Statistics

Descriptive statistics is what we can say about a sample by observing the sample itself. This is somewhat limited and mostly consists of summarisations of the data, e.g. like aggregates on a column in a database table.

Inferential statistics is what we can say about a population based on what we know about a sample. That means that we can infer (deduce or conclude from evidence rather than from explicit statements) about the population based on a smaller sample.

Probability is what we can generally say about samples from a population. So if we know 10 % of the population are left handed, we can expect 10 % of a sample randomly taken to be left handed.

One possible outcome of a a sample space. The sample space for tossing a coin is {head, tail}

A set of possible outcomes of an experiment. The sample space for tossing a coin is {head, tail}

An event is a possible outcome of an experiment, e.g. the event head when we toss a coin.

The probability of an outcome is always greater than 0 and less than 1, and the sum of the probability of all possible outcomes is 1, .

Centrality and variability Centrality: mean, median, mode

The mean / average is the sum of a value divided with the number of values. Most useful with homogeneous data - variables of one type. categorical or binary.

The exact middle value of the data set. If n is even, the median is the mean value of the two middle elements

The mode is the most frequent element. 1 , 1, 2, 3, 4 = mode = 1

Measure of the amount of variation on a set of values. Low standard deviation indicates that the values are closer to the mean - the distribution is less wide A high standard deviation indicates that the values are spread out on a wider range

Variability : Dispersion of the data Centrality: centrality measures determine the relative significance of a node in a social network

Correlation analysis is concerned with relations between variables, e.g. if one goes up, what happens to the other?

A correlation coefficient is statistic measure of the degree that one variable Y is a function of another variable X.

The correlation coefficient value ranges from -1 to 1, where 1 indicates perfect correlation, 0 indicates no correlation, and -1 indicates perfect negative correlation.

No

Used to infer about the population based on our knowledge about a sample.

In inferential statistics, the null hypothesis is a general statement or default position that there is no relationship between two measured phenomena An example: Hypothesis: drinking large amounts of alcohol makes you fall over. Null-Hypothesis: people will fall over the same amount whether they drink alcohol or not.

We usually take the approach of rejecting the null-hypothesis; saying that the idea that there is no correlation is unlikely • rather than confirming our hypothesis.

The confidence interval is the limits within which a certain percentage (say 95% or 99%) of sample means will fall. Given observations x1-xn and 95 % confidence level, there is 95 % probability of that the mean of a sample will fall in this interval

a result has statistical significance when it is very unlikely to have occurred given the null hypothesis.

Falsely rejecting the null-hypothesis - false positive. “You are pregnant” when he is not

Falsely accepting the null-hypothesis - false negative. “You are not pregnant” when she is