t-test Flashcards
t-test
- when we have 1 IV with 2 levels
- estimates whether the population means under the 2 levels are different
- estimates based on difference between the measured sample means
independent t-test
between participants / independent groups
paired t-test
within participants/ repeated measures
true experimental
random allocation
variance between IV levels
variance we assume is accounted for by manipulation of IV
variance within IV levels
difference between participants within the groups (levels)
- reflected by standard deviation
how does variance between IV levels arise
- manipulation of IV
- individual differences
- experimental error
experimental error
random or constant
random error
chance fluctuation in measurement
e.g. hitting stop watch too early or late
constant error
confounds that influence measurement of DV between IV levels
- bias
e.g. giving one group practice and one group not
sources of variance within IV levels
- individual differences
- experimental error (random not including constant)
null hypothesis
- no difference between the population means and sample means
- H0: u1-u2=0
or
u1=u2
what does t-distribution represent
- distribution of sampled mean differences when the null hypothesis is true
features of t-distributions
- mean of 0
- ## s.d. = s.e
s.e.
standard error
the extent to which an individual sampled mean difference deviates from 0
t-value
difference between sample means
reflected in standard error units
(don’t need to memorize formula)
ESEd
s=variance
n=sample size
t-value closer to 0
small variance between IV levels relative to within IV levels
t-value further from 0
larger between IV levels than within IV levels
- shows difference of manipulation of IV
in order to claim value of t is significant…
it must fall outside of the 95% bounds, in the 2.5% tails
if t > critical value
reject the null
larger degrees of freedom
more reliable the estimate
d.f. fro 2 sample independent t-test
what is t-distribution mediated by
degrees of freedom
assumptions of independent t-tests
- normality
- homogeneity of variance
- equivalent sample sizes
- independence of observations
normality - independent
DV should be normally distributed, under each level of IV
homogeneity of variance
the variance in the DV, under each level of the IV, should be reasonably equivalent
- check using Levene’s test in SPSS
Levene’s test
SPSS
- we want a non-significant result
- under H0: no difference between variances under each level of IV (homogeneity)
- but it p<0.05 we reject null - heterogeneity
- use row below is violated
independence of observtions
scores under each IV level should be independent
what do we do if we violate assumptions of independent t-test
Mann-Whitney U test
p<a
reject null
how to get a t-test result from SPSS output
paired t-test
- related/ dependent t-test
- used for within-subjects/ repeated measures design
t calculation for paired
don’t need to memorize
what contributes to variance for within-subjects design
- experimental error
- manipulation of IV
assumptions of paired t-test
- normality
- sample size roughly equal
normality - paired
- distribution of difference scores between IV levels should be aprox. normal
- ok to assume if n>30
non-parametric equivalent of paired t-test
Wilcoxon T test
- if assumptions are violated
paired t-test: SPSS output
degrees of freedom for paired t-test
df = ( n - 1)
effect size measure
Cohen’s d
Cohen’s d
the magnitude of difference between two IV level means, expressed in standard deviation units
Cohen’s d formula
… ignore the sign (remove negative sign)
- express to 2 d.p
interpreting Cohen’s d effect size
e.g. bigger effect size, further apart population means, less overlap
t
magnitude of difference between two IV level means, expressed in ESE units
why t not Cohen’s d
takes sample size into account
t-test design write up
- IV: levels, subjects design (between or within), steps taken to eliminate confounds (random allocation for IT or counterbalancing for paired)
- DV: what was measured
t-test results write up: step 1: descriptive statistics in the table
in table put:
- measure of central tendency as mean
- measure of spread: standard deviation
- interval estimates: 95% confidence interval around mean (upper and lower)
t-test results write up: step 2: results of inferential statistics
- Descriptive statistics are reported in table 1
- state test used (paired of independent t-test) and what it revealed e.g. an independent t-test revealed that dog owners told that their dog showed potentially were significantly quicker to complete the course than those owners told their dog had no potential,
- state test statistic as t(df) = _.__, p = .__
- if needed (equal variances not assumed)
- state if result was significant and direction of significance (which IV was higher)
- mean difference and 95% CIs around mean difference
- the effect size: Cohen’s d (if significant report as small, medium large, if not significant report alongside t statistic after p value)
- e.g. the mean time difference was 87.80 seconds (95% CI [x,x], demonstrating a large effect size, d = X.
discussion
summary of findings with no statistical jargon e.g. no significant
- provide direct answer to research question
e.g. paired- we found evidence of an impact of alcohol consumption of students’ performance on an arcade game.
e.g. independent- dog owners advised their dog showed agillity potential achieved faster course completion than those advised their dog did not showe potential. Manipulatin the information given to the owners about their dog’s agility potential appears to have influenced their later agility performance
