ED+A Flashcards
Hypothetico-deductive reasoning
Hypothesis created not by induction, experiments used to falsify hypothesis. Can be ‘good’ hypothesis however arguably there is no way of proving it to be true.
Hypothesis
Preposition tentatively put forward to explain an observation.
Alternate Hypothesis
(H1) Hypothesis makes a specific prediction about results which can later be tested.
Theory
Set of general ideas or rules to explain a group of observations. More general than hypothesis, less speculative.
Paradigm
Describes a whole way of thinking or a particular way of viewing the world.
Paradigm shift
Dramatic change in the way we think about a subject when evidence has accumulated in favour of rejecting a previous set of hypotheses or theories, or a creative genius moment.
Null Hypothesis
(H0) Form of hypothesis we test using statistics following an observation. Predicts NOTHING will happen/No effect/No difference or relationship. Hope to reject is data supports alternate hypothesis. Only one null.
Statistics
Branch of mathematics scientists use for an objective assessment of patterns in data from experiments or observations.
Nominal data
CATEGORICAL In the form of categories with names (e.g male or female). Non-quantitative.
Discrete data
QUANTITATIVE Count how many individuals in each group of Nominal data. Quantitative and always in the form of whole numbers.
Ordinal data
CATEGORICAL Ranked in order of size or on a rating scale (e.g 1st, 2nd). Not quantitative as we do not know the difference between 1st and 2nd, only that 1st is larger (e.g strongly agree, disagree)
Continuous data
QUANTITATIVE (e.g temperature, time) Subjective decision between continuous and discrete.
Descriptive statistics
Measures calculated from a data-set which summarise some characteristic of the data (central tendancy or variability)
Sample size
(n) number of individuals sampled.
Frequency
Number of times something occurs, or a count of the number of items in a category.
Mean
A measure of central tendency. Average of a sample of numbers
Median
A measure of central tendency. Middle number in a sample of numbers when placed in order. If sample is even then the average of the two middle numbers is taken.
Mode
A measure of central tendency. The most common number.
Measures of central tendency
Mean, Median, Mode - all tell about the position of the middle of the sample.
Frequency histogram
Graph showing the frequency of quantitative observations in each category.
Discrete - categories represent each possible total count made. Continuous - categories are arbitrary (1.-0, 11-20) you decide.
Distribution
Shape of data set as seen on frequency histogram. Described by mathematical equations.
Deviate
Distance between a data point/observations and the mean. Also known as residual.
Sum of Squares
(SS) total of all the squared deviates for a particular data-set. Gets rid of minus signs, quantifies the magnitude of the total variability but ignores direction of variability.
Variance
(S^2) Average size of the deviates. Measure of variability. Sample variance is an estimate of population variance.
Standard deviation
(s) Average size of deviates by square rooting variance we get a measure of variation unaffected by sample size. Standard deviation of 2.5 means the average data point is 2.5 times larger or smaller than the mean.
Population
All individuals in a group
Sample
Sub-set of population normally chosen to represent the population.
Normal distribution
‘Bell curve’ or Gaussian distribution. Continuous - useful, symmetrical, 68.5% of all data points in normal population will be within one standard deviation of mean.
Standard Error of the mean
Measure of confidence in sample mean as an estimate of real population mean. Small SEM = good estimate. If error bars do not overlap sample means are different. SEM decreases with sample size as more data means more confidence. = Standard deviation of a population of sample means.95% confidence interval.
Skew
Skewed to right = long tail to the distribution on the right and no symmetry (mode closer to left than right) = Not normal.
Parametric statistics/statistical tests
make several key assumptions about distibution. e.g it is normal.
Non parametric statistics/test
fewer assumptions about data.
Poisson distribution
Common for discrete data if maximum possible count is larger than mean. Many different shapes, if mean is near to zero = heavily skewed normal distribution, mean is big = normal distribution
Binomial distribution
good for discrete data where maximum possible count is close to the mean.
Bar chart
type of graph used for visualising differences between samples.
Scatter graph
Graph usually used for visualising trends between variables.
Statistical significance
Can obtain probability (p) that data is consistent with null hypothesis. p is small = high chance that effect is biologically meaningful/statistically significant if less than 0.05. Threshold decided before test.
Independent samples T-test
(t) Tests for a difference between means of two independent samples of continuous data. Are the samples from the same population with a single mean? Null is no difference between means, if true then t=0. If far from zero either way then not due to random choice and reject null so there is a difference between means. PARAMETRIC
Degrees of freedom
(df) modified sample size
One tailed test
test on specific null hypothesis ‘there is not a negative/positive relationship between A and B’. Interested in only positive or only negative deviations of statistic. p-value associated with a particular t value is halved.
Two tailed test
Test on general hypothesis ‘there is no relationship between A and B’ Interested in both positive and negative deviations of the statistic from its expected distribution.
Type I error
Rejection of null hypothesis when it is in fact true. Probability of making is easy to calculate, if p-value is less than 0.05 and we reject then there is a 5% chance it is in fact true.
Type II error
Failure to reject null hypothesis when it is in fact false. Harder to estimate, influenced by design of experiment, sample size and statistical test we choose.
Independence
Data points are independent if they have nothing special in common except for the treatment or variable of interest.
Confound
not being able to tell if any observed difference between two groups was a result of the treatment or if it was caused by the confounding variables.
Repeated measures
repeated observations made on the same subjects. Not independent.
Pseudoreplication
Use of non-independent data points as if they were actually independent e.g replicates that are from the same animal when seeing a difference between treatments.
Paired design
‘before and after studies’ collection of two samples that are not independent of each other. Average change in a variable caused by treatment, look at effect we are examining rather than variation between different individuals.
Homogeneity of variance
variance in each sample in the test is the same.
Transformation
when using parametric tests often assume data is normal. if not simple transformants e.g taking square root or log of data can solve it.
Paired t-test
T test analysing two samples of data in a pair (e.g before and after) Not independent.
Levene’s test
Test for homogeneity of variance. Null hypothesis is variances of samples are the same.
Shapiro-Wilk test
Test for normality, null is that the data are normally distributed. Significant p value means reject meaning data is not normal.
Two-sample Wilcoxon test
also known as Mann-Whitney U test, Non parametric equivalent of independent samples t-test. Examines difference between two samples of ranked data. Significant p value means reject null (two samples come from a single population with a single mean rank. samples are independent.
Welch two-sample t-test
If variances of samples are significantly different (levenes test) assumption of independent samples t-test are not met. Data must be normal, small tweak to degrees of freedom. difference between means of two independent samples of continuous data
Paired-samples wilcoxon test
Non-parametric equivalent of paired t-test. Examines difference between two samples of ranked data (Two-sample wilcoxon) but it doesnt assume samples are independent - asssumes paired.
Chi-squared test
(X^2) Examines differences between observed and expected counts or frequencies. Ask whether frequencies of individual observations made in two or more categories are significantly different from frequencies we would expect if null hypothesis is true. Quantify the deviation of observed frequencies from expected frequencies. Probability of finding a value of chi-squared at least as large as our observed value if null is true
Two way Chi-squared test
test when 2 sets of categories simultaneously. Quantify the deviation of observed frequencies from the expected frequencies.
Contingency table
Table of conserved counts or frequencies in a number of categories (male female, juvenile adult)
Trend
Relationship between two variables. +ve = both increase
Causal relationship
trend or relationship between two variables where changes in one causes change in the other.
Correlation
Changes in one variable coincide with changes in the other but causalty is not understood or important. CAn be a result of causal relationship but will aslo be generated when they share a common cause.
Covary
Variables that correlate
Pearsons correlation coefficient
Parametric test used to test the significance of correlations between two variables. Must be normally distributed and relationship must be linear.
Spearman’s rank correlation coefficient
(rho) non parametric statistic used to test significance of correlations between variables. Can be used when linearity and normality are violated.
Data Dredging
Use of certain statistics to test large numbers of possible relationships between variables in the absence of specific hypotheses formulated in advance. Spots patterns and generating new hypotheses, not used to assess nulls before data is collected.
ANOVA
analysis of variance. Tests for differences between groups or samples and caused by changes in more than one variable (factor), each difference value that each variable can take is a level. Tests one null.
Multi-way ANOVA
tests more than one null hypothesis simultaneously
F-ratio
statistic used to test null in ANOVA. Compares relative amounts of variation among (between) groups and within groups of sum of squares. Large value means large variation among compared to within and therefore our samples are likely to be significant. Can calculate a p-value for a particular value of F which tells us the probability of getting as much among-group variations we have observed if our null hypothesis is actually true.
Grand mean
Mean of all data points in groups in ANOVA.
Group mean
Mean of the data points in an individual group/sample in ANOVA. larger variation between groups means larger f becomes more likely to reject the null.
Among group sum of squares
(SSamong) total amount of variation among groups. add squared differences between each data point and the relevant grand mean.
Within-group sum of squares
(SSwithin) total amount of variation within groups, add up squared differences between each data point and relevant group mean
Among group mean square
(MSamong) average size of difference between group means and grand mean.
Within group mean square
(MSwithin) average size of difference between data points and relevant group mean
ANOVA table
results of ANOVA normally presented in table showing among and within groups sums of squares, mean squares, df and F and p.
Post-hoc tests
operate like simple t-tests telling us whether individual pairs of samples/levels are different. Chance of type I increases. E.g ANOVA proves difference between 3 data sets, post hoc decides how different they are from each other.
Residual
Difference between the prediction of your statistical model and an individual. In the contest of regression - residual is the distance along y axis between an individual data point and the line of best fit. Variation in y which is not explained by variation in x.
Kruskal-Wallis test
Non parametric equivalent of one-way ANOVA. Tests null hypothesis that there is no difference between mean ranks of two or more groups/samples. No assumptions. One factor at a time.
Interaction
interaction between two factors in ANOVA occurs when the effect of one factor on the response variable are influenced by another factor.
Nested ANOVA
analyse datasets which include some replicates which are not independent
Repeared-measures ANOVA
special form of nested ANOVA where non independent replicate data points are recorded at different times from the same individual.
Linear regression
parametirc test analysing relationships or trends where the pattern of cause and effect is known to exist or is of interest. Tests for effect of changes in one variable (independent = x) on changes in second variable (dependent = y). Tests the null that there is no relationship between changes in x and y. F is measure of amount of variation in y which is explaoned by variation in x large = small p. both are continuous and linear relationship, residuals are normally distributed.
Line of best fit
Line which represents the most plausible alternative hypothesis (the most plausible relationship between x and y)
r^2
more intuitive measure of the strength of the relationship we are studying/effect size. Proportion of the total amount of variation in y which is explained by variation in x. SSregression/SStotal.
Regression equation
Line of best fit. y=mx+c predicts values of y for a particular value of x but only within the range of x values available.
ANCOVA
analysis of covariance combines ANOVA and linear regression. test effects of a mixture of continuous and discrete independent variables in a continuous response variable.
Covariate
Describes a continuous independent variable in situations where there is a mixture of continuous and discrete independent variables.
SStotal, SSresidual, SSregression
Sums of squares used in linear regression allow us to quantify the amount of variation in y which is explained by variation in x. SStotal-SSresidual=SSregression (calculate the amount of variability in y that is actually explained by changes in x)
