# The sample of compare and contrast essay

This calculator uses the following formulas to compute sample size and power, respectively: $$n_A=\kappa n_B \;\text{ and }\; n_B=\left(\frac{p_A(1-p_A)}{\kappa}+p_B(1-p_B)\right) \left(\frac{z_{1-\alpha}+z_{1-\beta/2}}{|p_A-p_B|-\delta}\right)^2$$
$$1-\beta= 2\left[\Phi\left(z-z_{1-\alpha}\right)+\Phi\left(-z-z_{1-\alpha}\right)\right]-1 \quad ,\quad z=\frac{|p_A-p_B|-\delta}{\sqrt{\frac{p_A(1-p_A)}{n_A}+\frac{p_B(1-p_B)}{n_B}}}$$ where

• $\kappa=n_A/n_B$ is the matching ratio
• $\Phi$ is the standard Normal distribution function
• $\Phi^{-1}$ is the standard Normal quantile function
• $\alpha$ is Type I error
• $\beta$ is Type II error, meaning $1-\beta$ is power
• $\delta$ is the testing margin

"1 Corinthians 13"
I, ______, take you, ______, as the love of my life. I vow to be patient with you and the circumstances in our lives. I vow to be kind to all people we come across. I vow not to be boastful of our love or about our accomplishments. I promise to be proud of you, but not proud in love for though I will strive for perfection, I know I can never reach it. I promise not to be quick to anger, but to think before I speak and act. I vow not to keep a record of wrongs, but to always keep the happy memories alive. Through God, our love will never fail.

I carried out a questionnaire exercise 4 years ago, attempting to replicate (as far as possible with only me as the resource) a questionnaire study done over a period of 3 years, with an initial population of 128,000, reducing to 2,000 by the end of the study by issuing a single online questionnaire to a very much smaller population based in a different part of the same country, whose population had not been part of the initial exercise. The results are all in SPSS but I also have them available in Excel. I carried out a descriptive analysis of the findings from my questionnaire and compared my results with the same questions from the original survey but am now being asked to compare my results in more depth with those from the original questionnaire. My statistical knowledge is sketchy 🙁 so I am not even sure whether the question I am going to ask here is a “good one”!). For both studies, only gender and age bands are known and I was wondering whether it would be possible to use the two sample t test to say whether the two populations are similar (or not) in their responses to individual questions in the two questionnaires. I have several books that I have consulted and online papers and I still can’t answer the question. Are you able to shed any light please? Thank you.

Most of the people find it difficult to differentiate a frog from a toad. They normally mix them up. Although they seem so similar in appearance, they certainly have numerous dissimilarities too.
Frogs are found in many different shapes, sizes, colors, and textures. Frogs have smooth, wet skin. They live most of the time in or near water. They have different eye colors including brown, silver, green, gold and red along with different shapes and sizes of pupil. Some of the frogs have sticky padding on their feet while others have webbed feet. It is obvious that not even all the frogs have same qualities.

## The sample of compare and contrast essay

Most of the people find it difficult to differentiate a frog from a toad. They normally mix them up. Although they seem so similar in appearance, they certainly have numerous dissimilarities too.
Frogs are found in many different shapes, sizes, colors, and textures. Frogs have smooth, wet skin. They live most of the time in or near water. They have different eye colors including brown, silver, green, gold and red along with different shapes and sizes of pupil. Some of the frogs have sticky padding on their feet while others have webbed feet. It is obvious that not even all the frogs have same qualities.