Chapter 2 Flashcards
α-level
the probability of making a Type I error (usually this value is 0.05).
Alternative hypothesis
the prediction that there will be an effect (i.e., that your experimental manipulation will have some effect or that certain variables will relate to each other).
β-level
the probability of making a Type II error (Cohen, 1992, suggests a maximum value of 0.2).
Bonferroni correction
a correction applied to the α -level to control the overall Type I error rate when multiple significance tests are carried out. Each test conducted should use a criterion of significance of the α -level (normally 0.05) divided by the number of tests conducted. This is a simple but effective correction, but tends to be too strict when lots of tests are performed.
Central limit theorem
this theorem states that when samples are large (above about 30) the sampling distribution will take the shape of a normal distribution regardless of the shape of the population from which the sample was drawn. For small samples the t -distribution better approximates the shape of the sampling distribution. We also know from this theorem that the standard deviation of the sampling distribution (i.e., the standard error of the sample mean ) will be equal to the standard deviation of the sample ( s ) divided by the square root of the sample size ( N ).
Confidence interval
for a given statistic calculated for a sample of observations (e.g., the mean), the confidence interval is a range of values around that statistic that are believed to contain, in a certain proportion of samples (e.g., 95%), the true value of that statistic (i.e., the population parameter). What that also means is that for the other proportion of samples (e.g., 5%), the confidence interval won’t contain that true value. The trouble is, you don’t know which category your particular sample falls into.
Degrees of freedom
Essentially it is the number of ‘entities’ that are free to vary when estimating some kind of statistical , parameter. In a more practical sense, it has a bearing on significance tests for many commonly used test statistics (such as the F-statistic , t-statistic , chi-square test ) and determines the exact form of the probability distribution for these test statistics .
Deviance
the fact or state of diverging from usual or accepted standards, especially in social or sexual behaviour
Experimental hypothesis
synonym for alternative hypothesis; the prediction that there will be an effect (i.e., that your experimental manipulation will have some effect or that certain variables will relate to each other).
Experiment wise error rate
the probability of making a Type I error in an experiment involving one or more statistical comparisons when the null hypothesis is true in each case.
Family wise error rate
the probability of making a Type I error in any family of tests when the null hypothesis is true in each case. The ‘family of tests’ can be loosely defined as a set of tests conducted on the same data set and addressing the same empirical question.
Why do we use samples?
We are usually interested in populations, but because we cannot collect data from every human being (or whatever) in the population, we collect data from a small subset of the population (known as a sample) and use these data to infer things about the population as a whole.
What is the mean and how do we tell if it’s representative of our data?
The mean is a simple statistical model of the centre of a distribution of scores. A hypothetical estimate of the ‘typical’ score. We use the variance, or standard deviation, to tell us whether it is representative of our data. The standard deviation is a measure of how much error there is associated with the mean: a small standard deviation indicates that the mean is a good representation of our data.
What’s the difference between the standard deviation and the standard error?
The standard deviation tells us how much observations in our sample differ from the mean value within our sample. The standard error tells us not about how the sample mean represents the sample itself, but how well the sample mean represents the population mean. The standard error is the standard deviation of the sampling distribution of a statistic. For a given statistic (e.g. the mean) it tells us how much variability there is in this statistic across samples from the same population. Large values, therefore, indicate that a statistic from a given sample may not be an accurate reflection of the population from which the sample came.
What do the sum of squares, variance and standard deviation represent? How do they differ?
All of these measures tell us something about how well the mean fits the observed sample data. Large values (relative to the scale of measurement) suggest the mean is a poor fit of the observed scores, and small values suggest a good fit. They are also, therefore, measures of dispersion, with large values indicating a spread-out distribution of scores and small values showing a more tightly packed distribution. These measures all represent the same thing, but differ in how they express it. The sum of squared errors is a ‘total’ and is, therefore, affected by the number of data points. The variance is the ‘average’ variability but in units squared. The standard deviation is the average variation but converted back to the original units of measurement. As such, the size of the standard deviation can be compared to the mean (because they are in the same units of measurement).
