Chapter 11 Flashcards
(15 cards)
statistical inference
drawing conclusion about a population parameter from a sample taken from the population
parameter vs. statistic vs. population vs. sample
- Parameter: descriptive index of a population
- Statistic: descriptive index of a sample
- Population: complete set of observations (not people)
- Sample: subset of observations
hypothesis testing
- Making a hypothesized statement about population parameter and its outcome, and what sample results are likely to occur if this hypothesis is correct
- Understanding that the value of what we’re studying will vary from sample to sample
inferential statistics
- Use hypothesis testing: creating a hypothesis and evaluating it based on what type of sample results are likely to occur if it’s true (unlikely = reject)
- Using inductive reasoning to reason from particular (sample) to general (population)
- The value of what you’re studying will vary from sample to sample
- We want to discover what sample values will occur by chance, and with what probability
probability samples
samples for which the probability of each element’s inclusion of the sample is known (ex. Random sampling)
random sample
- sample drawn so that each possible sample has equal probability of being selected from the population
- Even though it’s random, the characteristics will still vary from sample to sample
- The larger the random sample, the less variation and less sampling error
- Results in equal probability of all possible samples, but not equal probability of all possible sample means
It is legitimate to generalize from random samples to the population
2 types of random sampling
- Sampling with replacement: an element may appear more than once in one sample
- Sampling without replacement: an element may appear only once in one sample -> Typical of behavioural sciences; standard error of the mean is smaller this way
casual sampling
human tries to act as a randomizer – this is ineffective – use a table of random numbers or a random number generator
random sampling distribution of the mean
The frequency distribution of sample means that would result if we drew a random sample of size n from the population, computed its mean, and then repeated the process many times
expected value
- mean of a random sampling distribution of X bar
- Is the same as the mean of the population of scores from which samples were drawn
- This is true regardless of n, stdv, or shape of population
standard error of the mean
- standard deviation of random sampling distribution of the mean
- Depends on n and stdev of population
- When n is small, Ox is large -> sampling errors are large
- When n is large, Ox is small -> sampling errors are small
- — As sample size increases, the magnitude of the sampling error decreases
- — If the sample size is quadrupled, the standard error of the mean will be cut in half
shape of sampling distribution of x bar
- If the population of scores is normally distributed, the sampling distribution of X bar will also be normally distributed, regardless of sample size
- The mean of X bar will equal mu
- Standard deviation of X bar is the standard error of the mean
central limit theorem
- regardless of shape of distribution in parent population, the sampling distribution of the mean approaches a normal distribution with greater n
- Sampling distributon of X bar may be treated as though it were normally distributed as long as there are at least 25+ cases, regardless of shape of distribution in parent population
2 generalizations of central limit theorem
- Even for non-normal parent populations, the shape of the sampling distribution of the mean rapidly approaches normality as n increases
- As n increases, the variability of the sampling distribution of X bar decreases; the decrease is accurately described by the standard error of estimate even if the parent population is non-normal
using the random sampling distribution of the mean to determine the probability with which sample means would fall between certain limits
68% are within 1 SD
95% are within 1.96 SD
99% are within 2.576 SD
