Where is the location of null hypothesis in research articles?
typically you have to infer the null hypothesis from the purpose statement
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.
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
Type I error:
you reject the null hypothesis when the outcome of null hypothesis is actually true
Type II error:
you do not reject the null hypothesis but the outcome of the null hypothesis is actually false
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
How small of a p-value is small enough?
- convention is that alpha=0.05, or one Type I error in every 20 experiments/studies
the probability of a difference occuring purely by chance
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."
the extent to which a researcher is willing to be wrong is the alpha level
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
When can you reject the null hypothesis?
if the difference b/w groups is unlikely to be due to chance/random error
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
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
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
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
statement that population parameter will meet some test of difference for some specified probability for any sample
statement that population parameter will fall within interval for some specified probability (confidence level) for any sample
Confidence interval estimation:
a probability that the population parameter falls somewhere w/in the interval
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
Confidence interval provides range of values:
The width of the confidence interval gives some idea about:
how uncertain we are about the unkown population parameter.
A very wide confidence interval may indicate that:
more data should be collected before anything very definite can be said about the parameter
What are confidence intervals more informative than simple results of hypothesis tests?
they provide a range of plausible values for the unknown parameter
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
- samples that have no effect on each other
- two samples: unparied t-test
- more than two samples: anaylysis of variance (ANOVA)
- matched pairs
- one group tested more than once
- two samples: paired t-test
- more than two samples: repeated measures analysis of variance
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
- 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
- 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
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
examines relationships between variables as opposed to comparison (how alike measures of variables are)
Correlation coefficients: (-1 to 0 to +1)
quantify the strength and direction of association between two variables
What is considered a "medium/modest correlation"?
What is considered a "large/strong" correlation?
What type of graph is used to visually represent degree of association?
direct association between 2 variables. As one variable becomes larger, the other also becomes large, and vice versa
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
- used for prediction
- simple linear regression
- multivariate regression
used to estimate population parameters
Validity of parametric statistics depends on certain:
assumptions about the data
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
What happens if the assumptions cannot be met?
researchers must use nonparametric statistics
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
- 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
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