STAT1201 Data sheet 0 - 0.01 (Strong evidence) 1.1 - 0.05 (Moderate evidence) 0.05 - 0.1 (Weak evidence) 1.1 + (Inconclusive) General values: aggregate(LogAddedSugar ~ Sex, data=floss, mean) Ways of viewing the data: table(sleep$Disturbance) prop. table(table(sleep$Disturbance) ) xyplot(LogCadmium ~ Distance, data) To make something a factor: river$Flooding = factor(river$Flooding) (when the question asks, when the variable is categorical or when the df are funny). Interquartile range: Q3 - Q1 Five-number summary: Min, 0.25, 0.5, 0.75, Max Draw vertical lines at the 0.25, 0.5 and 0.75 quantiles to where they meet the curve and then follow them across to see the corresponding times. To find outliers from a five number summary: 1.5 x IQR -> subtract that value from the first quantile and then add to the third quantile for the reasonable bounds. Expected number = np Variance = Var(X)= (for each value of x (0, 1, 2, 3 etc.) you need to subtract the expected value (2), square this and times that by the probability) Sample Variance: s2 = SS = sum of squared derivations from the mean = mean Sample Standard Deviation: Predictor variable: make predictions from it (horizontal axis) Response variable: giving the response to the value of the other variable (vertical axis) Pearson correlation coefficient (r): measures the strength of a linear relationship. Least-Squares line: the line that minimises the sum of the squared prediction. ^yj=b0+b1xj Errors in prediction: ej=yj-^yj Area of a rectangle: base length x height (for a density curve the area must be 1) The area of a triangle is a half the base length times the height which again should equal 1 Eg. For triangles > P(160?X?175)=1-(P(X?160)+P(X?175)). We use to denote the conditional probability of _ occurring if _ has occurred P(A|B) = P (A and B) P(B) Multiplication rule: P(A and B) = P(A)P(B) Probability (eg. Deck of cards questions) = sum(dbinom(5:9, 9, 0.2) or
The probability P(X>6) can be found using sum(dbinom(x=6:9,size=9,prob=0.2)) or 1- pbinom(q=5,size=9,prob=0.2) in R. Expected value: if you look at just the statistics, the expected number of outcomes (the sum of all the outcomes multiplied by how often they occur) = Variance of a discrete random variable: Standard deviation of a discrete random variable : The expected value of a single random sample from a population is the population mean, The population standard deviation: The law of large numbers: as the number of trials increases, sample proportions get closer to probabilities and the sample mean gets closer to the expected value. Binomial Distribution (A Bernoulli trial): random process which has two possible outcomes, usually labelled 'success' and 'failure'. If X is the count from n-trials with success probability p then we write: X ~ Binomial (n,p). The count of successes in a series of independent Bernoulli trials, with a constant probability of success, has what is called the Binomial distribution. Note that if p=0.5 then the Binomial distribution is symmetric. If p<0.5 then the distribution is skewed to the right while if p>0.5 then it is skewed to