Biostatistics

Front 1

interval data

Back 1

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

Front 3

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

Front 8

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

Front 12

As the sample size from the population increases, the standard error of the mean (SEM) ______.

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Decreases

Front 13

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.

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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

Front 25

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

Front 26

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).

Front 27

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)

Front 31

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)

Front 33

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.

Front 38

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.