If you’re here, chances are that you’ve probably used Julius to help you run descriptive statistics on your data to explore the relationships. You have probably tested your dataset for normality and homogeneity of variances. If you haven’t done these steps, you can go check out my guides on how to run descriptive statistics on Julius and how to run tests to determine if your data is suitable for parametric or non-parametric testing!

This particular guide is going to go over some of the parametric tests you can run on Julius. For simplicity sake, in each example you have already ran a normalcy test and determined that these datasets do follow normal distribution and have equal variance’s. Let’s check out some tests!

**Students T-Test (Independent T-Test)**

This test is used to determine if there is any statistically significant differences between the means of two independent groups (groups that do not influence one another).

*Situation: Researchers want to determine if there is a significant difference in exam scores between two different teaching methods. They randomly assigned 20 students to Group A (hands on approach to teaching), and then 20 to Group B (more independent studying). After the teaching period ends, both groups get the same test. Here are the results:*

group_a | group_b |
---|---|

75 | 78 |

80 | 82 |

85 | 87 |

90 | 91 |

92 | 93 |

78 | 90 |

83 | 85 |

87 | 89 |

79 | 81 |

81 | 83 |

82 | 84 |

84 | 86 |

86 | 88 |

88 | 90 |

91 | 92 |

77 | 79 |

76 | 77 |

89 | 90 |

85 | 86 |

83 | 84 |

*Determine if there is any difference between the groups mean test score.*

**Question 1a:** is there any statistically significant difference between Group A’s mean test score compared to Group B?

**Prompt 1a:** Perform an independent samples t-test to compare the means of Group A and Group B, please.

There was no statistically significant difference between Group A and Group B means, but let’s explore the effect size of this data regardless using Cohen’s d. But before we run this, what is effect size you ask? Effect size tells us how big the difference is between two groups, with 0.2 being small effect, 0.5 being medium, and 0.8 being large effect. Let’s prompt Julius to run this test:

**Question 1b:** what is the effect size for the comparison between Group A and Group B?

**Prompt 1b:** Calculate Cohen’s d for the comparison between Group A and Group B, please.

Julius has effectively calculated the effect size of this relationship. It also gives us an idea on what the value means, such as the direction of magnitude (Group A having slightly lower mean than Group B).

Now let’s visualize the data to get a better understanding of the characteristics:

**Question 1c:** What does our data look like?

**Prompt 1c:** Can you provide a visualization of the data so that we can see the slight differences between Groups A and B?

Great! Julius has provided a visualization of the median scores via a boxplot. Boxplots are useful to show distributions of numeric data values. They provide information on the central tendency and spread of the data (the “whiskers” or the lines at the top and bottom of the box show us how far the data spreads, with maximum and minimum values). The shaded area is referred to as the “interquartile range” (IQR), with this example showing that ~25% of the data falling below the median (lower quartile), and ~25% of the data falling above the median line (upper quartile).

**Paired Samples T-Test**

These tests are used when we have **two sets of measurements** collected from the **same individual** under **two different conditions**. This is the perfect test to use if:

- You want to see if there is a difference between before and after treatments
- When two different treatments are applied to the same individual, or
- Any
**paired**comparisons where each measurement is not independent from one another.

Let’s run a paired samples t-test!

*Situation: A pharmaceutical company is testing the effectiveness of a new medication for lowering blood pressure within 8 hours. They recruit 20 people who are diagnosed with hypertension. They measure their blood pressure levels before administering the medication, then wait 8 hours and remeasure their blood pressure. Below is the data they collected:*

student | before_score | after_score |
---|---|---|

1 | 140 | 130 |

2 | 150 | 140 |

3 | 160 | 150 |

4 | 155 | 145 |

5 | 165 | 155 |

6 | 148 | 138 |

7 | 152 | 142 |

8 | 158 | 148 |

9 | 145 | 135 |

10 | 147 | 137 |

11 | 155 | 145 |

12 | 160 | 150 |

13 | 157 | 147 |

14 | 150 | 153 |

15 | 143 | 140 |

16 | 155 | 133 |

17 | 158 | 145 |

18 | 162 | 148 |

19 | 156 | 152 |

20 | 148 | 146 |

*Determine if there is any difference between the blood pressure readings.*

**Question 2a:** is there any difference between the before and after blood pressure score?

**Prompt 2a:** can we run a paired samples t-test comparing the before_score and after_score to see if there is any difference between the groups?

Julius was able to run a paired t-test and produce the results (t(38) = 8.267, p ≤ 0.001). This is great, but what next? A visualization! Since I’ve already went over how to prompt for this, I will just provide the visualization below:

Now I’ll ask for a summary of the paired samples t-test result to get an overview of the findings:

**Prompt 2b:** can you provide a summary of the paired samples t-test results please?

Perfect, Julius has provided me with a breakdown of my steps and statistical analyses. We are almost done! I should conduct a Cohen’s d to quantify the magnitude of difference between the before and after scores. Since I have already done this in the previous example, I will just record the value.

**Cohen’s d = -1.849,** suggesting that there is a large negative effect size. This means that the medication had a substantial impact on the reduction of patient’s blood pressure. The negative value indicates the direction of the effect, meaning that there is a decrease in scores from the before_score to after_score.

Finally, let’s look at the variability of the responses amongst patients by using a **change score analysis.** This analysis examines the distribution of the change scores (difference between the before and after scores) to better understand how each participant varied in their response to the drug. It can help us determine if the drug was consistent in the effect it had amongst all participants.

**Question 2c:** what is the variability of responses between participants?

**Prompt 2c:** can you perform a change score analysis to further understand the variability of the response to the drug?

Now we understand a lot more about the the average change score and some of the variability each participant experienced! Feel free to play around with the dataset to explore other options Julius has.

Keywords: AI statistics, AI statistical analysis, GPT, parametric tests, students t-test, independent t-test, paired samples t-test, descriptive statistics, cohen’s d, change score analysis