Love is not... Love is...

Loving another is not about spending time together, not talking about the daily happenings in life, not dressing up for a date, not doing something for the other, those are aspects of a relationship that does not epitomize love.

What matters more in a relationship is the desire to keep the other company, the desire to find out more about the other, the desire to understand the other, the desire to impress the other constantly. 

These might seem like the same thing when translated into actions, but they are fundamentally different at the intention level.

Everyone have different perspectives on what constitutes love. What is yours? 

What does p-value represent?

The P is a probability that ranges from zero to one that measures the chance that the sample mean is different, given that the population have the same mean. To be more specific, the p-value can be MAINLY classified into 2 categories: 1-tail p-value and 2-tail p-value. In fact, p-values have many tails.

(Note: When you use p-value, you are assuming that the population mean is the SAME.In the A' level syllabus, we are assuming that the population mean are the same, and are calculating the probability that the the sample mean is different by chance.)

1-tail p-value is used when the difference you observed can only be in ONE direction. (This is used in our calculations, when we say that the alternative hypothesis is more/less than our null hypothesis)

2-tail p-value is used when the difference you observed can be in BOTH direction. (When we observe that the alternative hypothesis IS NOT EQUAL to our null hypothesis.)

In MOST cases, people tend to use 2-tail p-values instead of 1-tail p-value MAINLY because when the p-value is LARGE in the opposite direction, one HAVE TO conclude that the difference is due to CHANCE, and it IS NOT statistically significant. This results in a dilemma, because the LARGE difference tells you that difference is NOT due chance. Hence, to prevent such a situation, people tend to use 2-tail p-values.

In hypothesis testing, the p-value is the probability of obtaining a result as extreme as the one observed. We use the p-value as a guage to determine if our null hypothesis should be rejected or not. Your threshold p-value(or your level of significance, or confidence level) should be set to a value based on the consequence of missing a true difference, or to falsely finding a difference. However, conventionally, it is set to 0.05. After we get the p-value, we compare it to our threshold p-value, and compare the difference and conclude whether or not to reject our null hypothesis.

To conclude on your value of p-value, you can either comment that it is by coincidence(with the chance equal to your p-value) that the difference is as large as you observed even though your population mean is the same, or that your population mean is different from the start.

The p-value IS NOT the probability that the null hypothesis is true, because we are conducting the test based on the assumption that the difference is by chance ALONE.(pls notify me if there's any error here) It is also not the probability of falsely rejecting the null hypothesis. This is further explained here

A simple example of calculation of p-value can be found here

Source:

http://www.graphpad.com/articles/pvalue.htm

http://en.wikipedia.org/wiki/P-value

http://www.isixsigma.com/dictionary/P-Value-301.htm

http://economics.about.com/od/termsbeginningwithp/g/pvaluedef.htm

Other source:

p-value in science

This is interesting

Quiz For The Week

Do Singaporeans working overseas pay income tax to the Singapore government? Likewise, do foreigners working in Singapore pay income tax to their government?

Basically, from the information i gathered, MOST countries collect taxes based on where the income is generated from, regardless of citizenship. Hence, in both cases in the question, since the income is generated in Singapore, they pay tax to the Singapore government, not their own government.

Some other interesting things i've found out:
Tax rates for foreigners are lower than that for Singaporeans.
You can apply for 'reduced tax' based on your number of days spent in Singapore, and you only get taxed on your income generated in Singapore.

source

What is the solution of arg(e^z), where z=x + yi. Find not only the solution, but also the proof.

arg(e^z)
=arg(e^(x+yi))
=arg(e^x) + arg(e^yi)
=(0) + arg(cos(y) + i(sin(y))) Note:arg(e^x)= 0
=tan-1(sin(y)/cos(y)) Note:cos(y) is the horizontal component
=tan-1(tan(y)) and sin(y) is the vertical component
=y

here's a picture i drew to aid you in your understanding.

(this is the edited one to fit with the background of my blog, the original one was drawn with black lines against a white background. this is edited using photoshop.)

Sound is produced when there is a change in air pressure. What do you think?

HOW IS SOUND PRODUCED?

A vibrating object compresses air which travels in the form of waves to your eardrum, causing it to vibrate upon collision.(Note: Sound waves are particles in motion.) Nerves in your ear detect those vibrations and perceive them as sound.

More Information

Sound, which is a series of wave fronts(high pressure) and wave valleys (low pressure), is characterized by the difference in pressure between the wave front and wave valley and the pitch is determined by the closeness between the wave fronts.

please visit here for more details on sound.

Source: Wikipedia, Physics source

alright, here's one aspect of production of sound. There's another aspect which i'm not very sure in, the one on sound being produced via the vibration of molecules. Logically, it produces sound, because vibration will push the air molecules towards other air molecules, which is an increase in pressure(compression in the longitudinal wave profile). And when the vibrating source is moving back to it's original position, it creates a space of hollowness, which corresponds to the rarefaction in the wave profile. As such, it will not clash with the answer of sound being produced when there's a change in pressure. But still, i'll check it out with credible sources, and if my proposal's positive, i'll not post again. but i'll update you all if my proposal's negative.