Point Estimate
a single number, single number that is used to estimate an unknown population parameter,You have the advantage of being very precise, but you do not have much confidence that the point estimate is correct.
Interval Estimate
A range of values as an estimate of an unknown quantity, Does not have the precision of point estimates, but they do give more confidence
confidence interval
When the estimate is accompanied by a specific level of confidence (or probability) You have less precision, but you are more confident of the estimate.
confidence level
The confidence we have that the parameter lies in the confidence interval
Level of Confidence
*increase in confidence requires increase in the width of the confidence interval
*Trade off between precision and confidence
Sample size
*larger samples yield smaller intervals
*larger samples allows a more precise estimate of the population parameter, -number of observations necessary to represent a population
Estimation
the inferential process of using sample statistics to estimate population parameters
sampling error
differences between a sample and the entire population. A sample will not give a perfect picture of the whole population
what are the two ways to make estimates
point estimate and interval estimate
There is a trade off between ____.
precision and confidence
When to use estimation
three situations: 1) estimation is used after hyposthesis test when Ho is rejected. 2) estimation is used when you already know that there is an effect an simply want to find out how much. 3) estimation is used when you simply want some basic information
The logic of estimation
both estimation and hypothesis testing are inferential statistical techniques that involve using sample data as the basis for drawing conclusions about an unknown population parameter
statistical inference
using sample statistics to help answer questions about population parameters
How is estimation different from hypothesis testing
hypothesis requires a yes or no answer and estimation measures the value of the population mean after treatment to determine how much effect the treatment has
how are hypothesis and estimation similar?
They both make use of sample data and either z-scores or t statistics to find out about unknown populations
When to use Hypothesis Testing
When you want to know whether a treatment had an effect, or not
Inferential Statistics
Uses sample data to draw conclusions about an unknown population
basic logic between estimation and hypothesis testing
based on the fact that each population parameter has a corresponding sampling statistic you can compute a standard error that measures how much discrepancy is expected, on average, between the statistic and the parameter
Four situations for hypothesis testing
The z score test
The single-sample t
The independent-measures t
The repeated-measures t
Focus on estimation for the t statistic
sample mean population mean
t = (or mean difference) - (or mean difference)
estimated standard error
when solving for the unknown population parameter what form is used
population (or mean difference) = sample mean (or mean difference) + or - t(estimated standard error)
How can we use the distribution to estimate what the t statistic ought to be
for a point estimate, the best bet is to use t = 0, the exact center of the distribution and is the most likely value, with probabilities decreasing steadily as you move away from zero toward the tails of the distribution. for an interval estimate, we wil
if a hypothesis test fails to reject the null hypothesis should estimation be used
no, since the hypothesis failed to reject then there is not treatment effect and there would be no need for estimation
the estimation formula for a single-sample t is ___.
m = M + or - ts(M1-M2)
The independent-measures t statistic uses the data from two separate samples to evaluate the mean difference between two populations and we use this statistic to answer a yes-no-question: is there any difference between the two population means using:
the independent-measures t statistic is used to estimate the value of �1 - �2
repeated-measures t statistic will be used to estimate the mean difference for the general population, MD, using the mean difference for a sample, MD with the estimation formula for the repeated-measures t is ___.
mD = MD + or - ts(MD)
Before computing the estimated standard error, it is first necessary to calculate the sample variance using formula ___.
SM = square root of s squared divided by n
The point estimate will use t = 0 with formula:
� = M � tsM and for 2 samples use �1 - �2 = (M1 - M2)� ts(M1 - M2)
To gain more confidence in your estimate, you must ___.
increase the width of the interval
to have a smaller interval you must
give up confidence
The bigger the sample (n), the ____
smaller the interval
A bigger sample gives you more information about the population and allows you to ____,
make a more precise estimate
In addition to describing the size of the treatment effect, estimation can be used:
to get an indication of the "significance" of the effect
which two characteristics of the confidence interval shoud be noted in estimation?
what happens to the width of the interval when you change the level of confidence and what happens to the interval width if you had a different sample size
a bigger sample give you
more information about the population and allows you to make a more precise estimate
in estimation the sample size controls:
the magnitude of the standard error in the estimation formula
the estimation process begins by
solving the t-statistic equation for the unknown population mean (or mean difference)
as the percentage of confidence increases
the interval width gets larger (less precision)
for estimation, the t value is determined
by the level of confidence and must be looked up in the appropriate table