Statistic
A statistic is a piece of information that describes some aspect of a sample; statistics may be numerical or non-numerical.
Or a better definition:
Is a value that characterizes some aspect of a sample; the value of a statistic provides an estimate of the value of the corresponding parameter.
For ex, consider the heights of students in this class; possible statistics of interest include: average, maximum, minimum, standard deviation, number of students over 5’6”, etc.
Descriptive statistics
consists of methods used to organize and summarize information obtained from a particular sample
Inferential statistics
consists of methods used to draw conclusions (and measure the reliability of such conclusions) about a population based on information obtained from a particular sample
population
A population is the collection of all individuals or items under consideration in a statistical study.
Sample
A sample is the part of the population from which information is obtained.
parameter
A parameter is a particular value (usually unknown) that characterizes some aspect of the population
observational study
An observational study is a study where a researcher observes characteristics of subjects in samples from populations of interest,
i.e. a simple survey.
designed experiment
A designed experiment is a study where a researcher applies different treatments and controls and then observes the outcomes,
i.e. a controlled clinical trial.
(CONTROL AND RANDOMIZATION)
Drawing Conclusions from a Study
• In observational study, observed data already exist.
- Can only be used to make associative claims. B/c less control over confounding variables. (unknown variables that may influence our results)
• In a designed experiment, data doesn’t exist until the experiment is performed.
- Therefore, can be used to make causal claims.
• results of a study can be extended to population of interest if the sample is representative of the population.
What it means to be representative of a population?
sample expected to be representative of the population if subjects in the sample are randomly selected from the population.
= random sampling- all equally likely to be selected
2 types of conclusions we can reach from statistical studies.
- Population inferences: Results of the experiment can be generalized to a larger population.
- Causal claims: manipulated variable causes change in response.
The best way to obtain a sample that is representative of the population?
• is to sample the entire population, i.e. by conducting a census.
• However, conducting a census is very time consuming, expensive and sometimes impossible. Thus, we generally rely on sampling and experimentation
2 types of simple random sampling
- Sampling with replacement any member of the population can be selected more than once.
- Sampling without replacement a member of the population can be selected at most once.
