Test statistic
- (variance explained by model)/(variance not explained by model)
- effect/error
Type I error
- occurs when we believe that there is a genuine effect in our population when, in fact, there isn’t
- probability is the alpha-level (usually 0.5)
Type II error
- occurs when we believe that there is no effect in the population when, in reality, there is
- the probability is the beta-level (often 0.2)
Positive Study
- Significant difference Truth = difference - true positive Truth = no difference - type I error
Negative study
- No significant difference Truth = difference - type II error Truth = no difference - true negative
P - value
the level of marginal significance within a statistical hypothesis test representing the probability of the occurrence of a given event
Assumptions of a T-test
- data is measured as quantitative and continuous
- variances in these populations are roughly equal
- measurements in different treatments are independent (most important)
- data must be sampled from a normally distributed population
Homogeneity of variance
variances in populations are roughly equal
Homoscedasticity
variances in populations are equal
Heteroscedasticity
variances in populations are not equal
Calculating effect size
- signal/noise
- (difference between groups)/(variability of groups)
Rejecting or accepting null hypothesis using P-value
- the likelihood of observing the same or more extreme test statistic by chance alone, when hypothetically there can be no observable difference
- if p < 0.05 we reject our null hypothesis
Effect size
a standardised measure of the size of an effect
Standardised
comparable across studies
Cohen’s d
- an effect size used to indicate the standardised difference between two means
Calculating cohen’s d
d = (M1-M2)/SDpooled
Calculating SDpooled
sqrt((SD1^2+SD2^2)/2)
Pearson’s R
a measure of the linear correlation between two variables X and Y
Calculating pearson’s R
- make a table with x, y, xy, x^2 and y^2 along the top; sample number down side
- total all the columns
- (n∑xy-(∑x)(∑y)) / sqrt [n∑x^2-(∑x)^2][n∑y^2-(∑y)^2]
Small effect
r = 0.1
d = 0.2
the effect explains 1% of the total variance
Medium effect
r = 0.3
d = 0.5
the effect accounts for 9% of the total variance
Large effect
r = 0.5
d = 0.8
the effect accounts for 25% of variance
Reporting results of a t-test in APA style
the following should be reported:
- t
- df
- difference in means
- SD
- means
- p-value
- effect size (r or d)
