Research Methods Modules Flashcards
difference
is one group of people different to another in some way?
association
is one construct related to another?
prediction
does one construct influence another?
goal of psychological research
to make inferences about a population (inferring that what is typical for sample is typical for population)
population
everyone of interest to a research question
distributions of data can be described according to their
central tendency (eg. Mean) and variability (eg. Standard deviation)
the normal distribution
majority of observations in the middle, observations reduce in frequency towards the tails, the distribution is symmetrical
in a normal distribution, most observations are closed to m; these scores occur more
frequently; typical
the 2s Rule of Thumb
in a distribution with a normal shape, 95% of scores fall within approximately 2 standard deviations from the mean. These scores are typical
typical scores
are expected and occur frequently
extreme scores
are not expected and occur infrequently
distribution of sample means
made up of the sample means from all of the random samples of a certain size (n) that could possibly be obtained from a population
Central Limit Theorem tell us
the precise characteristics of a distribution of sample means for samples of any size (n). The distribution of sample means has equal mean to the population mean, for large sample sizes, the distribution of sample means will be normal, details of standard error, as sample size increases, standard error decreases and estimation of population mean becomes more precise
standard error
standard deviation of the distribution of sample means
when sample is large enough, it provides
a reliable estimate of the population mean
z-test standard error formula
standard error = standard deviation of population/(number of people in sample)^1/2
we can use 2s Rule of Thumb to test if our SAMPLE MEAN
is typical or extreme
hypothesis
a statement that predicts that something is going to happen
experimental hypothesis/alternative hypothesis
a statement that predicts an effect (one of difference or association)
null hypothesis
predicts that nothing is happening; a hypothesis of no effect (no difference, no association)
only one of null/experimental hypothesis can be
supported by research data at any one time
null hypothesis statistical notation
H0
experimental hypothesis statistical notation
H1
null hypothesis significance testing
propose a null hypothesis that a population parameter (mean) has a particular value. Proceed assuming the null hypothesis is true. Determine the probability of the sample mean occurring if the null hypothesis is true. If the probability of the sample mean occurring is small, reject the null hypothesis. If the probability is large, do not reject the null hypothesis
if the probability of the sample mean occurring is small,
reject the null hypothesis. Evidence for a difference. Extreme sample mean
if the probability of the sample mean occurring is large,
do not reject the null hypothesis. No evidence for a difference. Typical sample mean
determine the probability of the sample mean occurring if the null hypothesis is true. In other words,
what is the likelihood of our sample mean occurring if the mean of the population really is the value we predicted in the null hypothesis?
how to determine the probability of the sample mean occurring if the null hypothesis is true
involves a statistical test based on a normal distribution of sample means with the mean we predicted in our null hypothesis. Calculating critical limits to determine if our sample mean is typical or extreme
the 5% Alpha Level
defines which sample means in a distribution of sample means are expected or typical, and which are unlikely or extreme, if the null hypothesis is true
when the comparison distribution is perfectly normal, the critical limits set by the 5% Alpha Level are precisely
+/- 1.96 standard errors from the mean. 95% of the scores are inside these limits
if our sample mean is inside the limits set by the 5% Alpha Level, the probability is
greater than 5%, and therefore high (do not reject the null hypothesis)
if our sample mean is outside the limits set by the 5% Alpha Level, the probability is
less than 5%, and therefore low (reject the null hypothesis)
single sample z-test
how we determine the probability of our sample mean occurring after setting an Alpha Level of 5%
z-score
how many standard errors our sample mean is away from the null hypothesis
single sample z-test formula
z-score for sample mean = (sample mean - population mean)/(z-test standard error)
in single sample z-tests, the population standard
deviation is known
once z-score has been calculated, check whether it is more extreme than
+/- 1.96
if z-score is more extreme than +/- 1.96, the probability of sample mean occurring assuming the null hypothesis is true is
less than the Alpha Level of 5%, so probability is low and null hypothesis is rejected
steps for determining whether sample mean provides evidence to support null hypothesis or not
set Alpha Level (5%) then calculate z-score
we can’t use a single sample z-test and the normal distribution when the
population standard deviation isn’t known
we use the t-test and ‘t-distribution’ when
the population standard deviation isn’t known
in single sample t-tests, we use the sample standard deviation as an
estimate of the population standard deviation
t-test standard error formula
standard error = standard deviation of sample/(number of people in sample)^1/2
t-test formula
t-score for sample mean = (sample mean - population mean)/(t-test standard error)
almost all aspects of the process are the same when conducting a
single sample z-test or t-test
in the t-distribution, critical limits corresponding to Alpha Level of 5% will not be fixed at
+/- 1.96 as in z-test
t-distributions require that we consider
sample size and degrees of freedom (df)
degrees of freedom
one less than our sample size for single sample t-test (n-1)
critical limit in single sample t-test varies
along with df
to check if t-score is more extreme than critical limit taking df into account, use
SPSS or look up in back of textbook
Alpha Level of 5% still applies in t-tests, it’s just that we can’t automatically assume
critical limits of +/- 1.96
test value in SPSS value is the
null hypothesis value