My research is intended to see the difference in people’s responses to **sad vs. joyful faces**. I have gathered 10 faces, 5 sad and 5 joyful, and I have recruited 100 participants for my research.

I requested each participant to respond to each face, whose order of presentation was randomized for each participant. So now I have the dataset as follows :

```
Participant face observation
1 sad1 x1
1 sad2 x2
...
1 sad5 x5
1 joy1 x6
1 joy2 x7
...
1 joy5 x10
2 sad1 x11
2 sad2 x12
...
2 joy1 x16
2 joy2 x17
...
100 sad4 x999
100 sad5 x1000
```

where $x_i (i=1, cdots, 1000)$ are some observed values.

### Approach 1 : Repeated measure ANOVA

I just used the above data structure, and conducted repeated measure ANOVA. In `R`

,

```
aov(observation ~ face + Error(Participant/face), Data)
```

### Approach 2 : Comparison of “mean”s

I have converted the above data into the following :

```
Participant face mean_values
1 sad mean(x1, ... x5)
1 joy mean(x6, ... x10)
2 sad mean(x11, ... x15)
2 joy mean(x16, ... x20)
...
100 sad mean(x991, ... x995)
100 joy mean(x996, ... x1000)
```

And I have conducted the test with predictor `face`

and response `mean_values`

. In `R`

,

```
glm(mean_values ~ face, Data, family="Gaussian")
```

What is the difference between the two approaches? What is more “appropriate” approach to my data?