Inferential Testing

Question 1

When is the null hypothesis accepted?

Answer 1

If the statistical test is not significant the null hypothesis is accepted.

Null hypothesis = states there is ‘no difference’ or ‘no correlation’ between the conditions.

Question 2

What do statistical tests determine?

Answer 2

Statistical tests determine which hypothesis (null or alternative) is ‘true’ and thus which we accept and reject.

Question 3

The null hypothesis is accepted or rejected at a particular level of probability.

What is probability?

Answer 3

Probability is a measure of the likelihood that a particular event will occur, with 0 is a statistical impossibility and 1 a statistical certainty.

Probability is represented as = p

Question 4

What is the significance level?

Answer 4

There are no statistical certainties in Psychology but there is a significance level - the level at which researchers decide to accept or reject the null hypothesis.

Question 5

What is a type 1 error?

Give an example

Answer 5

This is where a Psychologist accepts the experimental hypothesis and rejects the null hypothesis when they SHOULD NOT as the result was due to chance.

This is an optimistic error or false positive as a significant different or correlation is found when one does not exist.

When someone repeats a study and gets different results the first study must have had a type 1 error.

Question 6

What is a type 2 error?

Give an example

Answer 6

This is where a Psychologist rejects the experimental hypothesis and accepts the null hypothesis when the SHOULD NOT as the results were NOT due to chance.

This is a pessimistic error or false negative.

Here a researcher concludes there is not a significant effect, when there really is.

Question 7

What makes each error more likely?

Answer 7

A type 1 error is more likely to be made if the significance level is too lenient (too high, e.g., 0.1 = 10%)

A type 2 error is more likely if the significance level is too stringent (too low, 0.01 = 1%), potential significant values may be missed.

Question 8

What is nominal data?

Give an example

Answer 8

Each item can only appear in one category. There is no order.

Example: asking people to name their favourite colour, shape or subject.

Question 9

What ordinal data?

Give an example

Answer 9

Data is collected on a numerical, ordered on a scale but intervals are flexible. So, a score of 8 is not twice as much as a score of 4.

May lack precision because it is based on subjective opinion rather than objective measure.

Example: rating how happy you are on a scale of 1-10 or 1st , 2nd & 3rd placement in a race.

Question 10

What is interval data?

Give an example

Answer 10

Data that is based on numerical scales that include unites of equal and precisely defined size.

This includes counting observations in an observational study (8 tallies is twice as much as 4 tallies) or use of ‘public’ unit of measurements.

Example: Time, temperature

Question 11

What are the levels of measurement?

Answer 11

Ordinal data

Interval data

Nominal data

Question 12

What is statistical testing?

Answer 12

Statistical tests are used to determine whether there is a difference or association/correlation found in a particular investigation is statistically significant (e.g., if the results of a test occurred by chance or there is a real effect).

Question 13

What is the criteria for statistical (inferential) tests?

Answer 13

There are three criteria’s when selecting a statistical tests.

Looking for a difference or a correlation/association

Is the experimental design related (repeated measures/matched pairs) or unrelated (independent groups)?

What is the level of measurement?

Question 14

Understand this

Answer 14

Question 15

What is a parametric test?

Answer 15

The related t-test, unrelated test and Pearson’s r are collectively known as parametric tests.

Parametric tests are more powerful and robust than other tests. If a research can use a parametric test they will do so, as these tests may be able to detect significance within some data sets than non-parametric tests cannot.

Question 16

What are the three criteria’s that must be met to use a parametric test?

Answer 16

Data must be interval level – parametric tests use the actual scores rather than ranked data.

The data should be drawn from a population which would be expected to show a normal distribution for the variable being measured. Variables that would produce a skewed distribution are not appropriate for parametric tests.

There should be similarity of variance – the set of scores in each condition should have a similar dispersion or spread. One way of determining variance is by comparing the standard deviations in each condition; if they are similar, a parametric test may be used. In a related design it is generally assumed that the two groups of scores have a similar spread.

Question 17

Look

Answer 17

Question 18

How to check for statistical significance?

Answer 18

To check for statistical significance the calculated value (result of the statistical test) is compared with a critical value in a table of critical values based on probabilities.

Question 19

What is the criteria to find the correct critical value?

Answer 19

To find the correct critical value, there are three criteria:

Hypothesis one-tailed (directional) or two-tailed (non-directional).

Number (N) of participants or degrees of freedom (df).

Level of significance (or p value).

Question 20

Note

Answer 20

The usual level of significance is 0.05 (or 5%)

This means there is a 5% chance that the results of a particular study sample occurred even if there was no real difference in the population (e.g., the null hypothesis is true)

Sometimes a more stringent (1%) level is used, e.g., drug trials.

Question 21

Characteristics of sign test

Answer 21

Used for repeated measures designs

Where data is nominal (categories) – if it is not then you must make it nominal

The sign test is a test of difference.

Question 22

How to calculate the sign test?

Answer 22

Enter pairs of related data in a table

For each pair, score plus [+] or minus -

Cross out all the data that remained the same

Count how many plus and minus you have in total

S = the number of less frequent sign (plus or minus).

Compare the calculated value (S) with critical table

Note: When subtracting if the answer is negative, we simply record the sign and if it is positive, we record a plus sign.

Examples: 110 – 122 = -12 = - recorded or 59 – 45 = +14 = + recorded

Question 23

How to use a critical value table?

Answer 23

In an exam you will be given a table like the table on your left.

Select the one-tailed or two-tailed row depending on the type of hypothesis (directional or non-directional) – hinted in question

Select the row that represents the number of participants in your study. For example, if your study had 9 participants, select row N = 9

Determine significance – Look at your calculated value. At the bottom of each critical table, there will be instructions given when your critical value is significant or not.

For a one tailed-test we can reject the null hypothesis (p ≤ 0.05) and accept the alternative hypothesis. But for a two tailed test we would have to accept the null hypothesis (p ≤ 0.05)

Question 24

Look

Answer 24

Question 24

Parametric degrees of freedom?

Answer 24

Formula for parametric tests is very complex and very unlikely to be used in an exam. You might be required to calculate the degrees of freedom (df): Pearson’s r: df = N – 2 Related t-test: df = N – 1 Unrelated t-test: df = NA + NB – 2 (NA is the number of participants in Condition A and NB is the number of participants in Condition B).