Flashcards in Part 3B Deck (34):
random variability between observations or statistics that is simply due to chance
how to assess sampling error:
the distribution of a statistic over repeated sampling from a specified population (a distribution of means)
what is the formal procedure for hypothesis testing?
1. start with sample of participants that is the same as a specific population (null hypothesis)
2. find out what population does
3. compare participants to that standard
how are sampling distributions created?
formed when samples of sample size n are repeatedly taken from a population
properties of sampling distributions of sample means
1. the mean of the sample means is equal to the population mean
2. the standard deviation of the sample means is equal to the population standard deviation divided by the square root of the sample size n (standard error of the mean)
the Central Limit Theorem
the larger the sample size that we draw from a population, the more normal the sampling distribution of the sample means become regardless of shape of population
Central Limit Theorem: if sample sizes of n greater than or equal to 30 are drawn from any population...
then the sampling distribution of the sample means approximates a normal distribution
Central Limit Theorem: if the population itself is normally distributed...
the sampling distribution of the sample means is normally distributed for ANY sample size n
what is the purpose of hypothesis testing?
to consider the probability that the results of a study could have come about if the experimental procedure had no effect (i.e. if null hypothesis is true)
a statement, or claim, about a population parameter
the alternative hypothesis
the hypothesis that participants did not come from the population of normal responders
the null hypothesis
the hypothesis that participants came from the population of normal responders
null hypothesis and alternative hypothesis must:
COMPLEMENT EACH OTHER
level of significance
maximum allowable probability of rejecting the null if it is true (the point at which the null is probably false) alpha=0.05
these present the point at which the null hypothesis is rejected (ex. reject when p<0.05)
reject null if:
we exceed the critical value
the results of a statistical test relating observed scores (generally means) to a standardized distribution
p-value (probability value)
the probability of obtaining an observed test statistic (calculated from the sample data) with a value that extreme if the null hypothesis is true
a set of measurements or observations in a study is statistically significant if it is unlikely to have occurred by chance (ex. less than 5% chance)
what are the types of hypothesis tests
one-tailed or two-tailed
rejects null if obtained value is too low or too high, only set one side/direction for rejection (i.e. Ha is DIRECTIONAL)
rejects null when obtained value is too extreme in either direction (i.e. Ha is NON DIRECTIONAL) (divide each tail to get 1/2 alpha level p)
Ha contains the symbol
Ha contains the symbol >, alpha (critical region is the area to the right of the test statistic)
Decision Rule based on test statistic (z)
z-observed>z-critical, reject Ho
conclusion of decision should always be phrased:
in relation to null hypothesis
to determine whether some factor is causal to the result, requires:
conducting an experimental study
at the end of the test, what are the two possible decisions?
reject null hypothesis or fail to reject null hypothesis
type I error
null hypothesis rejected when it is true
type II error
nulls hypothesis is not rejected when it is false
which error is preferable?
type II error (better than claiming an effect in error)
probability of correctly rejecting false null hypothesis