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25.04.2016
NNT (or number-needed-to-treat) is the reciprocal of the fractional improvement in a treated group minus the fractional improvement in an untreated group. However, it’s probably a good thing to have some idea about the 95% confidence interval of this figure. Where = the lower bound of the ARR 95% confidence interval and = the upper bound of the ARR 95% confidence interval.
Note: If the Number Needed to Treat (NNT) 95% confidence intervals pass through positive and negative numbers this means that the confidence intervals look as though they do not encapsulate the NNT. Please choose your Course type and Course code (and Instructor for Classroom students) from the drop down menus at the top of the page.
The 3rd video contains instructions on how to use SPSS to perform the calculations discussed in this lesson. Calculate and interpret a confidence interval for a population mean given a confidence level. Show the appropriate connections between the numerical and graphical summaries that support the confidence interval.
Show the appropriate connections between the numerical and graphical summaries that support the hypothesis test.
Historical Note: William Sealy Gosset (1876-1937) was a British industrial scientist and statistician best known for his discovery of the $t$-distribution. In a remarkable piece of work, Gosset found the appropriate distribution to use when $\sigma$ is unknown.
Click here to explore how the shape of the $t$-distribution changes with the degrees of freedom.
This hypothesis test is conducted in a manner similar to a test for a single mean where $\sigma$ is known, except that instead of using the population standard deviation, $\sigma$, in the calculations, we estimate this value using the sample standard deviation, $s$. We assume that the individuals chosen to participate in the study represent a (simple) random sample from the population. The interpretation of the results will follow the pattern established in the previous hypothesis tests. In Excel, the degrees of freedom ($df$) are given in cell E21.In SPSS, the degrees of freedom ($df$) are given in the output in the box labeled "One-Sample Test".
The birth weights of all children born on December 18, 1997 at the Mater Mothers' Hospital in Brisbane, Australia were recorded . Using this data set, test the hypothesis that the mean weight of babies born in Australia is 3373 grams.
Since the $P$-value is greater than the level of significance, we fail to reject the null hypothesis.
There is insufficient evidence to suggest that the mean weight of babies born in Australia is different from 3373 grams.
The procedure for finding confidence intervals when $\sigma$ is not known is very similar to the process when $\sigma$ is known. To construct the confidence interval when $\sigma$ is not known, we replace the population standard deviation, $\sigma$, with its point estimate, $s$. To test Pharaoh's ability to translate, Koehn took a random sample of 100 blocks of Spanish text, each of which contained 300 sentences, and used Pharaoh to translate each of these to English.
Koehn wants to find an estimate of the true mean BLEU score for text translated by the Pharaoh computer program. Recall the requirement of normality is satisfied if the data are approximately normally distributed or if the sample size is large.
It is impossible to know the true standard deviation of the BLEU scores for a new translation program like Pharaoh.
If we want to create a 95% confidence interval for $\mu$, with 99 degrees of freedom, then $ t^* = 1.9842 $. Answer the following questions using the data set BLEU-Scores, which gives the BLEU scores for $n=100$ translations from Spanish to English by the computer program Pharaoh.
A group of statisticians measured the weights of 2000 Belgian one Euro coins in eight batches. Typically, we round our computations to one more decimal place of precision than was given in the original data.


The coins were taken in batches, but we can think of the batches as a random sample of the possible coins that could be chosen. In practice we rarely know the true standard deviation $\sigma$ and will therefore be unable to calculate a z-score.
The $t$-distribution is similar to a normal distribution in that it is bell-shaped and symmetrical, but the exact shape of the $t$-distribution depends on the degrees of freedom ($df$). You will use ExcelSPSS to carry out hypothesis testing and create confidence intervals involving $t$-distributions. 7.1 Confidence Intervals for the Mean When Is Known A point estimate is a specific numerical value estimate of a parameter.
Three Properties of a Good Estimator unbiased estimator 1.The estimator should be an unbiased estimator. Three Properties of a Good Estimator consistent estimator 2.The estimator should be consistent. Confidence Intervals for the Mean When Is Known interval estimate An interval estimate of a parameter is an interval or a range of values used to estimate the parameter.
Confidence Level of an Interval Estimate confidence level The confidence level of an interval estimate of a parameter is the probability that the interval estimate will contain the parameter, assuming that a large number of samples are selected and that the estimation process on the same parameter is repeated.
Confidence Interval confidence interval A confidence interval is a specific interval estimate of a parameter determined by using data obtained from a sample and by using the specific confidence level of the estimate. Meaning of Alpha is the probability that our confidence interval does not contain the population mean.
Rounding Rule When you are computing a confidence interval for a population mean by using raw data, round off to one more decimal place than the number of decimal places in the original data.
Example 7-1: Days to Sell an Aveo A researcher wishes to estimate the number of days it takes an automobile dealer to sell a Chevrolet Aveo. What the confidence interval means In the formula for the confidence interval, the sample means will vary. Example 7-3: Credit Union Assets The following data represent a sample of the assets (in millions of dollars) of 30 credit unions in southwestern Pennsylvania. 6.  Understand how sample size, level of confidence and standard deviation affect confidence interval length. Other scenarios to think about:  What would happen to the length of our confidence intervals if we increase our sample size from 60 to 100?  Would our intervals decrease or increase in length?  What if the population standard deviation increased? 3.  How large a sample of one-bedroom apartments above would be needed to estimate the population mean within plus or minus $50 with 90% confidence?
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. We have no more reason to think that the true mean is above the sample mean than to think the true mean is below the sample mean. Not the answer you're looking for?Browse other questions tagged statistics or ask your own question. What is the smallest number of people in a group, so that it is guaranteed that three of them will have their birthday in the same month?
In a formal paper, should I censor "brainf**k", the name of a programming language? What sightseeing options are amenable for taking a 2 year old on a one day layover in Paris?
In other words, given the number of subjects who took part in the study, in what range does the true NNT lay (with 95% confidence). However, this actually means that the range passes through infinity (which does include the NNT). To find other confidence intervals, go to $Analyze \rightarrow Descriptive~Statistics \rightarrow Explore$. Use ExcelSPSS to find a 90% confidence interval for the true mean BLEU score for translations by the Pharaoh program. Use ExcelSPSS to find a 99% confidence interval for the true mean BLEU score for translations by the Pharaoh program. What do you notice about the confidence interval as the confidence level increased from 90% to 99%?


Find the confidence interval: Use ExcelSPSS to create a 99% confidence interval for the true mean. Present your observations in an English sentence, relating the result to the context of the problem.
Student's t-distribution gives us a new test statistic, $t$, that is calculated using the sample standard deviation ($s$) instead. That is, the expected value or the mean of the estimates obtained from samples of a given size is equal to the parameter being estimated. For a consistent estimator, as sample size increases, the value of the estimator approaches the value of the parameter estimated. Suppose the weights of oranges from a certain orange grove are normally distributed and the population standard deviation is 2.4 ounces. This means that 95% of all samples of size 36 will have the property that the interval from contains the population mean. Permission required for reproduction or display.19 The standard deviation of the population divided by the square root of the sample size equals the standard deviation of the sampling distribution. When you are computing a confidence interval for a population mean by using a sample mean and a standard deviation, round off to the same number of decimal places as given for the mean.
Assuming the standard deviation of the population is 0.8 year, find the best point estimate of the population mean and the 99% confidence interval of the population mean. Although the width of the confidence interval remains the same, each confidence interval created will vary according to the variation of the sample mean. Which of the assumptions listed above might be problematic in making inference to the population in Question 4? So the cases that you discuss, where the sample mean is below the true mean, are cancelled by the cases where the sample mean is above the true mean.
NNT confidence intervals that cross the "0" boundary require quite complex interpretation (going from improvement to harm, etc) and some even suggest that NNT should not be used when this occurs (arguing that NNT should only be used for statistically significant results). Watson Research Center developed methods to measure the quality of a translation from one language to another. Move the desired variable into the "Dependent List" and then press the "Statistics" button on the right of the window. You may notice that the output for doing a hypothesis test contains a category labeled "95% Confidence Interval of the Difference." This is different from the Confidence Interval of the Mean given in the $Explore$ function and will give you different values. A random sample of size = 36 oranges is selected and the mean weight is determined to be 8.6 ounces.
For a normally distributed variable, 95% of the observations will lie within 2 standard deviations of the mean.
21 The maximum error of the estimate is the maximum likely difference between the point estimate of a parameter and the actual value of the parameter. 25 One can say with 95% confidence that the interval between 52 and 56 days contains the population mean, based on a sample of 50 automobiles. However, we can say that, for a confidence level of 95%, 95% of the confidence intervals determined will actually contain. 30 One can be 95% confident that an interval built around a specific sample mean would contain the population mean. The error made in this case (distribution of scores is not really normal) is probably not too bad. That above $30$ we are OK is a rule of thumb, pretty good if the base distribution is not too ugly, but it can be significantly off in some situations. Find the best point estimate of the population mean and the 95% confidence interval of the population mean.
BLEU helps companies who develop translation software "to monitor the effect of daily changes to their systems in order to weed out bad ideas from good ideas".



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