Inferential Statistics: Null Hypothesis Testing

How is the two-tailed vs one-tailed tests differentiated in hypothesis statements?

"=" and not equal means it is a two tailed < or > (greater than, less than, greater or less equal to) = 1-tailed.

How do we calculate power?

1 - B. So for example if beta = .2 then the power should be 0.8.

How is power increased?

1) The bigger the sample the easier it is to detect a difference. So essentially bigger sample = more power to detect a difference. 2) A larger alpha creates a higher area of rejecting, making it easier to detect a difference (higher power).

What are the steps of hypothesis testing?

1) Use sample data to calculate a test statistic. 2) Judge test statistic vs. sampling distribution (whether it fall in or outside of rejection region. 3) define what accepting or rejecting null means in words. 4) Determine the effect size (magnitude of the finding) or where that difference lies (post-hoc tests).

What are the factors influencing effect size?

Sample size. If we have a small effect size we are going to need a bigger sample just to detect that small effect

How is the Null stated?

The null is stated in terms of population parameters only.

Example of statistics?

x bar = sample mean s = standard deviation for sample s squared = variance of sample n = sample mean

What are the 2 types of research hypothesis (alternative hypotheses specifically) ?

1) The mean of one group is higher/lower than the mean of another group/ a difference exists (Ho: M1= M2 Ha or H1: M1 does not equal M2). 2) Variables are correlated/one variable predicts another/variables are the same (Ho: p (population correlation coefficient) = 0 (meaning there is no relationship btw variables) and Ha or H1: P(population correlation coefficient) does not equal 0 meaning there is a relationship btw variables)

3) F-tests

1) one-way Anova (1 IV with three or more levels and 1 continuous DV) 2) 2-way Anova (2 IV's with no more than 2 levels & 1 continuos DV) 3) ANCOVA (3 or more levels and 1 continuous DV) 4) MANOVA (IV's with 2 or more levels & 2 related, continuous DV's)

What are the assumptions of hypothesis testing?

1) the theory of significance testing is based on the assumptions that our sample was randomly drawn from the population of interest. 2) Test a precise numerical stat hypothesis - we cannot state our exact numerical expectations so state hypothesis in terms of zero - no relationship. 3) Our significance test assumes that our null hypothesis is true. 4) Our research hypothesis typically predicts a result that entails rejecting the null hypothesis.

What 4 sampling distributions will we be using to do hypothesis testing?

1) z 2) t (dependent and independent t-tests) 3)F (Anova's and Multiple regression) 4) Xsquared (Chi-square)

Describe 1-tailed vs 2-tailed tests in terms of power?

1- tailed tests are more powerful than a 2-tailed test IF the directional prediction is correct. But it is LESS powerful than a 2-tailed test is the prediction is incorrect.

What does person's correlation coefficient do?

Also known as the "linear correlation coefficient"It measures the the strength and relationship of a linear relationship between two variables. The coefficient runs from -1 to +1, with zero being no relationship.

Why should you conduct a sample size calculation before conducting a survey?

Because it is best to calculate the sample size that you need for the effect size that you want, so that you don't spend more resources than you need to, by having more participants they need. AND it is also okay to calculate sample size needed for the amount of power that you want.

What is the symbol for power?

Beta.

What is the role of the critical value?

Divides sa,pling distributions into regions of acceptance and rejection. Critical value is defined by alpha and DF. ** located by consulting tables that consult critical values of different sampling distributions (z, t, f, x squared distribution tables).

What is effect size?

Effect size is equal to the critical parameter value - the hypothesized value. Essentially the differences between means are examined and a difference between means shows exactly how much effect a treatment has.

Error rate increasing as a factor of multiple comparison tests , when performing multiple hypothesis is called?

Familywise error rate = 1 - (95%)^n Meaning the more hypothesis tests you have within a test you are conducting (i.e looking a the effects of multiple predictors, or interactions amongst differ predictors) the more likely it is for you to commit a type 1 error.

What is the coefficient of determination?

Gives the proportion of the variance in one variable that is accounted for in another variable. Or think about it this way: It gives the proportion of the variance (fluctuation) of one variable that is predicted by another variable.

What is an example of a Null hypothesis and an alternative hypothesis?

Ho: M1 = M2 Ha: M1 does not equal M2

How can alpha differ depending on the test and sample size?

If we increase the number of comparison tests(i.e looking at the effect of multiple predictors, interactions amongst predictors etc.) the error rate will increase.

What does it mean to "reject the null?"

It means that we have found a statistically significant difference (adopt the alternative hypothesis). (the test statistic (t, z, or f). I fell outside the confidence intervals. The error rate (chance of saying diff when no diff exists) is lower if the CI (p-value) is lower.

What does hypothesis testing tell us?

It tells us the probability of obtaining a test statistic of a particular value given the null hypothesis is true.

What are the best sample sizes?

Larger samples sizes are better because the results are more reliable, they are precise, and have a high power. (but also cost more money).

Examples of parameters?

M (mew) = population mean O (sigma) = population standard deviation O (sigma) squared = population variance N = population mean

Measures of association and strength.

Measures of association strength (aka correlations ) can shield against overestimating the importance of statistically significant result. examples of these are: Peasrson's correlation coiefficent (r) and coefficient of determination (r squared).

What is power?

Power is depicted by Beta and power is the probability of detecting a difference given that a difference exists. or think about it this way: The probability of finding a statistically significant result given that there really is a difference in the population.

What is the difference between power and effect size?

Power is the probability of detecting a difference, given that a difference exists, to whereas effect size is a way to report the magnitude of the difference detected or the relationship, regardless of whether it's casual or not.

1) Z-test

Rarely used because we rarely know the standard deviation and mean of the population. Here is a good video for 1-tailed and 2-tsiled Z-scores.http://www.statisticshowto.com/hypothesis-testing-examples/

What is the area of rejection and area of acceptance under the curve when the alpha level is 0.05?

Region of rejection = 0.05 Region of acceptance = 0.95

What is the rule of thumb for effect sizes?

Small effect: 0.2 Medium effect: 0.5 Large effect: 0.8

What is a statistics equal to? A parameter?

Statistic = Sample Paramater = Population

2) T-tests

Test tests are of three kinds there is the 1- sample T-test (compare a groups mean to a set mean) and the Independent samples t-test (compare two independent groups to each other), and lastly the dependent, paired, or matched samples t-test (all mean the same thing) (these are variables that depend on one another, usually a within subjects design looking a time1 and time2). **One IV w. just two levels and 1 Coontinious DV.

What is the common/standard p-vaule?

The standard p-value is set at 0.05 (95% CI). However other p-values are also commonly used like alpha set at 0.10. Furthermore it is more likely to reject the null at a 0.10 alpha because the area of rejection is bigger, but at the same time there is a higher error rate and a bigger probability of committing a type 1 error.

what is the formula to calculate effect size?

To calculate effect size subtract the mean of one group from the mean of the other group and divide that by the standard deviation of the population form which the groups were sampled.

Are we trying to prove or disprove something? Why?

We are trying to disprove something (Ho) because it is easier to disprove something (Ho) than it is to prove it right.

What is the purpose for hypotheses testing?

We want to draw a conclusion about something we are questioning about in the population of interest. Draw conclusions about the population based on an obtained sample (sample statistics).

What is the Bonerroni Correction?

When we are making multiple comparisons, we must adjust the sig. level for each test, so that the overall type 1 error rate (alpha) across all comparisons is control

How else can you interpret alpha? (alpha inflation).

You can think about it in the following ways: - that there is a 5% chance that your results or outcome occurred by chance (95% chance they did not occur by chance). - the probability of rejecting the null, when the null is true is 5%. - the probability of making the wrong choice is 5%. OR - it is acceptable to have 5% probability of incorrectly rejecting the null. **The probability of making a type 1 error (concluding a difference exists when it does not) is 5%, therefore probability of NO TYPE 1 ERROR is 95%.

What is a type I error rate?

You can think of a a type I error as: - the probability of rejecting the null, when the null hypothesis is true. - rejecting the null when you should have not - Concluding a difference exists when there is no actual difference. -false positive OR - detecting an effect that is not present

What is a type II error rate?

You can think of a type II error rate as: -is when you fail to reject the null and you should have. -you are say that no difference exists when in fact there is a difference. - Retaining a false null hypothesis (false negative) OR - failing to detect an effect that is present

How do you calculate effect size for a case that has more than 2 treatments?

is the maximum mean - the minimum mean divided by the population standard deviation.

What does it mean to fail to reject the null?

it means that we have not found a statistically significant difference. (we accept the null hypothesis). The test statistic fell within the confidence intervals.

4) Chi-square (x squared)

measures a dichotomous IV and a dichotomous DV (categorical data and variables).