Inferential Statistics 1 (Sign Test) Flashcards
What do Descriptive Statistics help with?
Descriptive Statistics; mean, median, mode, range and standard deviation help you organise and summarise data.
What do Inferential Statistics help with?
Inferential Statistics refer to the statistical tests applied to quantitative data with the purpose of analysing these data and be able to interpret the findings.
Inferential statistics are ways of analysing data that help assess the strength of difference or association between variables.
What is the purpose of measuring this strength?
This strength is measured with the purpose of deciding whether the outcome has resulted as a consequence of what is being investigated or simply by chance alone.
What occurs based on the analyses?
Based on these analyses, the researcher can reach conclusions and decide whether a hypothesis is accepted or rejected. The researcher will accept a hypothesis if the results are statistically significant (relevant).
What is the Level of Significance?
The Level of Significance refers to the extent to which we tolerate a probability for the findings to have occurred by chance alone before we accept our findings to be accurate.
What is the general rule for accepting results to be accurate?
The general rule for accepting the results to be accurate is (p ≤ 0.05). This means the probability of the results to have occurred by chance alone is equal or less than 5%.
However, in some instances, when psychologists want to be more certain such as considering the effects of a new drug on health, they may use a more stringent probability such as (p ≤ 0.01). this means that the probability of the findings to have occurred by chance alone is 1%.
In other instances such as when conducting research on a new topic, they may use a more lenient significance level such as (p ≤ 0.10). This means that the probability of the findings to have occurred by chance alone is 10%.
Sign-test
Sign test is a basic example of inferential analyses. It is not a very rigorous test but it will help you get introduced to inferential statistics.
A sign test is used to analyse the difference of scores between the same subjects under two experimental conditions.
Each inferential test requires to meet a number of conditions (assumptions). The sign test requires:
1) It is a test of difference between conditions rather than association.
2) It need to be a repeated measures (related design).
3) The data needs to be (or have been converted to) nominal level of measurement.
Calculating the Sign-test
We are comparing two sets of results. They often refer to a ‘before’ and ‘after’ experimental treatment, for example, before-after training, medication, diet, etc). You will be shown tables with data indicating the difference between the two conditions.
Although less likely, you may be given the raw data to convert into categories (nominal date) - increase (+), decrease (-), neutral (=). You will then add a column to the table of data, decide what the difference between conditions is and represent it with a sign. These are your categories.
Next step is to add all the pluses and minuses. Ignore the neutrals. However, they will have to be accounted for later on when selecting number of participants. Select the lowest figure - the less frequent sign, that will be your calculated value of S.
If the null hypothesis is true (no effect of experimental treatment) then we expect to see approximately half of the differences as positive and half of the difference as negative. If the research hypothesis is true (there is an effect of treatment), we expect to see more positive differences.
Critical values
Remember that the purpose of conducting these tests is to decide whether the hypothesis can be accepted or rejected. In order to draw such conclusions we need to compare the calculated value of S with the critical values.
The critical values are provided on a table that will be given to you. When you look at these tables, you need to decide which figure is the one that is relevant to you. Which critical value is the one that you need to compare our calculated value to.
To identify the relevant critical value that you require for your comparison on this table, you need to consider:
- Number of participants
- Type of hypothesis
- Level of significance
Number of participants
Number of participants is usually represented in these tables as (N) or (n) generally presented on the left hand column. Remember we mentioned earlier that if any (neutral) values have been deducted, the number of participants needs to be adjusted.
Type of hypothesis
If you have a directional hypothesis, then this is a one-tailed hypothesis; predicting on a particular direction. If you had a non-directional hypothesis, then you have a two-tailed hypothesis. You are predicting an effect but not in any particular direction.
Level of significance
Remember, the general rule for accepting the results to be accurate is (p ≤ 0.05). Thus the probability of the results to have occurred by chance alone is equal or less than 5%. If any other level of significance is required, this will be expressed explicitly. Otherwise, assume the 5%.
Accepting or Rejecting Hypotheses
Once you have considered (N), (one or two tailed hypothesis) and (p), you can located the relevant critical value on the critical values table. You need to compare the calculated value of S to its critical value. For the sign test, the calculated value has to be equal or less than the critical value for the results to be regarded as significant. In other words, for the alternate hypothesis to be accepted or the null hypothesis rejected. Conversely, if the calculated value of S is greater than the critical value, then the alternate hypothesis needs to be rejected and the null hypothesis accepted.
