_hox2_nonMLM.Rmd

# hox 2 non-MLM anlaysis





## Disaggregation Completely

Ignore all nesting and dissagregate all variables.  This treats ward type and hospital size as a nurse-specific factor.  It erroneously assumes that all nurses are independent and that the treatement was randomized to individual nurses rather than wards. 

### Data Treatment

Requires no edicts to the dataset.

The simplest statistical test would be to compare the mean stress level of all nurses who participated in the stress training to the mean of all nurses that did not.  

#### Summary

```{r, results='asis'}
data_nurse %>% 
  furniture::table1(stress,
                    splitby = ~ expcon,
                    output = "html",
                    test = TRUE,
                    type = "full",
                    digits = 4)
```







### Independent Groups t-Test

#### Assumptions

The t-test assumes that the amount of variation or spread is the same in the two groups.  Thi sassumption of homogeneity of variance (HOV) across groups is tested via Levene's Test.  

```{r}
car::leveneTest(stress ~ expcon,        # continuous outcome ~ grouping var
                data = data_nurse,      
                center = "mean")        # the default is 'median'
```

#### Model Fitting

Since evidence of  a violation of HOV was found, `F(1, 998) = 64.037, p < .0001`, use the Welch (or Satterthwaite) approximation to the degrees of freedom to pool the variances for the t-test.

```{r}
nurse_t_ind <- t.test(stress ~ expcon,        # continuous outcome ~ grouping var
                      data = data_nurse,   
                      paired = FALSE,         # independnet groups are not paired
                      var.equal = FALSE)      # since HOV is violated

nurse_t_ind
```



#### Effect Size

A confidence interval around the mean difference is one type of quantificaiton of effect size.  While Cohen's $d$ is the most frequently published single measure of effect size, anothers do exits and may be more appropriate.  These include Hedge's $g$ and Glass' $\Delta$.


```{r}
effsize::cohen.d(stress ~ expcon, 
                 data = data_nurse)  # default is Cohen's d
```

```{r}
effsize::cohen.d(stress ~ expcon, 
                 data = data_nurse,
                 hedges.correction = TRUE)   # also do hedges g
```


```{r}
lsr::cohensD(stress ~ expcon,
             data = data_nurse)
```



#### Interpretation

The nurses participanting in the intervention had lower stress level, `(M = 4.61, SD = 1.05)`, than thoes who did not, `(M = 5.33, SD = 0.72)`, at the end of end of the program.  An independence-groups t-test between means was conducted using the Welch approximation to pool the standard deviation after evidence was found of a violation of the homogeneity of variance assumption, `F(1, 998) = 64.037, p < .0001`. This sample provides strong evidence the intervention was efective at lowering stress, `t(891.67) = 13.048, p < .0001, 95CI [0.633, 0.858], d = -0.825, g = -0.825`.


### Single-level Simple Regression


#### Model Fitting

```{r}
nurse_lm_simple <- lm(stress ~ expcon,  
                      data = data_nurse)

summary(nurse_lm_simple)
```

#### Assumptions


```{r}
plot(nurse_lm_simple, which = 1)
```

```{r}
plot(nurse_lm_simple, which = 2)
```


#### Effect Size

```{r}
summary(nurse_lm_simple)$r.squared
```

#### Interpretation





## Aggregate Individuals in Wards

### Data Treatment

Reduce from 3 levels to 2 levels by aggregating nurses belonging to the same ward.

Collapse each set of about 10 nurse to only 1 mean per ward 

```{r}
data_nurse %>% 
  dplyr::group_by(hospital, ward, wardid) %>% 
  dplyr::summarize(hospsize           = first(hospsize),
                   wardtype           = first(wardtype),
                   expcon             = first(expcon),
                   ward_mean_age      = mean(age),
                   ward_prop_gender   = mean(gender),
                   ward_mean_experien = mean(experien),
                   ward_mean_stress   = mean(stress)) %>% 
  dplyr::ungroup() %>% 
  furniture::table1(hospsize, wardtype,
                    ward_mean_age, ward_prop_gender, ward_mean_experien,
                    splitby    = ~ expcon,                                  # var to divide sample by
                    test       = TRUE,                                      # test groups different?
                    type       = "full",                                    # give the test statistic
                    output     = "html",                                    # output for latex
                    align      = c("l", "r", "r", "r"),                     # column alignment
                    caption    = "Compare genders on four main variables")  # title
```


Aggregate:   
* 
    + Each ward is entirely assigned the control group or the treatment group
    + Sample size: n = 100

Dissaggregate:
* Ignore the correlation between wards in the same hostial
* Treats the hospital size as if it were a ward attribute, not a hospital attribute

```{r}
nurse_ANOVA_ward <- data_nurse %>% 
  dplyr::group_by(expcon, hospsize, wardid) %>% 
  dplyr::summarize(stress_mean = mean(stress)) %>% 
  afex::aov_4(stress_mean ~ hospsize*expcon + (1|wardid),
              data = .)

summary(nurse_ANOVA_ward)
```

```{r}
nurse_ANOVA_ward %>% 
  emmeans::emmip(expcon~ hospsize, CIs = TRUE)
```



```{r}
nurse_ANOVA_ward %>% 
  emmeans::emmeans(~ expcon|hospsize)
```

```{r}
nurse_ANOVA_ward %>% 
  emmeans::emmeans(~ expcon|hospsize) %>% 
  pairs()
```

### Dissagregate: 





## RM ANOVA

### Aggregate: Collapse to Hospital Averages

Collapse to only 2 means per hospital: one for the control group and one for the treatment group


```{r}
nurse_rmANOVA_hosp <- data_nurse %>% 
  dplyr::group_by(expcon, hospsize, hospital) %>% 
  dplyr::summarize(stress_mean = mean(stress)) %>% 
  afex::aov_4(stress_mean ~ hospsize + (expcon|hospital),
              data = .)

summary(nurse_rmANOVA_hosp)
```

```{r}
nurse_rmANOVA_hosp %>% 
  emmeans::emmip(expcon~ hospsize, CIs = TRUE)
```



```{r}
nurse_rmANOVA_hosp %>% 
  emmeans::emmeans(~ expcon|hospsize)
```

```{r}
nurse_rmANOVA_hosp %>% 
  emmeans::emmeans(~ expcon|hospsize) %>% 
  pairs()
```