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| The derivation of general ideas from specific observations - not used by scientists |
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| Hypothetico-deductive reasoning |
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| Observations lead to plausible hypotheses, which we then attempt to falsify, if we cannot prove them false, they are good hypotheses, but not necessarily right |
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| A general set of ideas or rules used to explain a group of observations |
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| A change in the way we think about a subject |
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| H0, The form of a hypothesis that we formally test, it predicts nothing will happen |
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| A specific prediction about an experiment |
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| Data in categories with names |
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| Data that always rises in integers |
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| Non-quantitative ranked data, normally used in questionnaires |
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| Quantitative measurements on a continuous scale |
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| Measures calculated from a data set which summarise some characteristics of the data |
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| Measures of central tendancy |
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| A graph showing the total number of quantitative observations in each of a series of numerically ordered categories |
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| Total of all the squared deviates in a data set, squaring removes the minus, SS shows the magnitude of the variability but not the direction |
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| s2- the average size of the squared deviates in a sample - an estimate of the population variance |
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| s - the average size of deviates in a data set. |
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| All individuals in a group |
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| A sub-set of a population, meant to represent it |
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| Bell-shaped, Gaussian, 68.5 of all data points are in one SD |
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| Standard error of the mean |
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| A measure of the confidence we have in our sample mean as an estimate of the real mean |
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| If skewed to the right, there is a long tail to the right, atc. for left |
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| Tests which make many assumptions |
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| Tests which make fewer assumptions |
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| A distribution where a maximum possible count is far above the mean, resulting in a skew |
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| A distribution where the maximum count is close to the mean |
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| Used for visualising differences |
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| Used for visualising trends |
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| A measurement is not precise ifthere is an unbiased measurement error |
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| A measurement is accurate if it is free from bias, bias occurs when there is a systematic error in your measurements |
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| A confounding effect is something that influences your results in a way that can be confused with the effect you are studying |
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| Effects of a variable are only visible once above a certain point |
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| Effects of a variable are only visible below a certain point |
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| Independent samples t-test |
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| A statistical test designed to test for a difference between the means of two samples of continuous data |
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| The rejection of the null hypothesis when it is true |
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| The failure to reject the null hypothesis when it is false |
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| the use of non-independant data points as if the were independant |
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| A test designed were samples are not independant of each other, normally used to examine change |
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| If the variance is homogenous, it is the same in each sample |
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| A test which is used to examine differences between observed and expected counts |
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| Pearsons correlation coefficient |
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Definition
| The statistic used to test the significance of correlations between two variables. Can only be used with linear relationships and normal distributions |
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| Spearmans rank correlation coefficient |
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| Non-parametric correlation test |
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| Tests the null hypothesis that the samples means are not different |
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| Non-parametric one way ANOVA |
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| Combines anova and regression |
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| Clear, Precise, Plausible, Able to produce testable predictions |
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i=n
Thesumof:(Xi-Xwithalineoverit)2quared
i=n |
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i=n
s2=thesumof(xiXwithalineoverit)2quared
i=1
_____________________________________
n-1 |
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| 95% of samples are within |
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| Standard error of mean formula |
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| Which tests have more statistical power? |
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| Parametric test standard assumptions |
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Independance
Homogenity of variance |
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| Alternative t test if the variances are not the same |
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| To test if the variances are the same? |
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| If data is not normal, you can transform it by... |
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Definition
Squaring all the points, eliminating a right skew
square root arcsine all the points, eliminating a left skew |
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| Alternative T-test if the data is not normal |
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| adjust for chance of a type 1 error |
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| In regression, we analyse |
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| the affect of a variable on another variable |
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If events A and B are mutually inclusive, the probability of event A or B is
P(A or B) = |
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Definition
The sum of A and B
P(A) + P(B) |
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| The sum of the probability of A happening and not happening is |
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| If the two events are independent, the probability of A and B is |
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The product of the two probabilities
P(A and B) = P(A).P(B) |
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| Binomial probability distribution |
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Definition
n! x p^i x (1-p)^n-i
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i! x (n - i)!
Where the probability of the first outcome is p, the number of events i, and the amount of trials n |
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| As the binomial distribution gets bigger, we expect to see |
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m^i e^-m
_-------- = P(i)
i! |
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| Put ! after a number means x all numbers up to that, e.g. 3! is 1x2x3 |
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| The binomial probability distribution can be used to |
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| figure out the probability of a certain size deviation from an expectation |
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| To convert non-normal data to ordinal |
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| the sum of an infinite series |
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| the number by which ten has to be raised before it is equal to x |
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Z = (x1 - x2) / √(((s1^2)/n1)+(s2^2)/n2))
where z is the test statistic, n1 is the first sample size and n2 is the second, x1 is the first mean and x2 is the second, and s1 is the first standard deviation and s2 is the second |
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| To convert non-normal data to normal |
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Definition
| binomial, poisson, chi squared |
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| Kolmogorov-Smirnov, less powerful, more general, or shapiro-wilk |
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| Continuous data tests of difference |
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Definition
Not normal - Mann-whitney for two treatments
Kruskal-wallis for more than two
Wilcoxon for paired
Normal - t-test, paired or not, ANOVA or two way ANOVA |
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| Continuous data tests of trends |
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Definition
Normal - Spearmans rank
Non normal - Pearsons or regression |
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