statistics
percentage change
difference/original × 100
measues of central tendency
mean - modt sensitive
median - middle
mode - most frequent
measures of dispersion
range
standard deviation
mean
strengths: all data points are used (represented)
issues: distorted extreme scores
*we calculate when there are no extreme values
median
strengths: not affected by extreme scores, easy to calculate
issues: does not include all of the values
*use with extreme scores as it is representative and not as sensitive as the mean
mode
strengths: can be used for categorical data e.g. car, bus, not distorted by extreme scores
issues: does not include all the values
range
strengths: easy to calculate
issues: is easily distorted by extreme values
standard deviation
strengths: includes all values, making it more sensitive
issues: is distorted by extreme scores, more difficult to calculate than the range
skewed distributions
mode is always the highest point
median is always in the middle
mean is always the lowest point
normal distribution
symmetrical, bell-shaped, curve
raw dates tables
a record of individual data points collected from participants (repeated measures design)
frequency tables
tally charts
bar charts
show frequency data for discrete (separate) categorical/nominal variables
use bar charts when there us discrete or categorical/nominal data
y-axis: DV
x-axis: IV
bars DO NOT touch
histograms
y-axis: frequency of numerical data
x-axis: continuous variables
use histogram when there is continuous data
bars DO touch
correlation
relationship between covariables, use secondary data
experiment
manipulate the IV and measure the effect on the DV
correlation coefficient
used to measure the strength and nature of relationship between two covariables
strength and issues of correlation techniques
strengths: can provide valuable insight for future research, the secondary data can be used, which alleviates the concern over informed consent as the information is already in the public domain
issues: it is not possible to establish a cause and effect relationship, correlation only identifies linear relationships
statistical table
test of difference or test of association or correlation
related design or unrelated design
nominal data: sign test, chi-squared
at least ordinal data: wilcoxon, mann-whitney, spearman's rho
interval data: related t-test, unrelated t-test, Pearson's r
nominal data
categorical discrete data
e.g. country of birth, career choice
strength: easily generated from closed questions
issues: not possible for the data to express is true complexity, therefore it can appear overly simplistic
ordinal data (ranking)
categorical data have a natural order
e.g. rate of happiness, height of students
strengths: provides more detailed than nominal data as scores are ordered
issues: intervals between scores are not of equal value
there us not an equal distance between each point
interval data
dada that is ordered in some way, continuous
e.g. temperature, time, speed, age
strength: more informative, more reliable
issues: intervals are arbitrary
exists an equal distance between points
p = <0.05 (why the p-value of 0.05% significance is used by researchers)
there is less than a 5% likelihood that the findings gained are due to chance
there is a 95% confidence level that the findings were caused by the variable interaction
critical values
1.one-tailed or two-tailed
2. number of participants
3. level of significance or p-value
type 1 error + type 2 error
type 1: where are the null hypothesis is rejected in the alternative hypothesis is accepted
a researcher will have concluded that the results are statistically significant when in fact they are not
false positive
if the p value is too lenient (0.1) a type 1 era may have been made
type 2: exact opposite (too strict) (0.01)
statistical test question layout
the mann-Whitney statistical test is the most appropriate because this experiment involves a test of difference and uses an independent group design (unrelated) because the participants were randomly allocated to two different conditions. furthermore the data is ordinal as participants can be ranked.
statistical table question layout
the psychologist will not be able to accept the hypothesis. this is because the calculated value for a two-tailed (non-directional) test where n=15 and p=0.05 is 27 in this is greater than the critical value, which is 25.
statistical test question layout correlation
where DF is 1, the critical value for a one-tailed test, where p=0.05 is 2.71. as the calculated value is 2.981 (greater) it is significant at the 5% level.
calculating sign test
1. directional or non-directional
2. + or - or 0
3. calculate calculated value of S
e.g. 7- and 2+ SO S=2 }smallest
4. calculate value of N (number)
e.g. scores - number of 0s
5. find critical value
6. determine whether results are significant or not
7. write the conclusions
conclusions of sign test
there is no significant difference in the number of objects were called in the morning, compared to the afternoon, as the critical value for a two-tailed (non-directional) test where n=8 using the 0.05 level of significance is 0. as the calculated value of 2 is greater than the critical value of 0, the difference is not significant.
choosing a statistical test layout (difference)
chi-squared. the study is looking for a difference in food preferences between males and females. the study used in independent group's design as participants were either male or female. the data is nominal (categorical) as it involves counting the preference for either chocolate or crisps
choosing a statistical test (relationship)
spearmans rho. the study is looking at relationship/correlation/association between students rating of the memory ability and scores on a memory test. given that students rate, we can assume the data is at least ordinal as their exists a continuous scale of measurement and there is not an equal distance between each point