# Turkey vs. Germany: COVID-19

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In Turkey, some elements of society at all times examine Turkey to Germany and assume that we’re higher than Germany for lots of points. The identical applies to COVID-19 disaster administration; is that displays to true?

We’ll use two variables for in contrast parameters; the variety of each day new instances and each day new deaths.First, we’ll examine the imply of recent instances of the 2 nations. The dataset we’re going to make use of is right here.

```#load and tidying the dataset
deu\$date <- as.Date(deu\$date)
tur\$date <- as.Date(tur\$date) #constructing the perform evaluating means on grid desk
grid_comparing <- perform(column="new_cases"){ desk <-data.frame( deu=c(mean=mean(deu[[column]]),sd=sd(deu[[column]]),n=nrow(deu)), tur=c(mean=mean(tur[[column]]),sd=sd(tur[[column]]),n=nrow(tur))
) %>% spherical(2) grid.desk(desk)
} grid_comparing()
```

Above desk reveals that the imply of recent instances in Turkey is bigger than Germany. To test it, we’ll inference regarding the distinction between two means.

With a view to make statistical inference for the $mu_1-mu_2$, the $bar X_1-bar X_2$ pattern distribution should be roughly regular distribution. Whether it is assumed that the associated populations won’t be regular, $bar X_1-bar X_2$ pattern distribution is roughly regular solely within the quantity of related samples larger than 30 individually in line with the central restrict theorem. On this case, the distribution is assumed roughly regular.

If the variances of two populations $sigma_1^2$ and $sigma_2^2$ are recognized, z-distribution could be used for statistical inference. A extra widespread state of affairs, if the variances of inhabitants are unknown, we’ll as an alternative use samples variances $s_1^2$, $s_2^2$ and $t_{sd}$ distribution.

When $sigma_1^2$ and $sigma_2^2$ are unknown, two state of affairs are examined.

• $sigma_1^2=$ $sigma_2^2$: the belief they’re equal.
• $sigma_1^2neq$ $sigma_2^2$: the belief they don’t seem to be equal.

There’s a formal take a look at to test whether or not inhabitants variances are equal or not which is a speculation take a look at for the ratio of two inhabitants variances. A two-tailed speculation take a look at is used for this as proven under. $H_0: sigma_1^2/sigma_2^2=0$ $H_A: sigma_1^2/sigma_2^2neq1$

The take a look at statistic for $sigma_1^2/sigma_2^2$ : $F_{(sd_1,sd_2)}=$ ${s_1^2}/{s_2^2}$

The pattern volumes $n_1$ and $n_2$, levels of freedom of the samples $sd_1=n_1-1$ and $sd_2=n_2-1$. F-distribution is used to explain the pattern distribution of $S_1^2/S_2^2$

```var.take a look at(deu\$new_cases,tur\$new_cases) #	F take a look at to check two variances #information: deu\$new_cases and tur\$new_cases
#F = 1.675, num df = 117, denom df = 71, p-value = 0.01933
#various speculation: true ratio of variances is just not equal to 1
#95 p.c confidence interval:
# 1.088810 2.521096
#pattern estimates:
#ratio of variances # 1.674964 ```

On the %5 significance stage, as a result of p-value(0.01933) is lower than 0.05, the null speculation( $H_0$) is rejected and we assume that variances of the populations aren’t equal.

As a result of the variances aren’t equal we use Welch’s t-test to calculate take a look at statistic: $t_{sd}=$ $frac{(bar x_1-bar x_2)} {sqrt{(frac{s_1^2} {n_1}+frac{s_2^2} {n_2})}}$

The diploma of freedom: $sd=frac{(s_1^2/n_1 + s_2^2/n_2)^2} {(s_1^2/n_1)^2/(n_1-1)+(s_2^2/n_2)^2/(n_2-1)}$

Let’s see whether or not the imply of recent instances per day of Turkey( $mu_1$) larger than Germany( $mu_2$); to try this we’ll construct the speculation take a look at as proven under: $H_0: mu_1-mu_2 leq 0$ $H_A: mu_1-mu_2 > 0″ title=”H_A: mu_1-mu_2 > 0″ class=”latex” />

#default var.equal worth is ready to FALSE that signifies that the take a look at is Welch's t-test t.take a look at(tur\$new_cases,deu\$new_cases,various = "g") # Welch Two Pattern t-test #information: tur\$new_cases and deu\$new_cases #t = 2.7021, df = 177.67, p-value = 0.00378 #various speculation: true distinction in means is bigger than 0 #95 p.c confidence interval: # 252.8078 Inf #pattern estimates: #imply of x imply of y # 2162.306 1510.856

As proven above , on the %5 significance as a result of the p-value(0.00378) is les than 0.05 the choice speculation is accepted, which suggests when it comes to controlling the unfold of the illness, Turkey appears to be much less profitable than in Germany.

One other widespread thought in Turkish those who the well being system within the nation is significantly better than many European nations together with Germany; let’s test that with each day demise toll variable (new_deaths).

```grid_comparing("new_deaths")
```

It appears Turkey has a lot much less imply of each day deaths than Germany. Let’s test it.

```var.take a look at(deu\$new_deaths,tur\$new_deaths) #	F take a look at to check two variances #information: deu\$new_deaths and tur\$new_deaths
#F = 4.9262, num df = 117, denom df = 71, p-value = 1.586e-11
#various speculation: true ratio of variances is just not equal to 1
#95 p.c confidence interval:
# 3.202277 7.414748
#pattern estimates:
#ratio of variances # 4.926203
```

As described earlier than, we’ll use Welch’s t-test as a result of the variances aren’t equal as proven above(p-value = 1.586e-11 < 0.05).

```t.take a look at(deu\$new_deaths,tur\$new_deaths,various = "g") #	Welch Two Pattern t-test #information: deu\$new_deaths and tur\$new_deaths
#t = 1.0765, df = 175.74, p-value = 0.1416
#various speculation: true distinction in means is bigger than 0
#95 p.c confidence interval:
# -5.390404 Inf
#pattern estimates:
#imply of x imply of y # 69.88983 59.83333 ```

At %5 significance stage, various speculation is rejected(p-value = 0.1416 >0.05). This means that the imply of each day deaths of Germany is just not worst than Turkey’s.

June 1 is ready because the day of normalization by the Turkish authorities due to this fact many restrictions will likely be eliminated after that day. With a view to test the choice, first, we’ll decide match fashions for forecasting. To search out the match mannequin we’ll construct a perform that compares development regression fashions in a plot.

```models_plot <- perform(df=tur,column="new_cases"){ df<- df[!df[[column]]==0,]#take away all Zero rows to calculate the fashions correctly #exponential development mannequin information body exp_model <- lm(log(df[[column]])~index,information = df) exp_model_df <- information.body(index=df\$index,column=exp(fitted(exp_model))) names(exp_model_df) <- column #evaluating the development plots ggplot(df,mapping=aes(x=index,y=.information[[column]])) + geom_point() + stat_smooth(technique = 'lm', aes(color = 'linear'), se = FALSE) + stat_smooth(technique = 'lm', method = y ~ poly(x,2), aes(color = 'quadratic'), se= FALSE) + stat_smooth(technique = 'lm', method = y ~ poly(x,3), aes(color = 'cubic'), se = FALSE)+ stat_smooth(information=exp_model_df,technique = 'loess',mapping=aes(x=index,y=.information[[column]],color = 'exponential'), se = FALSE)+ labs(shade="Fashions",y=str_replace(column,"_"," "))+ theme_bw() } models_plot()
```

As we will see from the plot above, the cubic and quadratic regression fashions appear to suit the information extra. To have the ability to extra exact we'll create a perform that compares adjusted $R^2$.

```#evaluating mannequin accuracy
#quadratic cubic # 0.73 0.77 ```

The cubic development regression mannequin is significantly better than the quadratic development mannequin for Turkeys unfold of illness as proven above.

Now, let’s discover ought to the normalization day(June 1) is true. Within the following code chunk, we'll strive some index numbers to search out zero new instances.

```#forecasting zero level for brand spanking new instances in Turkey
model_cubic <- lm(method = new_cases ~ poly(index, 3), information = tur)
predict(model_cubic,newdata=information.body(index=c(77,78,79,80))) # 1 2 Three 4 #183.92149 111.23894 42.50292 -22.04057 ```

As proven above, index 80 goes to unfavourable, so it may be thought-about because the day of normalization. If we have a look at the dataset, we will see that day is June 1. So the federal government appears to be proper about the normalization calendar.

You are able to do the identical predictions for Germany utilizing the features we created earlier than.

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