Statistics: Significance Tests About Hypotheses Flashcards
What is the function of a significance test?
Used probability to provide a way to quantify how plausible a parameter is while controlling the chance of an incorrect inference.
What is a hypothesis in statistics?
A hypothesis is a statement about population, usually claiming that a parameter takes a particular numerical value or falls within a certain range of values.
WHat are the 4 steps of a significance test
- Assumptions
- Hypotheses
- Test statistic
- P-Value
- Conclusion
What may be involved in assumptions of a significance test
Randomisation used to data production, sample size or shape of population distribution.
Name and explain the two hypotheses about a population parameter:
The null hypothesis (H0) is a statement that the parameter takes a particular value while the alternative hypothesis (Ha) states that the parameter falls within a particular range of values. The null hypothesis usually represents no effect while the alternative hypothesis represents some effect.
What is meant by a test statistic? How is it measured?
How far the point estimate falls from the parameter given in the null hypothesis. This is usually measured by the number of standard errors between the point and the parameter.
What is meant by the P-Value?
The probability that the test statistic equals the observed value or a value even more extreme. It is calculated by presuming that the null hypothesis H0 is true. The smaller the P-Value the more likely the alt. hypothesis is true.
When can we reject the null hypothesis?
When the P-Value is very small such as 0.05.
What assumptions are involved in a significance test of a proportion?
Variable is categorical, Data obtained through randomization, Sample size is sufficiently large and sample proportion is approximately normal.
What form does the null hypothesis of a proportion take?
H0:p=p0
Differ between one sided and two sided alternative hypotheses
One sided only has values falling on one side of the null hypothesis value ( Ha: p>p0, (1/3)) while a two sided hypothesis includes all the possible values (Ha: p=/= p0 (1/3))
How do we calculate a two sided significance test?
By finding the tail probability in a single tail and doubling it.
What is a significance level?
a number such that we reject H0 if the P value is less than or equal to that number . This is usually 0.05
When are the results statistically significant?
When we can reject the null hypothesis
The sum of the p values for the one sided alternatives always equals ___
1.0
If a significance test for an experiment has a P score of 0.012 at a 0.05 significance level, is the alternative hypothesis true?
No, we simply do not reject it.
What assumptions are made for a significance test for a population mean?
It is quantitative, Acquired through randomisation and has a normal distribution.
What is the relationship between two sided tests and confidence intervals?
If P-Value < 0.05 in a two sided test then a 95% confidence interval does not contain the H0 value
When is a normal distribution not crucial in a t statistic
When using a two tail test.
What is the relationship between sample size and test statistics?
The test statistic tends to be larger as the sample size increases and the P-value decreases.
What is meat by the rejection region?
A collection of test statistic values for which a test rejects H0. These are the z test statistics that occur when the sample sample proportion falls at least 1.96 standard errors from the null hypothesis value.
What affects the choice of significance level?
How serious the effect of a type 1 error would be.
What can create the probability of type 2 error to be larger?
Making a type 1 error smaller, as the sample size decreases.
What are ordinal variables?
Categorical variables which have an order
Give 2 reasons why confidence intervals are more informative than significance tests
A significance test merely indicates whether a particular parameter value on H0 ( such as m=0) is plausible. When a P-value is small, the significance test indicates that the hypothesized value is not plausible, but it tells us little about what parameter values are plausible while a confidence interval displays an entire interval of believable values, this can show if H0 is badly false as you can see if the values in the parameter are far from H0.
What is meant by the power of a test?
The probability of rejecting H0 when it is false.
