Inferential Statistics Flashcards
What form can inferential statistics take?
Estimation
Hypothesis Testing
Types for estimation
Point estimation
Interval estimation
What is estimation?
Using sample data we estimate the distribution of a parameter in the population from which the sample was drawn
What is point estimation?
Estimate a singe value for a parameter that will be close t true value of the parameter - effect size
What is interval estimation
Find an interval that has a given probability of including the true value of the parameter within its specified range
What is the interval in interval estimation?
Confidence interval
What is the probability in interval estimation?
Confidence coefficient
What is hypothesis testing?
We test the null hypothesis that a specified parameter of the population has a specified value by looking at the samples value
What are hypotheses?
Conjectural statements that provisionally link two variables
What are theories?
Sets of definite propositions or facts that are more or less verified already
How does one examine the relationship between two variables?
Probability theory
What is Poppers logic re hypothesis testing?
To prove something is very difficult.
To disprove something is relatively easy.
Hence science does not use the method of verification but methods of falsifiability.
What is the null hypothesis also known as?
H0
What do statistical methods try to do with respect to H0?
Try to refute this statement using statistical inference
What is another name for the alternate hypothesis?
H1
How can one state a hypothesis?
One-tailed
Two-tailed
What is a one tailed hypothesis?
Refers to the statement that differences between groups occurs in one direction only e.g. A->B
What would the alternative hypothesis be in a one-tailed hypothesis?
A is not -> B
What is a two-tailed hypothesis?
Refers to the statement that differences exist between two groups but the direction of the difference is not specified i.e. may be A->B or B->A
What would alternative hypothesis be in a two-tailed hypothesis?
A=B
What happens to significance levels in a two tailed hypothesis?
They are halved
Which type of hypothesis needs a larger difference to reject the null hypothesis?
Two tailed
Why do two tailed hypothesis need a larger difference to reject the null hypothesis?
Significance levels are halved
Which type of hypothesis are considered more rigorous?
Two-tailed
Why are two-tailed hypotheses considered more rigorous?
Significance level is halved so larger differences are needed to reject the null hypothesis
How is the null hypothesis tested?
By gathering data relevant to the hypothesis and determining how well it fits H0
What is used when we test how our data fits with H0?
Significant level, p
What is the significance level, p?
The probability of rejecting H0 when H0 is true
What does a higher significance level, p mean?
The higher the p, the better the fit between the data and H0
What does a low p value suggest?
Casts doubt upon the validity of H0
What can we assume if the value of p is very low?
We can reject H0
What are random errors?
Fluctuations in direction in measured data due to precision limitations of measurement devide
What are random errors often a result of?
Researchers inability to take measurement in the same way to get the same result
What are systematic errors?
Reproducible errors that are consistently in the same direction
What errors can occur during hypothesis testing?
Type 1
Type 2
What happens in Type 1 errors?
Incorrect rejection of the null hypothesis - false positive claim in favour of research hypothesis
What is the likelihood os a Type 1 error?
alpha
At what alpha level can we mainly avoid Type 1 errors?
<0.05
What is another name for alpha?
Level of statistical significance i.e. p
What can lead to Type 1 errors?
Repeated testing of hypothesis using same data
Multiple subset analysis
Secondary analysis
Why does multiple testing of same data lead to type 1 error?
At least one test will be positive in 20 if p is set at 0.05
What is a Type 2 error?
Incorrect acceptance of the null hypothesis - false negative rejection of research hypothesis
What is the name of the likelihood of a type 2 error?
Beta
What can lead to Type 2 error?
Small sample size
Large variance