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38 Cards in this Set
- Front
- Back
interval data
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data with a numerical value, absolute difference between 2 values can alway be determined by subtraction
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nominal or categorical data
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data not measured on an interval scale (non-numeric), such as gender, state of birth or presence of disease
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ordinal data
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data which is categorical, but has inherent ordering. Example: level of health (excellent, good, fair, poor)
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variance
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dispersion about the mean. measured as the average squared deviation from the mean. variance=sum of (value associate with member of population-population mean)^2/number of population members
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standard deviation
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square root of the variance (square root of the average squared deviation from the mean)
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normal (Gaussian) distribution
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bell-shaped curve. ~68% of population within 1 SD, 95% within 2 SDs
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stratified random sample
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population divided in subpopulation (strata) prior to random sampling
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bias
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systematic difference between the characteristics of the sample and the population
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two ways to obtain data
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experimental and observational
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sample standard deviation (equation)
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s=√(Σ〖(X-X ̅ )〗^2/n-1)
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standard error of the mean (SEM), (xbar subscript xbar)
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standard deviation of all possible sample means, measures the uncertainty in the estimate of the mean
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As the sample size from the population increases, the standard error of the mean (SEM) ______.
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Decreases
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The more variable the total population is the standard error of the mean (SEM) _______.
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Increases
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Term which states:
-normal distribution of sample means indepent of the the original population -mean value of all sample means=mean of original population -SD of all possible means of samples (SEM) depends on both the SD of the original population and the sample size. |
Central Limit Theorem
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median
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the value that half the population falls below, 0.5(n+1) observation
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25th percentile point (lowest quartile) formula
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0.25 (n+1) observation
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interquartile range
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the interval between the 25th and 75th percentile points
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percentile which corresponds to mean + 0.67 standard deviation (in a normal distribution)
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75th percentile
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Percentile which corresponds to mean + 1 standard deviation (in a normal distribution)
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84th percentile
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Percentile which corresponds to mean + 2 standard deviations
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97.5the percentile
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Null hypothesis
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Hypothesis that there is no effect introduced by a treatment
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Analysis of variance
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Class of related procedure to test for differences between groups
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Parametric statistical methods
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Procedures comparing groups based on population parameters within normal distribution (i.e. mean, standard deviation)
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Non-parametric statistical methods
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Procedures comparing groups based on frequencies, ranks or percentiles
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Formula for variance within the treatment groups
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s_within^2=1/4(s_control^2+s_(treatment 1)^2+s_(treatment 2)^2+s_(treatment 3)^2),
S^2 is variance, for study with a control and 3 treatment groups |
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If the null hypothesis is true, what is the relationship between the within-groups variance and between-groups variance?
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About equal (both are estimates of the same population variance).
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About equal (both are estimates of the same population variance).
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F=population variance estimated from sample means/population variance estimated as average of sample variances (F=s_between^2 / s_within^2)
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What is a “big” F?
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There is a larger than expected variability within the samples, so rejection of the null hypothesis that all the samples were drawn from the same population. Report a P-value < 0.05.
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What is single factor or one way analysis of variance?
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Analysis of variance with one factor distinguishing different experimental groups.
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Degree-of-freedom parameters
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Numerator =Number of samples (m) minus 1, Denominator = number of samples (m) times 1 less than the size of each sample. Vn=m-1. Vd=m(n—1)
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t ratio formula
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t= difference in sample meand/standard error of difference of sample means, or
t=(mean1-mean2)/SqRt((s^2_one/n)+(s^2_two/n)) |
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pooled variance estimate
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s^2=1/2(s^2_one + S^2_two)
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two-tailed t test
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Statistical test in which extreme values of t that lead us to reject the null hypothesis lie in both tails of the distribution (i.e. both ends of the bell curve)
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When determining the critical values of t (either calculating or using a table) what information must be known?
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Degrees of freedom (Ʋ). This is determined by sample size n. Ʋ=2(n-1).
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How is the t-test and analysis of variance related?
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They t-test is simply a special case of analysis of variance applied to two groups.
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When the experimental design involves multiple groups should a t-test or analysis of variance be used?
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Analysis of variance. T-test is designed only for 2 group analysis.
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What is the Bonferroni t test?
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First perform an analysis of variance to test the overall null hypothesis. then use a multiple-comparison procedure to isolate the treatment(s) producing the different results.
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What is the Bonferri inequality formula?
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αT < kα, or αT/k < α. k is the number of statistical tests. Cut-off value is α. (i.e. combined t-test cut-off value is no more than k times α.
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