Statistical Inference Flashcards
What is statistical inference?
The process of using what we know about a sample to make probabilistic statements about the broader population. Using probability theory, we can estimate what is going on in the population based on the sample.
What is probability?
The proportion of times that an outcome would occur in a very long sequence of similar observations
What is a probability distribution? What does the sum of probabilities equal?
A probability distribution lists the possible outcomes of an event and their probabilities. It assigns a probability to each possible value of a variable, which is between 0 and 1. The sum of all probabilities = 1
What is the empirical rule concerning standard deviations?
About 68% of observations fall within 1 standard deviation. 95% of observations fall within 2 standard deviations and all or nearly all observations fall within 3 standard deviations.
Describe normally distributed data
Normally distributed data is symmetrical about the mean. It produces a bell-shaped curve, defined by two parameters (the mean and the standard deviation). It follows the empirical rule.
Explain the central limit theorem
The central limit theorem states that the more samples taken, the more likely that the mean of the sampling distribution will be the population mean, so long as the population size is large enough.
What are the two types of estimate?
Point estimate (a single number that is a guess of a value) and a confidence interval (an interval of numbers around the point estimate we believe contains the parameter value).
What do confidence intervals allow you to do?
Confidence intervals allow you to state how confident you are that an estimated value lies close to the actual value.
What is a statistical significance test? How do they work?
A statistical significance test uses data to summarise the evidence about a hypothesis – by comparing point estimates of the parameters with the values predicted by the hypothesis.
What is the purpose of a null hypothesis?
A null hypothesis is a statement that something takes a particular, exact value. By analysing whether data contradicts the null hypothesis, we can suggest that an alternative hypothesis is true to guide our future investigations.
What is a test statistic?
A test statistic summarises how far the estimate falls from the parameter value in the null hypothesis
What is the p-value?
A p-value is the probability of us obtaining our particular sample if the null hypothesis is true. The probability of obtaining results at least as extreme OR MORE than actually observed.
What does a small p-value indicate is the case for your null hypothesis? What does a moderate to large p-value indicate?
A small p-value indicates that there is strong evidence against the null hypothesis. A moderate to large p-value provides support for a null hypothesis.
What does the value of a p-value have to be less than for a null hypothesis to be rejected? What is this value known as?
A p-value has to be below or equal to 0.05 for a null hypothesis to be rejected. This is known as the a level or the significance level.
If your p-value is bellow the significance level, what hypothesis must you accept?
If a p-value is below the significance level, then this means that you must reject the null hypothesis and accept an alternative one.
Can you ever reject a null hypothesis?
You can never reject a null hypothesis, but you can FAIL TO ACCEPT IT.
What is the definition for statistical significance?
Statistical significance is based on the p-value. If the p-value is above 0.05, this may have occurred by chance, yet if below this value we can say that this is not explainable by chance alone.
What is the definition of homoscedasticity?
Homoscedasticity refers to the condition where the variance of the error terms (residuals) in a regression model is constant across all levels of the independent variables, meaning the spread of data points is roughly the same.
