It was published that children who have longer first names tend to achieve highe

ID: 3062738 • Letter: I

Question

It was published that children who have longer first names tend to achieve higher grades (%) in elementary school. For example, Zai (short name, only three letters) may achieve a lower grade than Kabiralina (much longer name, ten letters). A study was conducted to investigate the influence of name length on grades from a local sixth grade class. Is there such a relationship?
The appropriate test for this problem is:

correlation

regression

multiple regression

NAMES GRADES
Aaralyn 76
Baldasarre 72
Cai 84
Daenerys 71
Ean 74
Famke 79
Gainella 73
Hakizimana 73
Ichnoyotl 74
Jadzia 88
Kabiralina 83
Lakshmina 75
Maconaquea 73
Nahuati 87
Ofek 77
Paitalyi 74
Qi 87
Raghnallia 81
Sada 73
Tabananica 79
Ulfah 89
Vadim 84
Wahmenita 88
Xanthusia 79
Yael 85
Zagiri 81

Explanation / Answer

The appropriate test for the problem is correlation.

Explanation: We will find the correlation coefficient between the "number of letters in the first name of the student" and the "marks obtained by the corresponding student.

If the correlation coefficient between the above mentioned two variables is positive then then we will conclude that "children with longer first name tend to achieve higher grades" or "children with shorter first name tend to achieve lower percentage".

If the correlation coefficient is 0 then we will conclude the above mentioned two variables are uncorrelated or in other words "number of letters in the first name of the student" do not affect "marks obtained by the corresponding student”.

If the correlation coefficient is negative then we will conclude children with longer first name tend to achieve lower grades or children with shorter first name tend to achieve higher grades.

The value of correlation coefficient(r) must be in between -1 & 1 ( -1<= r<=1)

Now, we have calculated the correlation coefficient between the variables using the CORREL function in excel. The number of letters in the first name for different students are obtained using LEN function in excel.

NAMES

number of letters

GRADES

Aaralyn

Baldasarre

Cai

Daenerys

Ean

Famke

Gainella

Hakizimana

Ichnoyotl

Jadzia

Kabiralina

Lakshmina

Maconaquea

Nahuati

Ofek

Paitalyi

Raghnallia

Sada

Tabananica

Ulfah

Vadim

Wahmenita

Xanthusia

Yael

Zagiri

Correlation coefficient = -0.29111 (using excel CORREL function)

So, from the value of the correlation coefficient it is clear that the variables are sightly negatively correlated.

Hence, it is expected that children with longer first name tend to achieve lower grades or children with shorter first name tend to achieve higher grades.

So, the relationship between length of the student's first name and their corresponding marks(grades) is slightly inversely proportional.