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Presentation by:- Chandan kr singh
                      Anita Gupta
                    Sushant Yadav
   It is a statistical measure used in the context of
    sampling analysis for comparing a variance to a
    theoretical variance.
   As a non-parametric test it can used to
    determine if categorical data shows
    dependency or the two classifications are
    independent.
   It is also used to make comparisons between
    theoretical populations and actual data when
    categories are used.
   The significance level of a statistical hypothesis
    test is a fixed probability of wrongly rejecting
    the null hypothesis H0, if it is in fact true.
   It is the probability of a type I error and is set
    by the investigator in relation to the
    consequences of such an error. That is, we want
    to make the significance level as small as
    possible in order to protect the null hypothesis
    and to prevent, as far as possible, the
    investigator from inadvertently making false
    claims.
   OBSERVED VALUE STATISTICS The value of
    a characteristic determined as the result of a
    single observation.
   EXPECTED VALUE of a random variable is
    the integral of the random variable with
    respect to its probability measure.
   DEGREES OF FREEDOM is the number of
    values in the final calculation of a statistic
    that are free to vary.
CONDITION OF    CONDITION OF HOME      TOTAL
    CHILD           CLEAN DIRTY
    CLEAN           70      50             120
    FAIRLY CLEAN    80      20             100
    DIRTY           35      45             80
    total           185     115            300




State whether the two attributes, condition of home and
condition of child are independent (Use Chi-Square test for the
purpose)
We assumed that the two attributes are not
    related to each other.
    Condition of home and condition of child
    are not independent.
                           O-E 2
          Chi-Square =∑     E


                         𝑅𝑜𝑤 𝑇𝑜𝑡 𝑎 𝑙 × 𝐶𝑜𝑙 𝑢 𝑚𝑛 𝑇𝑜𝑡 𝑎 𝑙
•        Expected value=
                               𝐺𝑟𝑎𝑛𝑑 𝑇𝑜𝑡 𝑎 𝑙
Group   Observed   Expected   (O – E)   (O-E)2    (O-E)2
        value(O)   value(E)                         E
CC      70         74         -4        16        0.216
CDC     50         46          4        16        0.347
FC      80         61.67       18.33    335.98    5.448
FDC     20         38.33      -18.33    335.98    8.765
DC      35         49.33      -14.33    205.34    4.162
DDC     45         30.67       14.33    205.34    6.695
                                          TOTAL =25.633


So, the chi-square value 25.633
Once the calculation is over we compare value with the
table value, which can be calculated after the degree of
freedom.
 Degree of Freedom=(r-1)(c-1)
                     =(3-1)(2-1)
                     = 2×1
                     =2
 Now we need to check value from the table with
  respective to level of significance and degree of
  freedom that is 1% or 0.01 and 2……
    The table value is 9.210
 Hence the calculated value is more than the

  table value.
 So, our hypothesis is rejected.
Chi square

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Chi square

  • 1. Presentation by:- Chandan kr singh Anita Gupta Sushant Yadav
  • 2. It is a statistical measure used in the context of sampling analysis for comparing a variance to a theoretical variance.  As a non-parametric test it can used to determine if categorical data shows dependency or the two classifications are independent.  It is also used to make comparisons between theoretical populations and actual data when categories are used.
  • 3. The significance level of a statistical hypothesis test is a fixed probability of wrongly rejecting the null hypothesis H0, if it is in fact true.  It is the probability of a type I error and is set by the investigator in relation to the consequences of such an error. That is, we want to make the significance level as small as possible in order to protect the null hypothesis and to prevent, as far as possible, the investigator from inadvertently making false claims.
  • 4. OBSERVED VALUE STATISTICS The value of a characteristic determined as the result of a single observation.  EXPECTED VALUE of a random variable is the integral of the random variable with respect to its probability measure.  DEGREES OF FREEDOM is the number of values in the final calculation of a statistic that are free to vary.
  • 5. CONDITION OF CONDITION OF HOME TOTAL CHILD CLEAN DIRTY CLEAN 70 50 120 FAIRLY CLEAN 80 20 100 DIRTY 35 45 80 total 185 115 300 State whether the two attributes, condition of home and condition of child are independent (Use Chi-Square test for the purpose)
  • 6. We assumed that the two attributes are not related to each other. Condition of home and condition of child are not independent. O-E 2  Chi-Square =∑ E 𝑅𝑜𝑤 𝑇𝑜𝑡 𝑎 𝑙 × 𝐶𝑜𝑙 𝑢 𝑚𝑛 𝑇𝑜𝑡 𝑎 𝑙 • Expected value= 𝐺𝑟𝑎𝑛𝑑 𝑇𝑜𝑡 𝑎 𝑙
  • 7. Group Observed Expected (O – E) (O-E)2 (O-E)2 value(O) value(E) E CC 70 74 -4 16 0.216 CDC 50 46 4 16 0.347 FC 80 61.67 18.33 335.98 5.448 FDC 20 38.33 -18.33 335.98 8.765 DC 35 49.33 -14.33 205.34 4.162 DDC 45 30.67 14.33 205.34 6.695 TOTAL =25.633 So, the chi-square value 25.633 Once the calculation is over we compare value with the table value, which can be calculated after the degree of freedom.
  • 8.  Degree of Freedom=(r-1)(c-1) =(3-1)(2-1) = 2×1 =2 Now we need to check value from the table with respective to level of significance and degree of freedom that is 1% or 0.01 and 2…… The table value is 9.210  Hence the calculated value is more than the table value.  So, our hypothesis is rejected.