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. Amw – यह उष्ण कटिबंधीय (मानसूनी) आर्द्र मुख्य जलवायु प्रदेश है जिसमें सबसे ठण्डे माह का तापमान 18 डीग्री सेंटीग्रेड से ऊपर रहता है तथा इसमें लघु शुष्क ऋतु भी होती है। ऐसी जलवायु भारत में कांकण एवं मालाबार तटवर्ती क्षेत्रों में पायी जाती है जिनमें गोवा दक्षिणी पश्चिमी महाराष्ट्र, पश्चिमी कर्नाटक, केरल तथा कन्याकुमारी तक फैला तमिलनाडु तट सम्मिलित है। इनके अतिरिक्त त्रिपुरा व दक्षिणी मिजोरम में भी यह जलवायु मिलती है। यहाँ शीतकाल शुष्क रहता है तथा ग्रीष्म काल एवं वर्षा काल में मानसूनी पवनों द्वारा वर्षा होती है। इस क्षेत्र में 200 से.मी. से अधिक वार्षिक वर्षा प्राप्त होती है, फलस्वरूप सदाबहार वनस्पति पायी जाती है। यह क्षेत्र सह्याद्री पर्वत का पश्चिमी भाग है, जो मानसूनी पवनों की अरब सागरीय शाखा के एकदम सामने पड़ता है तथा इसका दक्षिणी भाग मानसूनी पवनों के प्रवेश पर ही स्थित है, फलस्वरूप पर्याप्त वर्षा प्राप्त होती है तथा कर्क…
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You research two groups and put them in categories single, married or divorced:
The numbers are definitely different, but …
The Chi-Square Test gives a “p” value to help you decide!
| Beach | Cruise | |
| Men | 209 | 280 |
| Women | 225 | 248 |
If Gender (Man or Woman) does affect Preferred Holiday we say they are dependent.
By doing some special calculations (explained later), we come up with a “p” value:
p value is 0.132
Now, p < 0.05 is the usual test for dependence. In this case, p is greater than 0.05, so we believe the variables are independent (ie not linked together).
In other words, Men and Women probably do not have a different preference for Beach Holidays or Cruises.
“p” is the probability the variables are independent.
Imagine that the previous example was in fact two random samples of Men each time:
 |
 |
| Men: Beach 209, Cruise 280 |
Men: Beach 225, Cruise 248 |
Is it likely you would get such different results surveying Men each time?
Well the “p” value of 0.132 says that it really could happen every so often.
Surveys are random after all. We expect slightly different results each time, right?
So most people want to see a p-value less than 0.05 before they are happy to say the results show the groups have a different response.
Let’s see another example:
| Cat | Dog | |
| Men | 207 | 282 |
| Women | 231 | 242 |
By doing the calculations (shown later), we come up with:
P value is 0.043
In this case p < 0.05, so this result is thought of as being “significant” meaning we think the variables are not independent.
In other words, because 0.043 < 0.05 we think that Gender is linked to Pet Preference (Men and Women have different preferences for Cats and Dogs).
Just out of interest, notice that the numbers in our two examples are similar, but the resulting p-values are very different: 0.132 and 0.043. This shows how sensitive the test is!
It is just a choice! Using p<0.05 is common, but we could have chosen p<0.01 to be even more sure that the groups behave differently, or any value really.
So how do we calculate this p-value? We use the Chi-Square Test!
Note: Chi Sounds like “Hi” but with a K, so say Chi-Square like “Ki square”
And Chi is the greek letter Χ, so we can also write it Χ2
Important points before we get started:
Hypothesis: A statement that might be true, which can then be tested.
The two hypotheses are.
| Cat | Dog | |
| Men | 207 | 282 |
| Women | 231 | 242 |
| Cat | Dog | ||
| Men | 207 | 282 | 489 |
| Women | 231 | 242 | 473 |
| 438 | 524 | 962 |
Multiply each row total by each column total and divide by the overall total:
| Cat | Dog | ||
| Men | 489×438/962 | 489×524/962 | 489 |
| Women | 473×438/962 | 473×524/962 | 473 |
| 438 | 524 | 962 |
Which gives us:
| Cat | Dog | ||
| Men | 222.64 | 266.36 | 489 |
| Women | 215.36 | 257.64 | 473 |
| 438 | 524 | 962 |
| Cat | Dog | ||
| Men | (207-222.64)2222.64 | (282-266.36)2266.36 | 489 |
| Women | (231-215.36)2215.36 | (242-257.64)2257.64 | 473 |
| 438 | 524 | 962 |
Which is:
| Cat | Dog | ||
| Men | 1.099 | 0.918 | 489 |
| Women | 1.136 | 0.949 | 473 |
| 438 | 524 | 962 |
1.099 + 0.918 + 1.136 + 0.949 = 4.102
Chi-Square is 4.102
To get from Chi-Square to p-value is a difficult calculation, so either look it up in a table, or use the Chi-Square Calculator.
But first you will need a “Degree of Freedom” (DF)
Multiply (rows − 1) by (columns − 1)
Example: DF = (2 − 1)(2 − 1) = 1×1 = 1
The result is:
p = 0.04283
Done!
This is the formula for Chi-Square:
A Helpful Video
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