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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

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 pvalue. If pvalue is small enough, we reject the null hypothesis and conclude there is a difference

How small of a pvalue is small enough?
 alpha
 convention is that alpha=0.05, or one Type I error in every 20 experiments/studies

pvalue:
the probability of a difference occuring purely by chance

a pvalue of 0.05 could be interpreted as:
"Given the data we have, there is a 5% chance that there really is no difference."

Alpha Level:
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 5in100 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 pvalue 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 pvalues

hypothesis test:
statement that population parameter will meet some test of difference for some specified probability for any sample

confidence interval:
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

Independent samples:
 samples that have no effect on each other
 two samples: unparied ttest
 more than two samples: anaylysis of variance (ANOVA)

Dependent samples:
 matched pairs
 one group tested more than once
 two samples: paired ttest
 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

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

nondirectional 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

Directional vs. NonDirectional
onetailed test, w/ .05 all in one direction, makes it easier to reject the null hypothesis than a twotailed 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 onetailed test, but the data turn out to be in the direction opposite to that expected, the researcher cannot reject the null hypothesis

Correlation:
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"?
0.300.45

What is considered a "large/strong" correlation?
.5100

What type of graph is used to visually represent degree of association?
scatter plots

Positive correlation:
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

Regression:
 used for prediction
 simple linear regression
 multivariate regression

Parametric Statistics:
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 scaletherefore 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 pvalue, we find probability that the sample was different due to sampling variability
 try to see if recorded value occurred by chance and chance alone

Nonparametric 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

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? nonparametric?)
 overall strengths and weaknesses of the study
 other issues

