Section 9.6 Summary
Subsection 9.6.1 Glossary
- Statistical Inference
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Methods for gaining insight regarding the population parameters from the observed data.
- Point Estimation
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An attempt to obtain the best guess of the value of a population parameter. An estimator is a statistic that produces such a guess. The estimate is the observed value of the estimator.
- Confidence Interval
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An interval that is most likely to contain the population parameter. The confidence level of the interval is the sampling probability that the confidence interval contains the parameter value.
- Hypothesis Testing
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A method for determining between two hypothesis, with one of the two being the currently accepted hypothesis. A determination is based on the value of the test statistic. The probability of falsely rejecting the currently accepted hypothesis is the significance level of the test.
- Comparing Samples
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Samples emerge from different populations or under different experimental conditions. Statistical inference may be used to compare the distributions of the samples to each other.
- Regression
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Relates different variables that are measured on the same sample. Regression models are used to describe the effect of one of the variables on the distribution of the other one. The former is called the explanatory variable and the later is called the response.
- Missing Value
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An observation for which the value of the measurement is not recorded.
Ruses the symbol “NA” to identify a missing value.
Subsection 9.6.2 Discuss in the forum
A data set may contain missing values. Missing value is an observation of a variable for which the value is not recorded. Most statistical procedures delete observations with missing values and conduct the inference on the remaining observations.
Some people say that the method of deleting observations with missing values is dangerous and may lead to biased analysis. The reason is that missing values may contain information. What is your opinion?
When you formulate your answer to this question it may be useful to come up with an example from you own field of interest. Think of an example in which a missing value contains information relevant for inference or an example in which it does not. In the former case try to assess the possible effects on the analysis that may emerge due to the deletion of observations with missing values.
For example, the goal in some clinical trials is to assess the effect of a new treatment on the survival of patients with a life-threatening illness. The trial is conducted for a given duration, say two years, and the time of death of the patients is recorded. The time of death is missing for patients that survived the entire duration of the trial. Yet, one is advised not to ignore these patients in the analysis of the outcome of the trial.
