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Interpreting significance

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  • Statistics/
  • Interpreting significance

The following scenarios help to practice interpreting data and writing a statement of significance. When writing a statement of significance, remember to state the obtained value, how it compares to the critical value, and the level of probability that the results were not due to chance. Remember you should also accept or reject the null hypothesis and make a statement of the findings. A statement of significance might look like this:

Based on the Mann Whitney test our UA = 95, which is less than the critical value 148 at p ≤ 0.05. Therefore, it appears that our results are not significant. We retain the null hypothesis. Therefore, noise has no effect on one's ability to recall a list of words.

1. You have done an experiment to see if providing a schema helps people to remember more words from a list. You hypothesize that those participants who are asked to think about summer holidays before they are read the list of words will remember more words from the list than those who have no schema activated.

A Mann-Whitney U test was applied to the data. The U value was 88. Using the chart below, write a statement of significance.

This is a directional test. Notice that your value of 88 is greater than the value of 86 (for 0.05) and less than the value of 91 (for 0.025). The statement of significance would read: The U value of 88 exceeds the critical value of 86 for p < 0.05. The null hypothesis is rejected. There is less than a 5% chance that our results are due only to chance. It appears that activating a schema prior to memorizing a list of words helps participants to remember more words from the list.

2. Your friends have carried out the Loftus experiment and need your help. They had two groups and hypothesized that those who were asked the speed of the car with a more intense verb would estimate higher speeds than those who were asked the question with a verb of lower intensity.

A Mann-Whitney U test was applied to the data. The U value was 52. Using the chart below, write a statement of significance.

This is a directional test. Notice that your value of 52 is less than the value of 73 (for 0.05). The statement of significance would read: The U value of 52 does not meet the critical value of 73 for p < 0.05. The null hypothesis is retained. The results are not statistically significant. It appears that the intensity of the verb does not have an effect on a participant's estimation of the speed of the car.

3. You have carried out a visual test to see if someone can detect an angular or a curved image faster in a set of angular letters. You hypothesized that the participants would take longer with the angular search than with the curved search.

A Wilcoxon signed ranks test was carried out on the data. The z value for this test was 1.99. Using the chart below, write a statement of significance.

This is a directional test. Notice that your value of 1.99 is greater than the value of 1.960 (for 0.025) and less than the value of 2.326 (for 0.01). The statement of significance would read: The z value of 1.99 exceeds the critical value of 1.96 for p < 0.025. The null hypothesis is rejected. There is less than a 2.5% chance that our results are due only to chance. It appears that participants will take longer to identify an angular letter among a list of angular letters than to find a curved letter among a list of angular letters.

4. You have replicated the Stroop test. The two conditions were that the person was asked to read the words as they were written, and then they were asked to say the colour of the word, which did not match the word itself. You had hypothesized that the higher the level of interference in this task, the longer it would take the participant to read the list.

A Wilcoxon signed ranks test was carried out on the data. The z value for this test was -2.78. Using the chart below, write a statement of significance.

This is a directional test. The sign on your z value is not important. Notice that your value of 2.78 is greater than the value of 2.576 (for 0.005) and less than the value of 3.291 (for 0.001). The statement of significance would read: The z value of -2.78 exceeds the critical value of -2.576 for p < 0.005. The null hypothesis is rejected. There is less than a 0.5% chance that our results are due only to chance. It appears that participants will take longer to read a list of coloured words when asked to carry out a task with a higher level of interference.

5. Your friends wanted to see if listening to Mozart, rather than listening to no music at all, would have an effect on one’s ability to memorize a list of words. They hypothesized that the participants who listened to Mozart would remember more words than those that listened to no music while memorizing the list.

A Mann-Whitney U test was applied to the data. The U value was 75.5. Using the chart below, write a statement of significance.

This is a directional test. Notice that your value of 75.5 is greater than the value of 73 (for 0.05) and less than the value of 77 (for 0.025). The statement of significance would read: The U value of 75.5 exceeds the critical value of 73 for p < 0.05. The null hypothesis is rejected. There is less than a 5% chance that our results are due only to chance. It appears that listening to Mozart music while memorizing a list of words results in the participants recalling more words than if they had not listened to any music.

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