lecture 5 - inferential statistics Flashcards
(27 cards)
what is a statistical inference?
- undertaking a statistical test to make an inference about data
- two methods:
hypothesis testing (p values)
estimation (confidence intervals)
why do we undertake research using statistics?
- to test a hypothesis
- are the results real?
- do the results matter?
what do we mean by estimation?
- an estimator of a population parameter: a statistic (i.e. mean, t statistic)
- an estimate of a population parameter: the value of the estimator for a particular sample
what is a statistical hypothesis?
an assumption about a population parameter
- if sample data are not consistent with the statistical hypothesis, the hypothesis is rejected
what are the two types of statistical hypotheses?
null
alternative
what is the null hypothesis?
The null hypothesis, denoted by H0, is usually the hypothesis that sample observations result purely from chance.
what is the alternative hypothesis?
The alternative hypothesis, denoted by H1or Ha, is the hypothesis that sample observations are influenced by some non-random cause.
how to decide to accept or reject the null hypothesis?
Decision to accept or reject null hypothesis based on p value
<=0.05
P value α=0.05 (0.01 or 0.10)
Decided a priori
what is the meaning of the p value?
The p-value for a hypothesis test is the probability of obtaining a value of the test statistic as or more extreme than the observed test statistic when the null hypothesis is true
what does the p value give an indication of?
Reporting the p-value associated with a test gives an indication of how common or rare the computed value of the test statistic is, given that H0 is true
how is the rejection region determined?
by α, the desired level of significance, or probability of committing a type I error or the probability of falsely rejecting the null
why might results be uncertain?
Type 2 error- failing to reject the null hypothesis
Conclude no effect when there is one (False negative)
Small sample size can make this more likely
what are the types of error?
Type I
Type II
what is the probability of making a type I and II error?
The probability of making a Type I error is the significance level, or alpha (α), while the probability of making a Type II error is beta (β).
what is a type I error (false positive)?
the test result says you have coronavirus, but you actually don’t.
what is a type II error?
the test result says you don’t have coronavirus, but you actually do.
is more data better?
Collecting more data than is necessary is costly in many ways
You have the statistical power to pick up smaller and smaller differences and label them as ‘significant’
Therefore, as a researcher/scientist you have an obligation not only to look at significance but the difference between the groups in means that you are testing – e.g. is a difference of 0.1 seconds in mean running time scientifically/practically relevant even if it is statistically significant?
what does measuring difference or effect size mean?
Allows us not only to identify significance but also the level/ size of the effect observed
The simplest one is mean differences e.g. difference in mean height = 0.1cm BUT scale dependent and disregards distribution shape!
Need a measure that can have a consistent scale e.g. standard deviation units
what is the convention of effect size?
Brace et al. suggest calculating effect size for t-tests by looking at the difference between means and dividing it by the mean SD (z-score)
Advantage = converts mean difference into SD units
Disadvantage = works for t-tests only, but not ALL statistical tests
what are the suggested definitions by Cohen (1969) for effect size?
For the behavioural sciences, Cohen’s 1969 work suggests the use of the following criterion for size of effect using d
Small effect = 0.2
Medium effect = 0.5
Large effect > 0.8
Note: other definitions exist
what is good power?
Statistical convention says that 0.8 is a good value that minimizes both type I and type II errors.
Power 0.80 represents a 20% chance of making a type II error.
Before conducting your study should conduct a power calculation
University has G*Power
Involves estimating an effect size ahead of time.
what is power = to?
1 - β
what are confidence intervals?
Confidence intervals
Estimated range of values that is likely to contain the unknown population parameter
Conventionally 95%, also 90% or 99%
Width of these values describes uncertainty
Related to our effect size
what does the confidence level mean in context?
If this included zero, no statistically significant difference between groups.
Very wide confidence interval may indicate a small sample.
We interpret an interval calculated at a 95% level as, we are 95% confident that the interval contains the true difference between the two population means in the wider population that the sample is drawn from.
