Topic 3 : Introduction to hypothesis testing Flashcards
In hypothesis testing, sample statistics are
used to assess the probability that the hypothesis in fact represents the true state of affairs
What is hypothesis testing (2)?
What it is+ based on
- A statistical procedure: uses sample data to evaluate a hypothesis about a population
- based on probability theory and CLT
The focal hypothesis is the
null hypothesis
The Null hypothesis
What it is+population
- A statement about a population parameter that is assumed to be true unless there is evidence to the contary
- The hypothesis that our participants of interest came from the population of normal responders (Or the same population as the control group)
The alternative hypothesis
What it is+population
- Summarizes the expected or perdicted outcome of the investigation
- The hypothesis that our participants of interest did not come from the population of normal responders
We are testing —- and if we reject that, that means we have support for —–
- Hnull
- Ha
Directional hypothesis +ex (2)
What it is + test type+ ex
- states that one measure (e.g. the mean of experimental group) will be more than or less than a comparison measure (e.g mean of control group)
- 1 tail test
- Ex: Ha: We think that the experimental group will score higher than the score in control group
A non-directional hypothesis + ex (2)
- States that two measures will be different from eachother but does not specify the direction of the difference
- Ex: Experimental group could have scored higher or lower than control group
Null hypothesis contains a statement of
equality
less than or equal, more and equal, equal
Alternative hypothesis contains a statement of
inequality
Such as less than, more than, DNE
Test statistic+ ex
- The results of a statistical test relating observed scores (generally means) to a standardized distribution
- Z, t
P- value + ex (2)
- The probability of obtaining an observed test statistic (calculated from the sample data) with a value that extreme if the null hypothesis is true
- Ex: The people in your group become less depressed on their own, not because of your treatment” How likley is that = p value
A very small p-value means that such an extreme observed outcome would be very —- under the null hypothesis.
unlikely
Level of significance (4)
maximium+ probability+ denoted by+ ex
- Your maximium allowable probability of rejecting the null if it is true
- The probability of saying that the null is false when it is true
- denoted by alpha
- ex: a= 0.05
By setting the level of significance as a small value, you are saying that you (3)
criteria+ smaller signif indicates…+ lower
- are making a stricter criterion for rejecting the null hypothesis. This means you’re less likely to reject the null hypothesis unless there’s strong evidence against it.
- Typically, a smaller level of significance (like 0.01 or 0.001) indicates a higher confidence requirement to reject the null hypothesis, leading to a lower chance of making a Type I error (false positive).
critical value
The point at which we decide to reject the null hypothesis
Curve in the test statistic and critical value graph
the null population
Curve in the test statistic and critical value graph and the relatinship between our data
We want to see how unlikely our data of interest (experimental group) is part of this null population
Statistical significance
likelihood that the difference between two or more variables is caused by something other than chance
We use a left tail test when (2)
Ha
- we think the experimental group is lower than whatever we are comparing it too
- HA<
We use a right tail test when
Ha
Our sample comes from a population where the true mean of that population is greater than the null pop mean
- The alternative hypothesis Ha contains the greater than symbol (>)
We use a two tail test when
The alternative hypothesis Ha contains the not equal symbol
We always want to frame our desicion in terms of the
null hypothesis
Making desicion with Z-scores
compare Z-observed to Z-critical
For a left-tailed test, if z-observed is —- than z-critical, then reject H0
smaller
For a right-tailed test, if z-observed is —- than z-critical, then reject H0
larger
For a two-tailed test, if z-observed is —- than z-critical, then reject H0
more extreme
For a left-tailed test, if z-observed is —- than z-critical, then fail to reject H0
larger
Steps for hypothesis testing (5)
- Identify the null and alternative hypothesis
- Specify the level of significance (alpha)
- Find critical value associated with that level of signifcance and shade in rejection regions
- calculate the observed test statistic based on collected data
- Is the observed test statistic in the rejection region?
Type 1 error
Occurs if the null hypothesis is rejected when its true (no affect but you say there is)
Type 2 error
Occurs if the bull hypothesis is not rejected when it is false (You dont find evidence of an effect but there actually is)
Probability of type 1 error denoted by
alpha
Type 2 error is denoted by
beta
Power (2)
Probability of correctly rejecting false null hypothesis
Detecting an effect thats there
Using small alpha values reduce our chance of making a
type 1 error
Power of a test + formula
The probability of making a correct desicion and rejecting the null hypothesis when it is in fact false
1-B
Ways to increase power
- the larger the sample size, the greater power of the test
- The higher level of signifcance (alpha) the higher power(increase the size of the rejection region)
- The higher the effect size
Higher values of the t-score indicate that ——. The smaller the t-value, ——-.
a large difference exists between the two sample sets
the more similarity exists between the two sample sets
