Introduction to Estimation: Access to Family Planning

Estimation. 

In this module you will learn how to estimate a population parameter based on the sample.  The parameters we will estimate are the population proportion, population mean, and the population variance.

Parameter and Statistic notation
Population Parameter Statistic
p p with hat on top
mu x with bar on top
sigma squared s squared

Typically population parameters are unknown, and we have to use statistics to estimate them.  It is impossible to find the parameters exactly if the population is large enough.  The only way to find the parameter exactly is by using the entire population to compute the parameters.  Unfortunately this is often difficult or impossible in practice. 

Access to Family Planning

The website for UN Gender Statistics Links to an external site. contains data on 52 quantitative and 11 qualitative indicators addressing relevant issues related to gender equality and /or women's empowerment. 

Consider the question:  Does a woman age 15 to 49 have access to family planning resources?  To answer this question we can select a simple random sample from the population of interest, find the proportion of women who have access to family planning resources.  This proportion is the estimate of the actual proportion of women who have access to family planning resources.   The two values do not have to be equal.  This is a problem, our estimate of population proportion is different from the actual population proportion.  That is the case generally.  To remedy this problem we can use an interval around the estimate of the population parameter.  The interval is more likely to "capture" the population parameter within its boundaries.

  • A confidence interval is a range of values around the estimate of a population parameter.
  • Confidence level (1 minus alpha) - if many confidence intervals were constructed, the confidence level is the proportion of the intervals that contain the population parameter.  For example, 95% confidence level implies that if you collected 1000 samples and computed the confidence interval for each, 95% of these intervals would contain the population parameter.
  • A critical value (z subscript alpha divided by 2 end subscript) for a confidence level 1 minus alpha is a z score that corresponds to the area under the standard normal curve between -z and z.  The area of the tails is alpha.  For the sampling distributions other than normal we use different notation (t alpha over 2, chi square alpha over 2, etc.).

The Margin of Error (E)

E equals C r i t i c a l space V a l u e cross times S tan d a r d space E r r o r