---
# System prepended metadata

title: Questions about multiple regression
tags: [exp_analysis, study_progress]

---

# Questions about multiple regression

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I am dealing with the verbal report results collecting from participants, and have encounter some problems with multiple regression.

To be brief, <span class='red'>**I want to know what should I do when my data doesn't meet the assumptions**</span>. Should I just skip the part, or need to change the models.

In the sections below, I will explain the details.

## Data collection
In the experiment, the verbal report was collected after listening the audio stimuli and move to the measurement room, and right before the participants start to move the walls (Therefore, what they see are only the sky and the ground.).

The instruction: 
Straight your arm, use the length of the arm to answer the distance you think between two walls.
![](https://hackmd.io/_uploads/rkaeKo28n.png)
The thing that the particpants report is how many arms between the two walls.
In the data analyzation, I multiply the answer with participants' arm length (measured before the experiment).


## Raw data reference
If you need, all of the data is in this spreadsheet: 
https://docs.google.com/spreadsheets/d/1E0JT6au-3LdO72ptNE4M1c75_adDeaABK6jOyTo-jRI/edit?usp=sharing

## Multiple Regression
![](https://hackmd.io/_uploads/BJgBc_aLh.png)　
Durbin-Watson is too low (siginificantly different from 2)

![](https://hackmd.io/_uploads/ryGY5OpUn.png)
The scatter plot also shows a little bit heteroscedasticity 

![](https://hackmd.io/_uploads/B1jWs_TL2.png)
The scatter plot for each phase after the outlier cleaning.
The R sqaure is low.

<span class = 'red'>The thing I want to know is that what should I do or report when multiple regression assumptions aren't met.</span> 


## ANOVA

Just showing you I have also done ANOVA test.
It's an one way repeated measure anova.
The data is average verbal report of each room size from each participant. (split into different phase)
![](https://hackmd.io/_uploads/rkXOhupUh.png)
![](https://hackmd.io/_uploads/Hkt_h_TL2.png)
The test of sphericity is significant so we need to look into Greenhouse-Geisser
![](https://hackmd.io/_uploads/BkpSaupL3.png)

Pair-wise
![](https://hackmd.io/_uploads/rk8da_6Ln.png)
![](https://hackmd.io/_uploads/ryCOT_6Uh.png)

# Questions about reaction time 
I have done an one way repeated measured anova test (input the reaction time split py phases).
I want to know if there are other things I can do.

## ANOVA results

From the plots, I think that different phases affect the reaction time but not the roomsize, so I do this kind of the anova test to see if reaction time is different in each phases.

![](https://hackmd.io/_uploads/SJiiCupI3.png)
![](https://hackmd.io/_uploads/B1D2ROpIn.png)

![](https://hackmd.io/_uploads/Bytp0_a8n.png)
![](https://hackmd.io/_uploads/S1RTA_p83.png)

The test of sphericity is significant so we need to look into Greenhouse-Geisser
![](https://hackmd.io/_uploads/SkGk1YT8h.png)

Pair wise
![](https://hackmd.io/_uploads/S1Ql1tpI3.png)
![](https://hackmd.io/_uploads/SJPe1KpLh.png)







