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84 Cards in this Set
- Front
- Back
for numerical one group data what test do you do?
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t-test one sample
Confidence interval (the easy way) |
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What are the question that should be asked about a sample?
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is this group representative of the population
is the sample random how far are the results form the norm |
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What are the steps for preforming a test
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1. state the Ho: x=
H alt: x does not = u 2. collect the data (will be given) 3. pick and preform a test statistic 4. critical value of t for significance 5. compare the measured t value with the critical value of t |
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t-test one sample
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used when there is one numerical data with one group with normal distribution
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critical vlaue of t for significance
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at what value of t is significant
two tailed 0.05 is base case, defing the central tendency 95% of the sample if t is outside the critical t value reject the Ho and t is significant |
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if t is > Critcal t
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there is a difference
reject Ho p<0.05 |
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if t is </= ti critical t
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fail to reject Ho there is no difference
p>0.05 |
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95% confidence intercal (the easy way) (t-test one group)
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represents the sample
if u is not in the range this is significant reject the Ho indicator of sample studied |
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95% CI (t-test one group)=
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x+/- t(0.05) (SEM)
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what do you do with ordinal or skewed data
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do not use a t-test
use the NP test based on medians rather than means parallel version of a t-test is the sign test |
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numerical data two groups
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1. paired
2. independent |
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paired data
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1 group measured twice
2 groups of data |
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independent data
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2 groups measured once
2 goups of people |
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if the Confindence levels overlap when doing an indepentent t-test what tells that tell you
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that they are not significant
when they do not overlap they are significant |
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if independent data is skewed or ordinal
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use the wilcoxon rank sum test
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problem with doing multiple pairings of t-test
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increases the chance of error each test has 5% chance of error and have to add them each time
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what can you do to account for multiple comparisons problems
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want 5% error as a whole
bonferoni correction |
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bonferone correction
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divide alpha/#of tests
spreading alpha across all the test |
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alpha priori
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doing the correction before the test are done
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ANOVA
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analysis of variance
start from a grand mean and see how different the groups are looking at the variation within the groups and between the goups |
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degrees of freedom for more than 1 group
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N(total number of subjects)- # groups
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variance between
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sume of (x-xi)2
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variance within
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sum of (Sdi)2
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f test (n,d)
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variation bw/variation w/in
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if f is > CV
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f is significant
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populaindivtion
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represents the entire group of individuals in whom are interested
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sample
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those who aer representative of the population
draw inferences from the sample about the population |
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sampling error
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we have to recognize that the information in the sample may not fully reflect what is true about the population
introduced by studying only some of the population |
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random sample
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individuals are selected randomly
everyne in the population has and equal chance of being selected |
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parameter of the population
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mean or proportion
estimate using data collected from the sample a sample satistic and a point estimate |
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sampling distribution of the mean
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if the sample size is large there should be a normal distribution
if the sample size is small the estimates of the mean follow a normal distribution if the sample is normally distributed the mean is an unbiased of the population (estimates true population mean) the variablity of the distribution is measured by the standard deviation of estimates |
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standard error of the mean(SEM)
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if we know the population standard deviation then the SEM is given by
cigma/square root of n |
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a large SEM
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indicates that the estimate is imprecise
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a small SEM
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the estimate is precise
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the SEM is reduced if
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the sample size is increased
the data is less variable |
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standard deviation describes
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the variation in the data values and shoul dbe quoted if you wish to illustrate variability in the data
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SEM describes
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the precision of the sample mean and should be quoted if you are interested in the mean of a set of data
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95% CI if the distribution of sample means lies within
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1.96 SD
range of values within which we are 95% confident that the true population mean lies |
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the samplng distribution of a proportion follows a ______ distribution
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binomial
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a wide CI indicates
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the estimate is imprecise
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a narrow CI indicates
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imprecision
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the width of CI depends on the size of
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SE, which depends on the sample size
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null hypothesis
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assumes no efect
difference in means is equal to 0 |
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alternative hypothesis
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holds if the null is not true
relates to the theory we are investigating |
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two tailed test
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where we do not specify a direction that the difference may take (higher or lower than the mean)
used most often |
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test statistic
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reflects the amount of evidence in the data against the null
usulaly the larger the value the greater the evidence |
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p-value
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is the probability of obtaining our resutls or something more extreme if the null is true
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non-parametric tests
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replace data with ranks
used with ordinal data or categorical data have less power than parametirc tests |
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primary aim of a hypothesis test
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is to provide an exact p value
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confidence interval provides
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quantifies the effect of interest and enables us to asses the clinical implications
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bioequivalence trials
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randomized trials that are interested in showing the rate and extent of absorption of new formulations of the drug is the same of the old
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equivalence range
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used in bioequivalent trials
the range that corresponds to an effect of clinical importance the CI for th effect lies within the equivalence range the two treatments are equal |
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type I error
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we reject the null when it is true and conclude there is an effect when there is none
will never our chosen significance level |
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type II error
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we do not reject the null when it is false and conclude that there is no evidence of an effect when there is
the power of the test (1-beta) the power is the probability of rejecting the null when it is false |
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power should be at least
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80%
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factors that affect power
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sample size (power increases with an increasing sample size
varibility of observation (power increases as the varibiltiy decreases effect of interest (the power of the test is greater for larger effects significance level (the power is greater if the significance level is larger |
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situations that involve multiple comparisons
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subgroup anaylyses
multiple comparisons for a single outcome variable (making pari wise comparisons between groups) multiple outcome variables interim analyses (when treatment comparisons are made at predetermined intermediate stages of a study data dredging (a priori) |
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multivarient anaylsis
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consider simultaneously the effects of one or more explanatory variables or more than one outcome variable
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instead of a t-test for skewed data use
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a sign test or a wilcoxon rank test
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sign test is based on
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medians
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wilcoxon signed rank test
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takes into account the ranks of the data as weel as their signs
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paired t-test
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the individuals are linked to each other in somw way
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can you use a sign test for paired data
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yes, use it whe the data is skewed or ordinal
asseses the medians |
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wilcoxon signed ranks tests for paired data
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takes into account not only of the signs of the difference but also their magnitude and therefore is more powerful than the sign test
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unpaired two sample t-test
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normal distribtion
based on means |
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wilcoxon rank sum test
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used when the data is skewed instead of a unpaired two sample t-test
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mann-whitney U test
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used when the data is skewed instead of a unpaired two sample t-test
gives identical results although it is slightly more complicated to carry out by hand |
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numerical data more than 2 groups use
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one-way analysis of variance (ANOVA)
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two types of variantion in the ANOVA
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between group variantion and within group variantion
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the ANOVA test is based on
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the ratio of the within group vairation and between group variation (F)
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non-parametric equivalent of the ANOVA
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Kruskal-Wallis test
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for categorical data use (a single proportion)
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the test of single proportions
individuals either have the desired trait or not (a proportion) used for normal distribution |
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the sign test applied to a proportion
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can be used to express a preference
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categorical data two proportions
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2 independent groups
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for 2 independent categorical groups use
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the chi-squared test
data is obtained as frequencies |
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if the assumptions are not satisfied (categorical data)
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use a fisher's exact test to obtain the p value
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related groups (categorical data)
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McNemar's test
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McNemar's test
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the 2 groups are related or dependent
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chi-squared test large contingency tables
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the data may be represented in an rxc table with r rows and c columns
the enteries in the table are frequencies every individual is represented once |
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when there is a 2x2 table use
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chi-squared test
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chi-squared test for trend
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takes into account the ordering of the groups
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power def.
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the chance of detecting a statisically significant, a specified effect if it exist
at least 80% |
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significance level (alpha)
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the cut off level below which we will reject a null
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varibility
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the standard deviation
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