Estimation

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FAMCO

Biostatistics

By: Dr. Bahnassy Courtesy of Sayed Hasan Alawami

Statistical inferences:

1. Estimation 2. Hypothesis testing

Estimation The General equation that we are going to use is: C.I. = Confidence interval. C.I. = Estimator + [Reliability coefficient x Stand error] = 1- Alpha.

N.B. From the equation: We are going to get two values when answering this equation. Also, it is important to know how to solve the equation’s codes. I.e. what are C.I, Estimator, reliability coefficient, standard error, and alpha? - C.I: is usually given in the question as in this example: Find 95% C.I. for the problem. - Estimator: usually, it is the mean or the proportion. Also, notice that the mean may be for one population or two. And the proportion, also, may be for one population or two. To clarify the estimator, for mean:: One mean Two means

Estimator = The Mean Estimator = Mean1 – Mean 2 (It is better to begin with the biggest value)

To clarify the estimator, for proportion:: Proportion = sample number / population One proportion Two proportions

Estimator = The proportion Estimator = Proportion 1 – Proportion 2

- Standard Error: also, the SE differs in the 4 conditions which already mentioned above. (mean, two mean, proportion, two proportion) Standard Error for:

- Alpha = Error. For example: alpha=0.05 - Reliability coefficient (Z): it can be found from the table that we already had with us.

How to use the table? First, notice that it will be easy for you to find it if you draw the normal distribution curve.

What do you mean ya Sayed ? Follow me and you will find out: 1. We studied that the normal distribution curve is a bell-shape. And the area under the curve equals 1.

2. We can divide the curve into two equal halves by an imaginary line.

3. The important point is that the numbers on the X-axis indicate the Reliability coefficient (z). For example, if the C.I. is 95% (from the question)..... That means it is 0.95 under the curve. And since we have two halves in the curve…. 0.95/2 = 0.475.

Now, look at the table and you will notice that 0.475 is written as 47.50. Anyway, you should look for the number that is on the first column. This will be the (Z) value, which equals 1.96.

4. Now, you have Reliability coefficient (z) and you can put it in the C.I equation.

After that, I hope you fully understood this: C.I. = Estimator +/- [Reliability coefficient x Stand error] And I hope you know how to extract the values from the question and put them on it.

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It is your turn now to try to solve the questions on the doctor’s slides.

There is one last thing I want to add to my first lecture before leaving, which is: There is another (Z) that you will find in other types of problems (PROBABILITY-questions). This (z) is calculated from this equation:

z = (x-u)/ SD X = the number that we want to study it. u= population mean. SD= standard deviation. PROBABILITY= number of time the event happens/ total number of observation.

This will be clear after answering the example: Suppose that the mean systolic blood pressure SBP in a normally distributed population is u= 115mg/100 ml and variance=225mg/100ml. find the probability that a randomly selected child will have a SBP<140. X= 140 z = (x-u)/ SD= 1.67

u=115

SD=15

And from the table we can see that 1.67 = 45.25% AND as we said before 45.25/100 =0.4525. (Notice in the curve where I wrote 0.4525) That means, the alpha= 0.5 – 0.4525 = 0.0475 The question asks for the Probability (P) that randomly selected child will have a SBP<140. 1. The total left area under the curve is equal to 0.5. 2. The total right area under the curve is equal to 0.5. However, only 0.4525 is included in our calculation since there is error equal to 0.0475. 3. 0.5 + 0.4525 = 0.9525 P(x <140) = p (z <1.67) =0.9525.

At the end, I hope that I SUCCEEDED to help you for better understanding. And I am going to ask you to forgive me for any And of course, mistakes I might have made, unconsciously if I already did, and you did not notice then, say GOOD BYE to some marks. Sayed Hasan Alawami 206 Special thanks to Mo'men Almo'men