Hey there! Sign in to join this conversationNew here? Join for free

Standard error of the difference between two proportions Watch

    • Thread Starter
    Offline

    3
    ReputationRep:
    I need to estimate SE[P_0 - 2P_1], where P_0 = 0.2048 and P_1 = 0.12.

    Here's the question for reference.

    I calculated the proportion, P_0, from the first sample, which had [; 256 ;] of the variable I'm looking at, in a sample of 1250. P_1 came from the fact that there are 150 out of 1250 in the second sample.

    The problem I'm facing is that if I do the transformation first (P_0 - 2P_1), I get -0.0352, which obviously won't work with the SQRT in the SE formula.

    We are also told that \pi _0 = 0.2 (this is the population proportion).

    Where am I going wrong? I can provide more info if needed. Also, apologies if some of my terminology is a bit off.

    Thanks!


    To clarify what I have already done:

    An earlier question asked me to estimate [; SE[P_0] ;], which I did by first calculating the proportion, [; P_0 = 256/1250 = 0.2048 ;], then putting this value into the SE formula as follows:

    SE[P_0] = SE[0.2048] = \sqrt\frac{0.2048(1-0.2048)}{1250} = 0.01141427037

    I used this formula as it was how I was taught to find the SE of a sample proportion.

    I then applied similar intuition for the next question, by first calculating [; P_1 ;], then the difference between the proportions:

    P_1 = \frac{150}{1250} = 0.12

    P_0 - 2P_1 = 0.2048 - 2(0.12) = -0.0352

    The problem I then face is that if I try to use the same SE formula from above, I get tripped up by the negative:

    [; SE[P_0 - 2P_1] = SE[-0.0352] = \sqrt\frac{-0.0352(1--0.0352)}{1250} = \sqrt{-0.00002915...};]
    Offline

    13
    ReputationRep:
    (Original post by danlocke)
    I need to estimate SE[P_0 - 2P_1], where P_0 = 0.2048 and P_1 = 0.12.
    You need to go via the formula for the addition of variance.

     \displaystyle V(\lambda X_1 + \mu X_2) = \lambda^2 V(X_1) + \mu^2 V(X_2)

    So, take your standard errors, turn them into variances, get the variance of the linear combination, then square root to get the standard error.
    • Thread Starter
    Offline

    3
    ReputationRep:
    (Original post by Gregorius)
    You need to go via the formula for the addition of variance.

     \displaystyle V(\lambda X_1 + \mu X_2) = \lambda^2 V(X_1) + \mu^2 V(X_2)

    So, take your standard errors, turn them into variances, get the variance of the linear combination, then square root to get the standard error.
    Ah, right. How does this look?
    Offline

    13
    ReputationRep:
    (Original post by danlocke)
    Ah, right. How does this look?
    Right approach, but you've lost the sample sizes...
    • Thread Starter
    Offline

    3
    ReputationRep:
    (Original post by Gregorius)
    Right approach, but you've lost the sample sizes...
    Ah, so I just needed to divide the original two formula for variance by n, right?
    Offline

    13
    ReputationRep:
    (Original post by danlocke)
    Ah, so I just needed to divide the original two formula for variance by n, right?
    Yes.
    • Thread Starter
    Offline

    3
    ReputationRep:
    (Original post by Gregorius)
    Yes.
    Great, would you say 0.02163... looks correct then? If you missed my edit, here's my working.
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    Would you like to hibernate through the winter months?
    Useful resources

    Make your revision easier

    Maths

    Maths Forum posting guidelines

    Not sure where to post? Read the updated guidelines here

    Equations

    How to use LaTex

    Writing equations the easy way

    Student revising

    Study habits of A* students

    Top tips from students who have already aced their exams

    Study Planner

    Create your own Study Planner

    Never miss a deadline again

    Polling station sign

    Thinking about a maths degree?

    Chat with other maths applicants

    Can you help? Study help unanswered threads

    Groups associated with this forum:

    View associated groups
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

    Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

    Quick reply
    Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.