Week 6 - Introduction to statistics

Question 1

statistics

Answer 1

tools for describing and measuring the properties of populations from samples.

Question 2

goal of statistics

Answer 2

To estimate the values of important parameters, including: means, proportions, variances, effects
To test hypotheses about those parameters - are estimates more extreme than we expect simply by chance? If yes, results are significant

Question 3

null hypothesis

Answer 3

a specific statement about a population parameter made for the purposes of argument. A good null hypothesis is a statement that would be interesting to reject.
Tested
Rejected in support of the alternative hypothesis

Question 4

alternative hypothesis

Answer 4

includes all other feasible values for the population parameter besides the value stated in the null hypothesis.

Question 5

hypothesis testing steps

Answer 5

State the hypotheses
Compute the test statistic with the data
Determine the p-value
Draw appropriate conclusions

Question 6

stating the hypothesis

Answer 6

Alternative hypothesis is two-sided (includes parameter values on both sides of the parameter value specified by the null hypothesis)

Question 7

test statistic

Answer 7

A number calculated from the data that is used to evaluate how compatible the data are with the result expected under the null hypothesis
Evaluates how well the observed result matches the result claimed by the null hypothesis
Some mismatch is expected by chance so is our result too extreme for chance to explain?
To decide we need a suitable test statistic
Then we need its p-value

Question 8

test statistic = signal/noise

Answer 8

Signal - value of interest
Noise - uncertainty of value

Question 9

the null distribution

Answer 9

The sampling distribution of outcomes for a test statistic under the assumption that the null hypothesis is true
Distribution of test statistic when the null is true
Shape varies for different test statistics and sample size but:
All possible values is on x-axis
The densities of values are on the y axis
Densities sum to 1, giving probabilities

Question 10

quantifying uncertainty: the p value

Answer 10

The probability of obtaining the data (or data showing as great or greater difference from the null hypothesis) if the null hypothesis were true
The refers to the probability of a specific event when sampling data under the null hypothesis: it is the probability of obtaining a result as extreme as or more extreme than the observed

Question 11

draw the appropriate conclusion

Answer 11

The significance level is a probability used as a criterion for rejecting the null hypothesis. If the p value is less than or equal to a then the null hypothesis is rejected. If the p-value is greater than a the null hypothesis is not rejected
The rejection threshold is called the significance level (a)
Usually a = 0.05

Question 12

reporting the results

Answer 12

Summary of statistical test:
The value of the test statistic
The sample size
The p-value

Question 13

type I error

Answer 13

rejecting the true null hypothesis. The significance level sets the probability of committing a Type I error. False positive

Question 14

type II error

Answer 14

failing to reject a false null hypothesis. False negative

Question 15

the power

Answer 15

of a test is the probability that a random sample will lead to rejection of a false null hypothesis.

Question 16

one sided test

Answer 16

the alternative hypothesis includes parameter values only one side of the value specified by the null hypothesis. Rejected only if the data depart from it in the direction stated by p-value.

Question 17

paired design

Answer 17

both treatments are applied to every sampled unit.
Similar conditions in each block - can control for some noise
Usually more powerful

Question 18

two sample design

Answer 18

each treatment group is composed of an independent, random sample of units.
Every plot is independent

Question 19

paired comparisons of means

Answer 19

Paired measurements are converted to a single measurement by taking the difference between them

Question 20

paired comparisons of means assumptions

Answer 20

The sampling units are randomly sampled from the population
The paired differences have a normal distribution in the population

Question 21

pooled sample variance

Answer 21

the average of the variances of the samples weighted by their degrees of freedom.

Question 22

two sided and two sample assumptions

Answer 22

Each of the two samples is a random sample from its population
The numerical value is normally distributed in each population
The standard deviation of the numerical variable is the same in both populations

Question 23

welch’s

Answer 23

compares the means of two groups and can be used even when the standard deviations of the two groups are not equal.

Question 24

contingency analysis

Answer 24

estimates and tests for an association between two or more categorical variables.

Question 25

Chi squared test H0 and Ha

Answer 25

H0: variables are independent

Ha: variables are not independent

Question 26

Chi squared test

Answer 26

If two events are independent, then, the probability of both occurring is equal to the probability of one event occurring times the probability of the other event occurring
Use degrees of freedom
Same assumptions as goodness-of-fit tests: samples are independent and no more than 20% of cells have an expected frequency of less than 5 and no cells have an expected frequency of less than 1