Lesson 15 Statistical Testing - The Sign Test Flashcards
Two different kinds of statistics
Descriptive statistics (such as measures of central tendency and dispersion)
Inferential statistics
“Level of statistical significance” defined
“The level at which the decision is made to reject the null hypothesis in favour of the experimental hypothesis. It states how sure we can be that the IV is having an effect on the DV and this is not due to the chance
“Chance” defined
“Something has no real cause, it just happens, e.g. by chance you are feeling happy today, there is no real cause that you can identify”
What are significance levels
From the results gained from our experiment (for both the control and the experimental conditions) we would look for whether a real difference exists between the two sets of data, and how certain we are that there is a real difference. If the two sets of data are very similar, then a statistical test might indicate that chocolate makes no real difference to mood and we might accept the null hypothesis. However, if there is a probability that there is a real difference between the two conditions (and this can be proved by conducting statistical tests) then we would accept the experimental hypothesis and reject the null hypothesis.
What is probability
Probability is a numerical measure that determines whether our results are due to chance or whether there is a real difference that exists between the experimental and control conditions (and therefore we can accept the experimental hypothesis). If a real difference exists (that can be calculated statistically) we can say that results are significant, and the null hypothesis can be rejected (and we would accept the experimental hypothesis)
What significance levels se in psychology
The conventional and standard level of significance is expressed as:
P<0.05 (5% level)
The 5% level of significance is mainly used in psychology because
A) It is not too strict or too lenient, but is a middle, fair value of significance
B) It minimises the chances of making a Type 1 or a Type 2 error
What does “p” stand for
“Probability”
and the 0.05 (5%) value illustrates the level of significance that has been chosen (5% level of probability that results are due to chance/fluke, therefore 95% certainty that our results are showing a real difference between control and experimental conditions)
Why is a 10% level of significance selected
Sometimes a 10% level of significance is selected, and this is expressed as; p<0.10 (10%), and this is often used when we allow a 10% margin of error, and we would be 90% certain that our results are really showing a significant difference
Why is a 1% level
Sometimes a very strict level of significance is selected at 1% which is expressed as: p<0.01 (which indicates there is a 1% probability that the results are due to chance). This is often used when research findings are critical and are very important e.g. when testing the effect of drugs on humans, we must make sure that results are not due to fluke but that a real difference occurs between the experimental and control conditions, and that is why we set a stricter significance level.
3 reasons why we use the sign test
1) We are looking for a difference between data, e.g. the drug HP10 makes people happy or not so happy
2) We are looking at paired or related data. The two related pieces of information could come from a repeated measures design or a matched pairs design because the participants are paired for the purposes of statistics, as one person tested twice.
3) The data is nominal (placed in categories, e.g. people are either happier or not happier once they have taken the drug HP10)
How to do the sign test
Step 1 State the Hypothesis- We now need to state either a one tailed directional or two tailed non directional hypothesis
Step 2 Record the data and work out the sign - 1) Record the difference between each pair of data (subtract the score for “drinking water” from the score for “drinking Speedup!)
2) Then record a (+) or a (–) for the values, this appears as signs (-) or (+)
Step 3 Find the calculated value of S - S is the symbol for the statistic we are calculating.
It is calculated by adding up the plus signs and the minus signs and selecting the SMALLER value.
Step 4 Find the critical value - N is the total number of participants (ignoring any participants that gained a change of 0, e.g. no positive or negative score overall
The hypothesis we stated earlier is two tailed non directional and therefore a two tailed test is used.
Now we use the table of critical values (below) and locate the 0.05 column for a two tailed non directional test and the row that begins with our N value (12).
For a two tailed test at p<0.05, we need to compare our S value to the critical value.
The calculated value of S must be EQUAL TO or LESS THAN the critical value for significance to be shown
