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tail to the right mean toward the tail positive skew mean > median > mode |
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tail to the left mean toward the tail negative skew mean < median < mode |
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Rejection of a true null False positive test |
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Acceptance of false null False negative test |
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Categorical data (race) Chi Square Discete numbers with no rank order |
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level of (pain, symptoms) Discrete numbers with rank order only , no magnitude of diffrence between |
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Continuous and ordered: distance between variables has meaning mean, sd, corelation, regression |
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Needs a zero point (blood cell counts) |
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continuous probability distribution that arises when estimating the mean of a normally distributed population in Measures the differences in the means Situations where the sample size (less than 30) is small and population standard deviation is unknown
DF = N +1 sample size = 18 |
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Descriptive numbers for samples |
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parameter = population statistic = sample |
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In general p should be less than 0.1 (small) an the number of trials should be >15 (large).
Need to be independent at a different time
Electrical system example: telephone calls arriving in a system. Astronomy example: photons arriving at a telescope. Biology example: the number of mutations on a given strand of DNA. |
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Linear Regression analysis |
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y= bx + a y = dependent b= slope a = intercept
linear regression is used to describe and association as inverse or |
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Events that can not happen together Probability of A or B happening P(A) + P (B) |
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events A or B occurring together or in succession
P(A) * P(B) |
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The class intervals are diffrent each data point must fit into one class open classes are not allowed |
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need fixed outcomes can be approximated by the normal distribution. |
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100 times the population standards deviation divided by mean |
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standard score (Z-scores) of normal distribution |
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the number of standard deviations from the mean |
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Regression Equation estimate |
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explains the dependent variables. The higher the correlation the better the regression equation |
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measures the extent that diffrent observations agree beyond what would be expected by chance alone.
K= Pobserved - Pexpected/ 100% - Pe |
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Reciver Opperator Test : determine the accuracy of the test.
Y axis = sen X axis = 1-spec (FPR)
Area under curve proportional to accuracy of the test |
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Used in Normal Distributions : more powerfull Data must be interval or ratio Can be used to describe measures of central tendancy |
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non-normally distributed data or Ordinal scale data |
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Average used for interval and ratio data |
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50% percentile not affected by outliers Usefull for Ordinal data |
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most usefull when two clusters exist. It is the highest point of the peak. Usfull for nominal data |
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range, standard deviation |
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can be influenced by outliers Applicable to all data sets nomianal, ordinal, interval, ratio |
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range betweeen the 25th and 75th interval. Directly related to the median Applicable to ordinal, interval, and range |
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Degree of scatter of individual data points about the sample mean
Usefull for normal distribution
= square root of varriance = sigma |
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= x-xi squared / n-1 = sigma saured
Applicable to interval and ratio data |
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Standard Error of the mean |
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scatter about the mean = SD/ square root of n.
SEM always < SD As n increases SEM decreases |
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probablity of making a type 1 error |
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probability of making a type II error should be less than .2 |
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1-B = probability of not making a type II error. = sensetivity
increase alpha = increase power increase n = increase power |
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Operating Charateristic Curve |
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function that relates the dependent variable B that results from independent values of alpha, and n |
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More powerfull than a two tailed test. Result must fall in either the top or bottom 5% of a distribution |
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t- test (diffence between means) ANOVA Multiple Comparison models |
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- Continuous data - Normal distribution - Variance same - not paired (independent)
Paired T-test for dependent |
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a / (a+b) / c (c+d)
OR shifts RR away from the Null. |
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increase prevalence increase PPV
TP / (TP+FP) = a/ a+b |
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Receiver operator Characteristics
Y = sensitivity X = FPR
The greater the area under the curve the greater the accuracy. |
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FNR = 1- sen = 1-TP 1-FNR = TP / sen |
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FPR = 1-spec = TN 1-FPR = TN/ Spec |
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used if the variables are both categorical/ dichotomous. DF= r-1
Chi squared pearsons = diffrences in proportions. |
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- Continuous data - 3 or more groups - Independent |
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- Continuous data - 3 groups or more - Skewed - Dependent |
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- Continuous data - 3 groups or more - Skewed - Independent |
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- Continuous data - 2 groups - Independent |
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-Continuous data -2 groups -Dependent / paired |
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test of multiple comparison for adjusted data |
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Univariate test to asses the diffrences in proportions. |
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Multivariate technique used for continuous data |
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Multivariate technique used for dichotomous or categorical data |
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test for linear trend w p values |
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Cox proportional hazard curve |
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adjusted for confounders in the survival analysis curve. |
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Comparison of Kaplan Meir Curves for treatments. |
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1.) Temporal 2.) Strenght of Ass 3.) Dose 4.) Consistency 5.) Plausibility 6.) Alt explanation 7.) Coherance |
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even if a population has a normal distribution the sample mean from repeated samples from this distribution approaches the normal distribution the larger the N . Sample size must be greater than 30 |
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R value give a indication of how closesly correlated |
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Chi Squared for dependent |
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