research methods statistics Flashcards
what are the 3 criteria for choosing a statistical test
- looking for a difference or a correlation / association?
- is experimental design related (repeated measures / matched pairs) or unrelated (independent groups)
- what is the level of measurement
unrelated design
using independent groups
related design
using repeated measures or matched pairs
test of difference designs
- unrelated design
- related design
test of difference, unrelated design producing nominal data.
what is the appropriate statistical test
chi- squared
test for difference, unrelated design producing ordinal data
what is the appropriate statistical test
Mann- Whitney
test for difference, unrelated design producing interval data
what is the appropriate statistical test
unrelated t-test
test for difference, related design producing nominal data
what is the appropriate statistical test
sign test
test for difference, related design producing ordinal data
what is the appropriate statistical test
Wilcoxon
test for difference, related design producing interval data
what is the appropriate statistical test
related t- test
test for association or correlation producing nominal data
what is the appropriate statistical test
chi- squared
test for association or correlation producing ordinal data what is the appropriate statistical test
spearman’s rank
test for association or correlation producing interval data
what is the appropriate statistical test
pearson’s rank
chi- squared test
used as a test of both difference and association / correlation.
data items must be unrelated
- test of difference, unrelated design, nominal data
or
- test of association or correlation, nominal data
mann - whitney
test of difference
unrelated design
ordinal data
unrelated t-test
test of difference
unrelated design
interval data
sign test
test of difference
related design
nominal data
wilcoxon
test of difference
related design
ordinal data
Related t test
test of difference
related design
interval data
spearman’s rank
test of association or correlation
ordinal data
pearson’s rank
test of association or correlation
interval data
nominal data
categories
each item can only appear in one category. there is no order.
e.g people naming their favourite football team.
ordinal data
placed in order, intervals are subjective
data is collected on a numerical, order scale but intervals are variable, so that a score of 8 is not twice as much as a score of 4
ordinal data lacks precision because it is based on subjective opinion rather than objective measures
there is no units
e.g asking someone to rate how much they like psych on a scale of 1 to 10 where 1 is do not like at all and 10 is absolutely love
interval data
units of equal size
interval data is based on numerical scales that include units of equal, precisely defined size.
this includes observations in a observational stay (8 tallies is twice as much as 4 tallies) or any public units of measurement (time, temperature, length)
interval data is better than ordinal data because more detail is preserved as the scores are not converted to ranks
what happens if the statistical test is not significant
the null hypothesis must be accepted
the null hypothesis states there is no difference or no correlation between the conditions
the statistical test determines which hypothesis (null or alternative) is true and thus we accept or reject.
the null hypothesis is accepted or rejected based on what
particular level of probability
probability is a measure of the likelihood that a particular event will occur, where 0 is a statistical impossibility and 1 a statistical certainties in psychology but there is a significance level - the point at which the null hypothesis is accepted or rejected.
what level of significance is used
0.05 or 5%
this means the probability that the observed effect occurred by chance is equal to or less than 5%
the calculated value
the value you calculate from the statistical test. this is compared to the critical value
what is the critical value
fund from the table of critical values at the 0.05 significance. based on probabilities
the calculated value is compare to the critical value
how do you find the correct critical value ( 3 criteria)
- hypothesis one tailed (directional) or 2 tailed (non directional)
- number (N) of participants or degrees of freedom (df)
- level of significant (or p value) 0.05
what is a type 1 error
the null hypothesis is rejected and the alternative hypothesis is accepted when the null hypothesis is true
this is an optimistic error or false positive as a significant difference or correlation is found when one does not exist.
what is a type 2 error
the null hypothesis is accepted but in reality the alternative hypothesis is true
this is a pessimistic error or false negative
why is a type 1 error is likely
is more likely to be made if the significance level is too lenient (too high e.g 0.1 or 10%)
when is a type 2 error likely
more likely if the significance level is too stringent (too low e.g 0.01 or 1%) as potentially significant values may be missed
what is an correlations
it illustrates the strength and direction of an association between 2 co-variables
what is a positive correlation
co-variables rise or fall together
what is a negative correlation
one co-variable rises and the other falls
what are the differences between correlations and experiments
- in an experiment the researcher manipulates the IV and records the effect on the DV. In a correlation there is no manipulation of variables and so cause and effect cannot be demonstrated
- in correlation the influence of EVs is not controlled so it may be that a third untested variable is causing the relationship between the co-variables (called an intervening variable)
evaluation of correlations
+ useful starting point for research. by assessing the strength and direction of a relationship, correlations provide a precise measure of how 2 variables are related. if variables are strongly related it may suggest hypothesis for future research
+ relatively economical. unlike a lab study, there is no need for a controlled environment and no manipulation of variables is required. correlations are less time-consuming than experiments
- no cause and effect. correlations are often present as causal when they only show how 2 variables are related. there may be intervening variables that explain the relationship
- methods used to measure variables may be flawed. for example, the method used to work out an aggression score might be low in reliability (observational categories might have been used). this would reduce the validity of the correlation study
what are the measures of central tendency (3)
- mean
- median
- mode
what is the mean (and evaluate)
arithmetic average, add up all the scores and divide by the number
+ sensitive. includes all the scores in the data set within the calculation. more of an overall impression of the average than median or mode
- may be unrepresentative. one very large or small number makes it distorted. the median or the mode tend not to so easily.
what is the median (and evaluate)
middle value, place scores in ascending order and select middle value. if there are 2 values in the middle, the mean of these is calculated
+ unaffected by extreme scores. the median is only focused on the middle value. it may be more representative of the data set as a whole
- less sensitive than the mean. not all scores are included in the calculation of the median. extreme values may be important
what is the mode (and evaluate)
most frequent or common value, used with categorical / nominal data
+ relevant to categorical data. when data is discrete i.e represented in categories. sometimes the mode is the only appropriate measure.
- an overly simple measure. there may be many models in a data set. it is not useful way of describing data when there are many modes.
what are the measures of dispersion (2)
- range
- standard deviation
what is range (and evaluate)
the difference between highest to lowest value (+1)
+ easy to calculate. arrange values in order and subtract largest from smallest. simple formula, easier than the standard deviation
- does not account for the distribution of the scores. the range does not indicate whether most numbers are closely grouped around the mean or spread out evenly. the standard deviation is a much better measure of dispersion in this respect
what is standard deviation (and evaluate)
measure of the average spread around the mean. the larger the standard deviation, the more spread out the data are.
+ more precise than the range. includes all values within the calculation. a more accurate picture of the overall distribution of the data set
- it may be misleading. may hide some of the characteristics of the data set. extreme values may not be revealed, unlike with the range
what is a normal distribution
symmetrical, bell shaped curve. most people are in the middle area of the curve with very few at the extreme ends.
the mean median and mode all occupy the same mid point of the curve
what is a skewed distribution
distribution that lean to one side or the other because most people are either at the lower or upper end of the distribution
what is a negative skew
most of the distribution is concentrated towards the right of the graph, resulting in a long tail on the left.
mode is the highest point of the peak then the median next to the left and the mean is dragged across to the left (if scores are arranged from lowest to highest)
what is a positive skew
most of the distribution is concentrated towards the left of the graph resulting in a long tail on the right
the mode is the highest point of the peak, the median comes next to the right and the mean is dragged across to the right (if scores are arranged from lowest to highest)
significance
the difference/ association between 2 sets of data is greater than what would occur by chance - coincidence or fluke.
to find out if the difference / association is significant we need to use a statistical test
how do you calculate the sign test
(test of difference, related design - nominal data)
1. the core for condition B is subtracted from condition A to produce the sign of difference (either a + or a -)
2. the total number of + and the total number of - should be calculated
3. participants who achieved the same score in condition A and condition B should be disregarded, and deducted from the N value.
4. the S value is the total of the less frequent sign
if S is equal or less than the critical value, then S is significant and the experimental hypothesis is retained.
