T test and Hypothesis Testing

Question 1

Hypothesis Testing

Answer 1

Statistical hypothesis are probabilistic mathematical statements concerning population values, stated in terms of the parameters used in the research. There are two types of statistical hypothesis =
1. Null hypothesis
and
2. Alternative hypothesis

Question 2

Steps in a t-test:

Answer 2

1. State the Null. This can be though as the opposite of what the researchers think will happen - usually that there will be no difference between the treatment and control group.
2. State the alternative. If the null is rejected, there are many possibilities.
3. Alpha is then set, typically value is 0.05, establishing a 95% confidence level.
4. Data is collected and test static is collected.
5. Acceptance and rejection regions are constructed. This is so there is a clear cut off to know when to either accept or reject the null.
6. A conclusion is drawn about the null - accept or reject.

Question 3

p-value

Answer 3

p-value = level of significance a test has or probability of making a type 1 error (reject the null when it is actually true)
Common p-values are 0.05 and 0.01. The smaller the value, the more likely that the null will be rejected.
Hypothesis test can see whether the assumptions are correct or if type 1 or type 2 error has been made.

Question 4

t-test

Answer 4

A t-test is an analysis of two populations means through the use of statistical examination.
Helps compare whether two groups have different average values. Asks whether the difference between two groups averages is unlikely to have occurred because of random chance in sample selection.
A t-test only includes 2 groups to be compared (more than 2 groups being compared = ANOVA)

Question 5

Paired t-test

Answer 5

DV is measured twice in each individual, The repeated measures t-test is used to see if two measurements of a single DV made on a single group differ significantly. Often used in pretest-posttest deign.

Question 6

t-Obtained and Critical-t

Answer 6

if the t-obtained is greater than the critical-t, the difference between the two samples means it lies in the region of rejection, thus we reject the null. At 0.05, region of rejection is at one end of the distribution only (can also be 0.025 at each end of the tail).

Question 7

Assumptions of a t-test:

Answer 7

1. Scale of measurement is continuous - ordinal or interval
2. Simple random sample (representative and random from total population).
3. Data when plotted = normal distribution (bell curve)
4. Reasonably large sample (increases normal distribution)
5. Homogeneity of variance (equal variance) - Levens or Bartletts test used on SPSS to verify
6. IV should consist of 2 categorical, independent groups e.g. male and female
7. Independence of observations - no relationship between the observations in each groups
8. No significant outliers
   * Data needs to meet all assumption for a VALID result*

Question 8

One tailed t-test

Answer 8

Test where all your alpha is allotted to test the statistical significance in ONE direction of interest. This means 0.05 is in one tail of the distribution of your test static. When using a one tailed test, you are testing for the possibility of a relationship in one direction and completely disregarding the possibility of a relationship in the other direction. This many occur when the consequences of missing an effect in the untested direction is in no way irresponsible or when you are testing a theory that has previously been tested and there was no relationship found at the other tail.

Question 9

Two tailed t-test

Answer 9

If using a significance value of 0.05, a two tailed t-test allots half of your alpha to test the statistical significance in one direction and half in the other direction.
This means 0.025 is in each end of the tail of the distribution of your test static.
When using a two tailed test, regardless of the direction of the relationship, you hypothesize you are testing for the possibility of the relationship in both directions.