Question

Please type responses as it is difficult for me to see written responses. Thank you

1) How does understanding the correlation between variables help us understand regression?

2) Provide two ways on how you might use regression while teaching a classroom of children.

3) What is one easy way to remember the differences between parametric and nonparametric tests? (Note: I'm not asking you to list the differences but HOW you can remember the differences. Feel free to be creative here - you are free to use mnemonics, diagrams, poetry, etc...!)

4) Provide two ways on how you might use chi-square tests in a classroom environment if you were a teacher.

Answer 1

1)

Correlation is a statistical measure which determines co-relationship or association of two variables.

Regression describes how an independent variable (say x ) is numerically related to the dependent variable (say y )

Regression indicates the impact of a unit change in the known variable (x) on the estimated variable (y).

For example , Suppose in a class we have marks of students in two subject say ( maths and science ) , and it is belived that those students who scores good marks in maths , they will also score better marks in science subject.

So , we can find aasociation between scores in two subjects , i,.e Correlation here between Exam score in Maths and Exam score in Science , is comes out to be possitive and closer to 1 i.e correalation greter than 0.8 , then we can conclude that their is strong relationship betwwen Exam score of studentperformance in two subjects (Maths and science )

Here regreesion model can be used , such that dependent vaiable is Exam score in maths , and independent variable is Exam score in science .

So after fitting regreesion model we can see for every increament of one score in Subject maths , what will be the estimated score in subject science .

2) Provide two ways on how you might use regression while teaching a classroom of children.

Ways in which we can use regression while teaching a classroom of children , are

1) Make scatter plots of of given variables

2) Do a linear regression to determine a best line of fit

3) Make a prediction based on the regression line

Like a a examples of two variable which are Height of students( say in inches ) of one class and their respective shoe size .

Here let Height of students in Inches be dependent vaiable , now we wish to estimate Shoe size for every unit increase in height of students.

First make scatter plot to better understand that if show size increases with increase in Height of students .

The fit a regression model of Shoe Size ( y ) ~ Height (X) for data collect from students in classroom.

Then use the fitted model to describe that for what increament in height of students , then estimated shoe size willl increase .

Another ways might be comparing marks of students in two subject say Maths and Science .

Here regreesion model can be used , such that dependent vaiable is Exam score in maths(x) , and independent variable is Exam score in science (y).

So after fitting regreesion model we can see for every increament of one score in Subject maths , what will be the estimated score in subject science .

3) What is one easy way to remember the differences between parametric and nonparametric test

Parametric Test -

A statistical test, in which specific assumptions are made about the population parameter is known as parametric test.

The parametric test is the hypothesis test which provides generalisations for making statements about the mean of the parent population. like assumption that there is the normal distribution of variable and the mean in known or assumed to be known.

Nonparametric test -

A statistical test used in the case of non-metric independent variables, is called non-parametric test.

The nonparametric test is defined as the hypothesis test which is not based on underlying assumptions, i.e. it does not require population’s distribution to be denoted by specific parameters.

The test is mainly based on differences in medians. Hence, it is alternately known as the distribution-free test.

So the test in which we are suppose to test likr Median of population , or where we are not sure about normality of samples or population , then we Use Non-parametric Test, otherwise is we wish to test mean , variance of population , aasuming normality we consider it to be parametric test .

i.e Parametric analyses to assess group means

      Nonparametric analyses to assess group median

Some Parametric test are - 1-sample t-test , 2 sample t-test , Anova etc

Some Non-Parametric test are - 1-sample Sign test , Wilcoxon test , Kruskal-Wallis, Mood’s median test , Mann-

                                                    Whitney test

4) Provide two ways on how you might use chi-square tests in a classroom environment if you were a teacher.

The Chi Square statistic is commonly used for testing relationships between categorical variables.

The null hypothesis of the Chi-Square test is that no relationship exists on the categorical variables in the population; they are independent .

The alternative hypothesis is that There are relationships between the categorical variables.

Now suppose we wish to to know association between average Marks scored by a student in two classs      ( say A, B) and studying in private tutions . i.e Is there an association between the choise of students studing in Private Tution and the students marks in exam .

Now we take a sample of say 100 students

Now we make frequency table of average marks of student ( from Class A and Class B ) for each category studing in Private Tution ( say Yes \ No )

i.e

Studing in private Tution

                           Yes           No

Class     A             a              b

Class     B             c              d

To analyse these data in StatsDirect you must select the 2 by 2 contingency table from the chi-square section of the analysis menu.

Here if we do not reject null hypothesis , this will indicates that there is no association between the choice of studing in Private Tution factor and the marks of the student in exam.