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Type I error:
you reject the null hypothesis when the outcome of null hypothesis is actually true
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Type II error:
you do not reject the null hypothesis but the outcome of the null hypothesis is actually false
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How can we control the probability of a Type I error?
use our data to calculate the probability that our finding is just due to chance, under the null hypothesis. This is called the p-value. If p-value is small enough, we reject the null hypothesis and conclude there is a difference
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How small of a p-value is small enough?
- alpha
- convention is that alpha=0.05, or one Type I error in every 20 experiments/studies
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p-value:
the probability of a difference occuring purely by chance
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a p-value of 0.05 could be interpreted as:
"Given the data we have, there is a 5% chance that there really is no difference."
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Alpha Level:
the extent to which a researcher is willing to be wrong is the alpha level
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How much error can we tolerate?
- researcher sets the significance level, also called alpha, at the outset of study
- value of alph determines how difficult it will be for the researchers to claim that their results are statistically significant
- alph level is expressed as a probability, most commonly p<.05
- --there is probability of less than 5-in-100 that the difference between groups is due to sampling error
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When can you reject the null hypothesis?
if the difference b/w groups is unlikely to be due to chance/random error
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If the p-value is less than the selected alpha, then you:
- reject the null hypothesis
- --conclude there is a difference b/w the groups
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If the actual (calulated) probability is less than what is acceptable to me, then...
I reject my null hypothesis: I conclude there is a difference b/w groups
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If the actual (calculated) probability is greater than what is acceptable to me (more than I want to risk), then...
I fail to reject my null hypothesis: I conclude that there is no difference b/w groups
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Power, or the probability of rejecting the null hypothesis depends on:
- sample size
- difference in means
- variation of your measurements
- alpha level you require for the p-values
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hypothesis test:
statement that population parameter will meet some test of difference for some specified probability for any sample
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confidence interval:
statement that population parameter will fall within interval for some specified probability (confidence level) for any sample
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Confidence interval estimation:
a probability that the population parameter falls somewhere w/in the interval
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a confidence interval gives estimated range of values which is likely to include:
the unknown population parameter, the estimated range being calculated from a given set of sample data
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Confidence interval provides range of values:
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The width of the confidence interval gives some idea about:
how uncertain we are about the unkown population parameter.
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A very wide confidence interval may indicate that:
more data should be collected before anything very definite can be said about the parameter
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What are confidence intervals more informative than simple results of hypothesis tests?
they provide a range of plausible values for the unknown parameter
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When making comparisons between groups/samples, the test used depends on:
- number of samples/groups compared
- independence or dependence of sample data
- level of data (nominal, ordinal, ratio, etc.)
- other assumptions met for parametric statistics
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Independent samples:
- samples that have no effect on each other
- two samples: unparied t-test
- more than two samples: anaylysis of variance (ANOVA)
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Dependent samples:
- matched pairs
- one group tested more than once
- two samples: paired t-test
- more than two samples: repeated measures analysis of variance
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Is the Difference b/w group means statistically significant?
- the test you conduct on data is determined by number of groups and kind of data you're analyzing
- the study data are plugged into a formula, and the "value" of the statistic is computed
- this value is then evaluated to see if it is likely or unlikely to be due to error
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Directional hypothesis:
- specifies which of the group means the researcher expects to be greater than the other(s)
- is justified only when evidence exists to support the expectation
- testing for a difference that goes in one direction
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non-directional hypothesis:
- specifies only that the group means will differ, not which one is expected to be greater than the other
- appropriate when existing evidence does not support the superiority of one method over the other(s)
- researcher can test for differences that go in either direction (two tails)
- probability of creating a Type I error needs to be split between the 2 directions
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Directional vs. Non-Directional
one-tailed test, w/ .05 all in one direction, makes it easier to reject the null hypothesis than a two-tailed test, which has to reach a .025 probability level at one of the ends for a difference to be statistically significant. If a researcher specifies a directional hypothesis and uses a one-tailed test, but the data turn out to be in the direction opposite to that expected, the researcher cannot reject the null hypothesis
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Correlation:
examines relationships between variables as opposed to comparison (how alike measures of variables are)
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Correlation coefficients: (-1 to 0 to +1)
quantify the strength and direction of association between two variables
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What is considered a "medium/modest correlation"?
0.30-0.45
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What is considered a "large/strong" correlation?
.5-100
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What type of graph is used to visually represent degree of association?
scatter plots
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Positive correlation:
direct association between 2 variables. As one variable becomes larger, the other also becomes large, and vice versa
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Negative (inverse) correlation:
as the value of one variable increases the associated variable decreases. As one variable becomes large, the other gets smaller, and vice versa
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Regression:
- used for prediction
- simple linear regression
- multivariate regression
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Parametric Statistics:
used to estimate population parameters
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Validity of parametric statistics depends on certain:
assumptions about the data
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List some assumptions made when estimating validity of parametric statistics:
- Sample randomly drawn from population has a normal distribution
- variances of samples being compared are roughly equal
- data are interval or ratio scale--therefore data can be subjected to arithmetic manipulations to calculate means and standard deviations
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What happens if the assumptions cannot be met?
researchers must use nonparametric statistics
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Why does lack of normality cause problems?
- when we calculate p-value, we find probability that the sample was different due to sampling variability
- try to see if recorded value occurred by chance and chance alone
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Non-parametric statistics:
- test done w/out assumption of normality, approximate normality, or symmetry
- test don't require mean and standard deviation. Mean can be easily influenced by outliers or skewness, and we aren't assuming normality, a mean no longer makes sense
- one deals w/ median rather than mean. Median judges location, makes more sense
- used w/ small samples, and w/ nominal and ordinal data
- assumptions for parametric statistics often can be violated w/out major problems, such as use w/ ordinal data and small samples
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KEY POINT: Tap into your statistics knowledge when critically appraising an article:
- validity of study in regard to your clinical question (population, age, diagnosis)
- variables studied (do they link w/ your question?)
- reliability of measures used in the study
- statistical analysis (parametric? non-parametric?)
- overall strengths and weaknesses of the study
- other issues
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