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| to measure life using statistics appied to life |
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| entire collection of measurements from all the organisms the reasearcher's interested in (total) |
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| numerical feature of the population (mean) |
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| every single individual in population has a chance |
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| representative of population |
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| does not accurately reflect the population of interest |
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| numerical feature of the sample |
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| difference between sample statistic and the population parameter |
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1) observations/questions
2) hypothesis
3) experiment
4) results
5) analyze results with statistics
6) conclusion |
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| - objects described by a set of data |
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| characteristics of individuals |
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qualitative (descriptive) data
ex. gender, eye color |
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| quantitative, unequal intervals, ranked values |
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| quantitative, equal increments, no meaningful zero value |
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| quantitative, equal intervals, meaningful zero value |
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| estimates of population parameters |
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| numerical feature of a sample |
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| central tendency fo ratio-interval scale data |
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| measure of central tendency used for ordinal-scale data (ranked) data |
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| measure of central tendency used for nominal-scale data |
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| (variability) sum of squares, variance, standard deviation, coefficient of variation (ratio-interval scale) |
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| measure of dispersion for ordinal-scale (difference between highest and lowest value) |
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| measures of dispersion for nominal-scale data (qualitative) |
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determines the probability of obtaining certain values
(histogram, probability density curve) |
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greatest frequency of occurrence is at mean
lowest frequency of occurence is at extremes
distribution is symmetrical about the mean |
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| asymmetrical, greater frquency of large values |
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| asymmetrical, greater frequency of extreme small values |
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| all values are around mean |
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| plateau, not peaked, greatest frequency are all values |
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| standardized normal distribution |
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mean - 0
standard deviation - 1
values converted to Z-scores |
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| frequency distribution of raw data |
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| frequency distribution of statistics (not raw data) |
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- standard deviation of many means
- single sample
- estimate of sampling distribution if multiple samples taken |
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- means of samples normally distributed as sample size increases
- standard deviation will decrease as sample size increases |
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| no difference or no relationship |
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| there is a difference or relationship |
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| there is a difference because |
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1) populations are different
2) sampling error |
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| achieved by using probabilities |
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| probability of obtaining your sample data and statistics from a population in which null hypothesis is true |
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| rejecting null hypothesis when it is true |
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| accepting null hypothesis when it is false |
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- one nominal-scale variable, compare frequency distribution to a priori ratio
- DF = k -1
- R&B = n/k > 2 |
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| purpose of continuity correction |
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| reduce risk of getting large critical value and reduce risk of type I error |
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- two nominal-scale variables
- frequency of occurrence of categories is independent of frequency of occurence of other variable
- DF = (r-1)(c-1)
- R&B = n/(r x c) > 6
- continuity correction (2x2) |
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- probability that sample of ratio-interval scale taken from a population with pre-determined mean
- mean = c (a priori constant)
- DF = n-1
two tailed: no difference
one tailed: direction of difference |
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| mean of population lies between two values |
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| if values in one sample are not related in any particular way to values in other sample |
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| if each value in one sample is associated with one particular value in the other sample |
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| assumptions for two sample testing |
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RSNDP (normal distribution)
- D'Agostino Pearson K^2 test for normality
Homoscedastic (equal variances) |
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| types of data transformation |
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| logarithmic transformation, square root transformation, arcsine square root transformation |
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| assumptions are not met, ordinal-scale data. do not test for differences in the parameter (mean) |
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- tests for differences in the means of two independent samples of ratio-interval scale data
- DF= (n1-1)(n2-1)
- normal distributions, equal variances
- nonparametric alternative: Mann-Whitney U test |
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tests for differences in the central tendency of two independent samples of ratio-interval scale data and ordinal-scale data (ranking) when assumptions of normality/homoscedasticity are not met
- DF = n |
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| data points that are much more extreme than all of the other data in the sample |
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- differences in the means of two paired samples of ratio-interval scale data, comparing difference between two means to zero
- DF = n(d) - 1 |
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| wilcoxon paired sample test |
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- differences in the central tendency of two paired samples of ratio-interval scale data when the normality assumption is not met
- ordinal-scale data
- calculated test stat uses n (sample size) |
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| logarithmic transformation |
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x' = log x
consistent (most common) |
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| square root transformation |
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x' = rad x
whole number counts |
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| arcsine square root transformation |
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x' = arcsin rad x
when data are proportions or percents |
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