Stats Flashcards
Type 1 error
A type 1 error (aka false positive) occurs when a researcher incorrectly rejects a true null hypothesis.
This means findings are reported as significant when they have actually occurred by chance.
o The risk of committing a type I error is reduced by using a lower value for p (e.g. a p-value of 0.01 means there is a 1% chance of committing a Type I error), also correct for multiple comparisons!
• Type 2 error
: A type II error (aka false negative) occurs when a researcher fails to reject a null hypothesis which is really false. Here a researcher concludes there is not a significant effect, when actually there is.
o The risk of committing a type II error is decreased by ensuring the test has enough power, which means having a sample size large enough to detect a practical difference when one truly exists
Null hypothesis
Proposes that no statistical significance exists in a set of observations and that effects seen are due to chance alone
Note: can never prove or disprove the null hypothesis, only provide insufficient/sufficient evidence to reject it
p value definition
The p value (a function of the observed sample results) is defined as the probability of obtaining a result equal to or more extreme that what was actually observed, assuming that the null hypothesis is true
Here, “more extreme” is dependent on the way the hypothesis is tested. Before the test is performed, a threshold value is chosen, called the significance level of the test, traditionally 5% (p<0.05) or 1% (p<0.01)
With p<0.05, a difference this big (or bigger) will occur 5% of the time (1 in 20) by chance (NOT that the chance of being wrong is 5%)
SD
Reflects the variability of means for a certain sample size, a measure of the precision with which the sample mean is estimated
Descriptive stats
Root variance
SEM
Standard error of the sample mean’s estimate of the true population mean.
It is a measure of the variability of means when many similar samples were taken from the population of possible measurements
SE = s/root n
Inferential statistics
Confidence intervals
Confidence intervals consist of a range of values (interval) that act as good estimates of/contain the unknown true population mean
A 95% confidence interval around the sample mean means that this interval will contain the true population mean 95% of the time
We can say that we are 95% confident that the true population mean is within this interval
95% CI = mean +/- (1.96xSEM)
The narrower the confidence interval, the more precise the estimate 🡪 as a general rule, as sample size increases the CI should become narrower
If CIs dont overlap with the means then we can say that there is a statistically significant difference at 0.05 significance level
However, if CIs include 0 we cannot say there is a significant difference - ‘does exam stress make people perform better or worse’
Effect size
effect size = mean of experimental group - mean of control group/SD (SD is pooled or averaged between groups)
Simpler way of wuantifying difference between groups - gives us an idea of the magnitude of the difference
Generally, effect size >0.8 indicates large effect
Effect size of 0.5 or 0.2 are considered moderate or small, respectively
Advantages:
Emphasises the size of the difference rather than confounding this with sample size
Particularly valuable for quantifying effectiveness of particular intervention
What will happen to SD and SEM as you increase sample size?
SD should in theory stay the same (imagine normal distribution)
SEM should decrease (disguise)
Why would you use SEM over SD?
To test differences between means rather than assess the spread and variability
T test
difference in means/SEM
Assumptions:
- Normality – populations tested must be normally distributed
- This can be tested graphically and/or statistically – Shapiro-Wilk test or Kolmogorov Smirnov test are frequently used
- Homoscedasticity (homogeneity of variance)
- The 2 samples tested should have the same finite variance, which can be tested for using Levene’s test
- Can get around requirement by using a ‘t test with unequal variance’ – uses an approximation
However, T tests (and ANOVAs) are generally very ‘robust’ and work well even if the above assumptions have been violated (especially the homogeneity of variance)
Z test
Used to determine whether 2 population means are significantly different when the variances are known and the sample size is large
The test statistic is assumed to have a normal distribution, and parameters such as SD should be known for accurate Z test to be performed
T test vs Z test:
- Z-test is a statistical hypothesis test that follows a normal distribution while T-test follows a Student’s T-distribution.
- A T-test is appropriate when you are handling small samples (n < 30) while a Z-test is appropriate when you are handling moderate to large samples (n > 30)
- T-test is more adaptable than Z-test since Z-test will often require certain conditions to be reliable. Additionally, T-test has many methods that will suit any need.
- T-tests are more commonly used than Z-tests.
- Z-tests are preferred than T-tests when standard deviations are known
ANOVA assumptions
Normal distribution of the dependent variable (population distributions are approximately normal)
Homogeneity of variances
Observations within each sample are independent of each other (does not apply for repeated measures ANOVA)
For repeated measures ANOVAs the assumption of sphericity must be met, which is the condition where the variances of the differences between all combinations of related groups are equal
Violation of sphericity is serious for RM ANOVA and causes the test to be too liberal (increase in type I error rate)
Repeated measures ANOVA
Equivalent to a one way ANOVA, but for related, not independent groups, and is the extension of the paired t test (needed if you are following one person over time and gathering multiple data points from them e.g. measure blood pressure at 5 time points for one person over the course of treatment)
Pearsons assumptions
WHat is r value?
Assumptions: relationship is linear, observations are independent
Pearson’s ‘r’ value is the correlation co-efficient derived by the product moment method
The ‘r2’ value is the square of this ‘r’ value and represents the ‘co-efficient of determination’
It ranges between 0 and 1 with 1 representing a perfect linear correlation between two variables
The p value gives the probability that the correlation is derived by chance alone.
