NB. You will need to create a Google account if you do not already have one.

Analysis:
Analyzing the results of your experiment will enable you to conclude whether or not your research hypothesis was supported. This analysis will cover use two types of statistics:

• Descriptive statistics, which compare the results obtained in the experimental and control conditions.
• Inferential statistics, which assess whether the difference between the two conditions is statistically significant.
Descriptive Statistics (Click)

The first part of your “Analysis” section will report and interpret descriptive statistics, which use a single number to describe a whole set of data. There are two kinds of descriptive statistics:

• Measures of central tendency, which summarize the overall value of a set of data.
• Measures of dispersion, which indicate the variability of a set of data.

There are several different measures of central tendency. We do not recommend or support experiments yielding nominal data (consisting in words, e.g., “yes” or “no”) but the appropriate measure would be the mode. The mode is simply the most frequent value. If your data is ordinal (consisting in ranks without measurable intervals, e.g., a 1 – 4 Likert scale), you should use the median. The median is the value dividing a set of ranked data in two: 50% of the data fall below, and 50% above, the median value. If your data is interval or ratio (consisting in measures with a unit, e.g., a speed in miles per hour) you should use the mean, which is simply the average value. However, the IB will accept the median for any numerical (non-nominal) data, as long as you use the recommended inferential statistics below. If you do so, make sure to explain that your test of significance will transform your data into ordinal data (see below.)

Likewise, there are several different measures of dispersion, but the one that is appropriate for ordinal data is the interquartile range (IQR). Just like the median, it looks at ranked data and subtracts the first quartile (below which 25% of the data falls) from the third quartile (below which 75% of the data falls). For interval/ratio data, you should use the standard deviation, which is the average difference between a set of values. The IB does not require a measure of dispersion for nominal data.

Diagram 1: Quartiles and Interquartile Range

Calculating Descriptive Statistics (Click)

To calculate your descriptive statistics, you may use an online calculator, such as this one, which we recommend.

• On the landing page, click “Descriptive Statistics”
• On the next page, click “Mean, Median and Mode Calculator”
• On the next page, enter the data (1) from your control condition, then click “Calculate”

(1) Enter your participants’ individual results, either one per line, or separated by commas. If there are decimals, make sure to use dots and not commas (e.g., “12.5” and not “12,5″).

Question 23:
What is the median or mean value of your participants’ results in the control condition?

Repeat the same operation for results from your experimental condition.

Question 24:
What is the median or mean value of your participants’ results in the experimental condition?

Go back to the “Descriptive Statistics” page and click on either “Variance and Standard Deviation Calculator” or on “Interquartile Range Calculator”.
On the next page, enter the data (individual results) from your control condition, then click “Calculate”.

Question 25:
What is the standard deviation or the interquartile range of the results from your control condition?

Repeat the same operation for results from your experimental condition.

Question 26:
What is the standard deviation or interquartile range of the results from your experimental condition?

Reporting Descriptive Statistics (Click)

Your descriptive statistics should be reported either in words or/and in a table. Either way, you need to provide all the information needed. For instance, your table should have a title, be fully labeled, specify the unit of measurement, etc. An example is provided below.

Table 1. Example of Table of Descriptive Statistics
Free Recall Performance in no-music v. music with lyrics conditions

Question 27:
Create a table to report your descriptive statistics.

Your descriptive statistics must also be represented in a graph. More precisely, your measures of central tendency for each condition have to be. Representing your measures of dispersion is optional.
This graph must meet the following requirements:

• It must address the research question, i.e., compare the behavior (DV) of participants in two different conditions (IV). This is done by representing the latter’s mean or median results.
• It must use a proper representation technique. When representing unrelated conditions on the x-axis (e.g., “no-music” and “music with lyrics), the proper technique is a bar graph, which has a large space in between each bar.
• It must be fully labeled. This includes:
• A title
• Axes titles
• Labels for each bar or legend

To create your graph, you can use the same website we recommended for your calculations.

• On the main page, click on “Descriptive Statistics”.
• On the next page, click on “Easy Bar Chart Creator” at the very bottom.
• On the next page, enter the name of your conditions and their median as in the example below.

Diagram 2. Creating a Bar Chart Online

On the next page, make sure to edit the chart as follows:

• Axes titles: the x-axis can be something like “condition”, while the title of the y-axis should  be your operationalized dependent variable. Don’t forget to click “Update Axes Titles”.
• Chart title: your graph needs one, and it should reflect your research research question, as well as indicate the statistic displayed. If the field is not long enough, leave it blank and add the title yourself as in the example below. Don’t forget to click “Update Chart Title”.
• Display bar values: this is up to, but usually good practice.
• Don’t forget to save your graph (either right-click and save or take a screenshot).

Diagram 3. Graphic Representation of Experimental Results
Median Free Recall Test Score After Studying With or Without Music With Lyrics

Question 28:
Create a graph to represent your measures of central tendency.

Interpreting Descriptive Statistics (Click)

To score high marks, it will not be enough to report your descriptive statistics. You will also need to interpret them. Some relevant questions you should answer are the following:

• How do the means or the medians of each condition compare? Are they quite similar or dissimilar? How large is the difference?
• What about the data for each condition? How variable is it? How large is the standard deviation compared to the mean, or the interquartile range (IQR) compared to the median? Are there any outliers?
• Were the results more variable in one condition than in the other?

NB. Outliers are defined as values that lie 1.5 IQR below the 1st quartile or above the 3rd quartile. If you suspect that outliers reflect “errors” (bad participant effect, participant not understanding instructions, typo, etc.), you should exclude them from your calculations.

Although entirely optional, your graph can support this interpretation by including the following information:

• Median
• First quartile
• Third quartile
• Maximum value (excluding outliers)
• Minimum value (excluding outliers)
• Outliers

All of this information can be depicted with a box-and-whiskers plot, with outliers added as dots. Such a graph would replace the one your created earlier. A good online tool to create such a graph is available here. A short video tutorial to use this tool is also available here. The result would look something like this:

Diagram 4. Graphic Representation of Experimental Results With Box, Whiskers and Dots

As can be seen below, the various elements (which are automatically labeled on hover) indicate the following:

• Horizontal line = median
• Box = first and third quartile (below which 25% and 75% of the data fall)
• Lower fence = minimum value excluding outliers
• Upper fence = maximum value excluding outliers
• Dots = outliers

Diagram 5. On Hover Labels of Box, Whiskers and Dots

Question 29:
Interpret your descriptive statistics (measures of central tendency and dispersion), making sure to answer the questions above.

Calculating Inferential Statistics Click)

Interpreting your descriptive statistics is very important, but it is not yet sufficient to conclude whether your results support your research hypothesis (or not). For this, you need to know if there is  a statistically significant difference between the results obtained in your two conditions. To answer this question, you will have to run an inferential test.

Whenever two conditions are compared, the data sets will rarely be exactly identical. The question is: is this difference random, i.e., merely to due to chance, or is it indicative of a real difference between the two conditions? To answer this question, a statistical test is needed that will calculate the probability of obtaining such a difference if the null hypothesis is true (p-value). If this probability is lower than a critical value, called “level of significance”, or alpha (α), then the difference is statistically significant, and the null hypothesis can be rejected. Otherwise, it has to be retained.

The appropriate statistical test depends on the research design of your experiment. Here, we assume that your data is either ordinal or cardinal. We do not recommend or support nominal data. The following also assumes that your study only compared 2 conditions, as the IB recommends.

• Independent measures: You should use the Mann-Whitney “sum of ranks” U-test. The U-value tells you how likely it is that a randomly selected value from one condition will have a higher rank than a randomly selected value from the other condition. Based on the size of the two samples, a “critical value” can be calculated, which is the level of U that would be expected purely based on chance. The difference between your two sets will be statistically significant if one of their U-values is lower than the critical value of U. Fortunately, the online tool that we recommended can do the calculations for you.
However, make sure to:
• Choose the appropriate test: Only use Man-Whitney if your experiment used independent measures.
• Select the appropriate “level of significance”: The online tool will automatically translate the U-value into a p-value. Usually, psychological research uses an α of .05, which means that the difference between two data sets is considered statistically significant if there is less than a 5% risk that it is due to chance, giving us a 95% confidence.
• Select the appropriate type of hypothesis: Your conclusion might be erroneous if your research hypothesis was directional (one-tailed) but you select “two-tailed” instead.
• Make sure to click on “calculation details” on the results page and take a screenshot. You will ABSOLUTELY need it in your appendices.

• Repeated measures: You should use the Wilcoxon “signed ranks” W-test. The W-value tells you how likely it is that a value from the first measure will be higher or lower than a value from the second (repeated) measure. Based on the size of the two samples, a “critical value” can be calculated, which is the level of W that would be expected purely based on chance. The difference between your two sets will be statistically significant if one of the two W-values (sum of positive or negative ranks) is lower than the critical value of W. Fortunately, the online tool that we recommended can do the calculations for you. However, make sure to:
• Choose the appropriate test: Only use Wilcoxon if your experiment used repeated measures.
• Select the appropriate “level of significance”: The online tool will automatically translate the W-value into a p-value. Usually, psychological research uses an α of .05, which means that the difference between two data sets is considered statistically significant if there is less than a 5% risk that it is due to chance, giving us a 95% confidence.
• Select the appropriate type of hypothesis: Your conclusion might be erroneous if your research hypothesis was directional (one-tailed) but you select “two-tailed” instead.
• Make sure to click on “calculation details” on the results page and take a screenshot. You will ABSOLUTELY need it in your appendices.

NB. Both the Mann-Whitney and the Wilcoxon tests operate on ranked data. That is the reason why the median (and IQR) were the most appropriate descriptive statistics for you to use.

Question 30:
Use the recommended online tool to calculate the following inferential statistics:

• The critical value of U (or W)
• The U-value (or W-value)
• The p-value

NB. Make sure to click on “calculation details” and to take a screenshot!

Reporting and Interpreting Inferential Statistics (Click)

When reporting your inferential statistics, you should indicate the following:

• The inferential test used (Mann-Whitney “sum of ranks” U-test or Wilcoxon “signed ranks” W-test)
• The type of hypothesis (directional or non-directional)
• The level of significance (α = .05)
• Whether U (or W) is inferior or superior to the critical value or U (or W)
• The p-value
• Whether p is inferior or superior to α

Next, interpreting these inferential statistics means concluding whether the difference between your two data sets is statistically significant, and thus whether your results are consistent with your research or with your null hypothesis.

• If the difference between the two data sets is not statistically significant, you should retain your null hypothesis and reject your research hypothesis (since the independent variable did not influence the dependent variable).
• If the difference between the two data sets is statistically significant, you should reject your null hypothesis and accept your research hypothesis (since the independent variable did influence the dependent variable).
• This is true, unless your research hypothesis was directional and the statistical difference goes in the other direction. In this case, you should retain the null hypothesis and reject the research hypothesis.

NB. Make sure to restate your hypotheses in full, and avoid using words such as “prove”.

Question 31:
Report and interpret your inferential statistics, making sure to include the following:

• The inferential test used (Mann-Whitney “sum of ranks” U-test or Wilcoxon “signed ranks” W-test)
• The type of hypothesis (directional or non-directional)
• The U-value (or W-value)
• The critical value of U (or W)
• Whether U (or W) is inferior or superior to the critical value or U (or W)
• The p-value
• The level of significance (α = .05)
• Whether p is inferior or superior to the level of significance (α = .05)
• Whether the difference between the two data sets is statistically significant
• What your research and null hypotheses were, and which one one you should retain / reject or accept.