Difference between revisions of "Manuals/calci/CHITEST"

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<div style="font-size:30px">'''CHITEST(ar,er)'''</div><br/>
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<div style="font-size:30px">'''CHITEST (ActualRange,ExpectedRange)'''</div><br/>
*<math>ar</math> is the array of observed values
+
*<math>ActualRange</math> is the array of observed values.
*<math>er</math> is the array of expected values
+
*<math>ExpectedRange</math> is the array of expected values.
 +
**CHITEST(), returns the test for independence.
  
 
==Description==
 
==Description==
*This function gives the Average for given set of numbers.
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* It is a test for independence.
*Average means Sum of all the given elements is divided by Number of the given elements.
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* This function gives the value from the chi-squared distribution and the appropriate degrees of freedom i.e it calculates <math>\chi^2</math> statistic and degrees of freedom, then calls CHIDIST.  
*It is also called Arithmetic mean. i.e If n numbers are given and each number is denoted by a<math>i</math>, where <math>i</math>=1 to n, then <math>A.M = \frac{1}{n}\sum_{i=1}^n (ai)= \frac{a1+a2+.....+an}{n} </math>.
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The conditions of <math>\chi^2</math> test is  
*In this function N1,N2,... are it can either be numbers,arrays,references of cells or we can enter the logical values directly.
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The table should be 2x2 or more than 2x2
*This function will show the result as Error, when the numbers are error values or text that cannot change into numbers.
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Each observations should not be dependent
*Also if the distribution is symmetric, then we can use this function to find the Central Tendency.
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All expected values should be 10 or greater. 
*The three most common measures of Central Tendency are: A.M, Median,& Mode.
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Each cell has an expected frequency of at least five.
A.M:  It is calculated by adding the given set of numbers and divided by the count of the given set of numbers.  
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*The <math>\chi^2</math> test first calculates a <math>\chi^2</math> statistic using the formula:
E.g:Average of 2,4,2,7,2,3 and 5 is 3.6
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<math>\chi^2 = \sum_{i=1}^{columns} \sum_{j=1}^{rows} \frac{(observed _{ij}-expected _{ij})^{2}}{grand total}</math>
  Median: It is the middle number of a sorted list(Ascending order) of numbers. E.g:The median of 2,2,2,3,4,5,7 is 3
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*<math>observed _{ij}</math> is the array of the observed values in a given set of values
Mode: It is the most frequently  repeated number in a given set of numbers. E.g.The mode of 2,2,2,3,4,5 and 7 is 2
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*<math>expected _{ij} = \frac{(column _i total)*(row _j total)}{grand total} </math>
 +
*observed and expected must have the same number of rows and columns and there must be atleast 2 values in each.
 +
*A low result of <math>\chi^2</math> is an indicator of independence.
 +
*From the formula of <math>\chi^2</math> we will get <math>\chi^2</math> is always positive or 0.
 +
*0 only if <math>observed _{ij} = expected _{ij}</math> for each <math>i</math> and <math>j</math>.  
 +
*CHITEST uses the <math>\chi^2</math> distribution with the number of Degrees of Freedom df.
 +
*where <math>df=(r-1)(c-1),r>1</math> and <math>c>1</math>.
 +
*If <math>r=1</math> and <math>c>1</math>, then <math>df = c-1</math> or if <math>r>1</math> and <math>c=1</math>, then <math>df = r-1</math>.
 +
  If <math>r = c = 1</math> then this function will give the error result
 +
*The obtained result is entered in the Chi square distribution table with the obtained degrees of freedom.
 +
*This returns the test for independence (probability).
  
*Sometimes CHITEST returns the error value, when ‘a’ and ‘b’ have a different number of data points.
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==ZOS==
 +
*The syntax is to calculate CHITEST in ZOS is <math>CHITEST (ActualRange,ExpectedRange)</math>.
 +
**where <math>ActualRange</math>is the array of observed values.
 +
**<math>ExpectedRange</math>is the array of expected values.
 +
*For e.g;CHITEST([60,72,86,45],[57.08,75.10,87.1,42.45])
 +
{{#ev:youtube|gh-b_MUMo9c|280|center|Chi-Squared Test}}
  
 +
==Examples==
 +
A student investigated the chance of getting viral fever in a school for a period that took vitamin tablets every day. The total number of students 880. In that 639 students didn't get viral fever and 241 students got fever .But the expected ratio is 1:3<br/>
 +
'''Answer'''
 +
*If the ratio is 1:3 and the total number of observed individuals is 880, then the expected numerical values should be: 660 will not get fever and 220 students will get fever. 
  
 
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{| class="wikitable" style="width:50%" align="center"
 
+
|-  
{| id="TABLE3" class="SpreadSheet blue"
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!
|- class="even"
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! No Fever
| class="   " |
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! Get Fever
 
+
|-
| class="        " | Column1
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! Observed Values
| class="        " | Column2
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| 639
| class="    " | Column3
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| 241
| class="  " | Column4
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|-
|- class="odd"
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! Expected Values
| class=" " | Row1
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| 660
| class="sshl_f " | 45
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| 220
| class="sshl_f" | 38
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|-
| class="sshl_f" | 0.000313
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! <math>\frac{(oi-ei)^2}{ei}</math>
| class="sshl_f" |
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| 0.668
|- class="even"
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| 2
| class="  " | Row2
 
| class="sshl_f  " | 10
 
| class="sshl_f" | 23
 
| class="SelectTD" |
 
| class="sshl_f" |
 
|- class="odd"
 
| Row3
 
| class="sshl_f" | 12
 
| class=" " | 26
 
| class="sshl_f" |
 
| class="sshl_f" |
 
|- class="even"
 
| Row4
 
| class="sshl_f " | 40.5
 
| class=" " | 49.36
 
| class="sshl_f" |
 
| class="sshl_f" |
 
|- class="odd"
 
| class="sshl_f" | Row5
 
| class="sshl_f" | 19.56
 
| class="sshl_f" | 16.44
 
| class="sshl_f" |
 
| class="sshl_f" |
 
|- class="even"
 
| class="sshl_f" | Row6
 
| class=" " | 17.05
 
| class="sshl_f " | 17.41
 
|
 
| class="sshl_f" |
 
 
|}
 
|}
  
  Let’s see an example
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*The <math>\chi^2</math> value is 2.668
 +
*Now <math>df=(r-1)(c-1) = (2-1)(2-1) = 1 </math>
 +
*From the Chi Squared Distribution probability table with <math>df</math> is 1, the <math>\chi^2</math> value of 2.668 is 0.10.<br/>
 +
CHITEST(or,er) = 0.10
  
B C
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==Related Videos==
  
45 38
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{{#ev:youtube|UPawNLQOv-8|280|center|Chi Square Test}}
  
10 23
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==See Also==
  
12 26
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*[[Manuals/calci/CHIDIST | CHIDIST]]
  
40.5 49.36
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==References==
 +
[http://en.wikipedia.org/wiki/Chi-squared_distribution  CHI-SQUARE Distribution]
  
19.56 16.44
 
  
17.05 17.41
 
  
CHITEST (a, b)
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*[[Z_API_Functions | List of Main Z Functions]]
  
i.e. =CHITEST (B2; C4, B5:C7) is 0.003
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*[[ Z3 |  Z3 home ]]

Latest revision as of 09:57, 2 June 2020

CHITEST (ActualRange,ExpectedRange)


  • is the array of observed values.
  • is the array of expected values.
    • CHITEST(), returns the test for independence.

Description

  • It is a test for independence.
  • This function gives the value from the chi-squared distribution and the appropriate degrees of freedom i.e it calculates  statistic and degrees of freedom, then calls CHIDIST.

The conditions of test is

The table should be 2x2 or more than 2x2
Each observations should not be dependent
All expected values should be 10 or greater. 
Each cell has an expected frequency of at least five.
  • The test first calculates a statistic using the formula:

  • is the array of the observed values in a given set of values
  • observed and expected must have the same number of rows and columns and there must be atleast 2 values in each.
  • A low result of is an indicator of independence.
  • From the formula of we will get is always positive or 0.
  • 0 only if for each and .
  • CHITEST uses the distribution with the number of Degrees of Freedom df.
  • where and .
  • If and , then or if and , then .
If  then this function will give the error result
  • The obtained result is entered in the Chi square distribution table with the obtained degrees of freedom.
  • This returns the test for independence (probability).

ZOS

  • The syntax is to calculate CHITEST in ZOS is .
    • where is the array of observed values.
    • is the array of expected values.
  • For e.g;CHITEST([60,72,86,45],[57.08,75.10,87.1,42.45])
Chi-Squared Test

Examples

A student investigated the chance of getting viral fever in a school for a period that took vitamin tablets every day. The total number of students 880. In that 639 students didn't get viral fever and 241 students got fever .But the expected ratio is 1:3
Answer

  • If the ratio is 1:3 and the total number of observed individuals is 880, then the expected numerical values should be: 660 will not get fever and 220 students will get fever.
No Fever Get Fever
Observed Values 639 241
Expected Values 660 220
0.668 2
  • The value is 2.668
  • Now
  • From the Chi Squared Distribution probability table with is 1, the value of 2.668 is 0.10.

CHITEST(or,er) = 0.10

Related Videos

Chi Square Test

See Also

References

CHI-SQUARE Distribution