FDA CA 1

Population

The entire set of relevant units of analysis.

Parameter

The value of a variable that characterises a population.

Sample

Any subset of the population.

Statistic

The value of a variable that characterises a sample.

Representative Sample

A sample is a good representative as long as it is randomly taken.

Sample Size vs. Reliability

Sample size does not determine reliability, but rather the precision of the sample.

Sample Size and Standard Error

With increasing sample size, standard error decreases.

Theorem

A mathematical statement that is proven to be true.

Dogma

An absolute thing (unquestionable statement).

Sample Size and True Population

The larger the sample size, the closer the sample is to the true population.

Fluctuation

It is linked to sample size.

Inaccuracy and Sample Size

Inaccuracy (lack of precision) stems from the sample size being too small.

Standard Error

Standard deviation of the standard distribution.

Confidence Interval (CI) and N

When N increases, the CI becomes more precise.

Point Estimates

The sample mean if obtained at random (nearly always wrong as subject to sampling error).

Interval Estimates

Specify a range of values instead of only one (more appropriate than point estimates).

Confidence

The probability that a specified interval contains the unknown population parameter.

X

Euler constant.

Probability

Area under the curve.

Two kinds of errors in samples

Random sampling errors and bias.

absolute zero

absence of what you are measuring

Packages

collections of R functions, data, documentation and compiled code in a well-defined format

Library

The directory where packages are stored

unit of analysis

where/who variables are being measured off of (atom of your research)

Nominal

classification (categorical)

Ordinal

classification and logical order (categorical)

Interval

classification + logical order + equal intervals (continuous)

Ratio

classification + logical order + equal intervals + absolute zero (continuous)

Variable

a characteristic that differs from subject to subject or time to time

2 tests for a null hypothesis (Difference in means)

• Is p < significance level (0.05) (yes? Reject H0)

• does the 95% confidence interval exclude expected value of H0? (yes? reject H0)

Signal/noise ratio

The basic rationale of any statistical test

Significance level (a)

The level of probability that determines which sample means are considered 'acceptable'

95% confidence = ?

a = 0.05

Level of risk relative to null hypothesis

Level of significance

Abstraction (in mind) in statistics

• Sampling distribution

• expected value under H0

• critical values

• acceptance/rejection regions

• significance level a

Data (observation) in statistics

• Empirical observations (realisations)

• observed statistics (a point estimate e.g. mean)

• test statistics (signal/noise) e.g. t-statistic

• confidence interval

• p-value

what is continuous data?

data that is measured, not counted and has infinite possibilities

what is discrete data?

data that is counted, not measured and has finite values

whats a type 1 error?

Type I (False Positive): A doctor tells a man that he is pregnant. (Obviously impossible)

whats a type 2 error?

Type II (False Negative): A doctor tells a clearly, heavily pregnant woman that she is not pregnant. (Missed the obvious reality)

statistically significant

- reject the null hypothesis(p or CI)
- observed difference is highly unlikely to be caused by randomness alone

non statistically significant

- fail to reject the null hypothesis
- observed difference is too small to conclude that drug has any effect and result isn’t solely random.

H0 (null hypothesis)

The drug does nothing

H1 (alternate hypothesis)

the drug does something

What is the best way to reduce the background noise and make your confidence interval narrower?

increase the sample size

which plots are used for univariate data

histograms and bar charts

which plots are used for bivariate data

dot plots and boxplots

modes of central tendency for a left skewed (negative) distribution

mean, median. mode

modes of central tendency for a right skewed (positive) distribution

mode, median, mean

When is correlation used?

When studying the possible association between two continuous variables

what is relative risk (RR)?

measures the strength and direction of the association of two categorical variables

what is a symettrical distribution?

mean = mode = median

symmetric distribution

mean = median = mode

unimodal

one mode only

Low SD

data tightly packed (tall narrow peak)

High SD

data heavily spread out (short, wide, flat hill)

what is another name for alpha?

Type 1 error(significance level)

In what type of distribution does the median come before the mean?

positively skewed distribution

what is a uniform distribution?

A distribution where every outcome has an equal chance of occurring

when is the expected value not 0?

when the true mean of the population is given and when there is a control and test group

what does he central limit theorem state as n increases?

the sampling distribution of the sample mean approaches a normal distribiution

standard error formula

SD / root of n

what is the dependent variable?

The outcome or response variable being predicted or explained by the model

what is the independent variable?

The explanatory or predictor variable

what data requires histograms?

continuous numerical data

what data requires bar charts?

categorical or nominal data

At what n value is the sampling distribution approximately normal?

when n is greater than or equal to 30

standard error relative to precision

A small standard error reflects high precision