BGCSE Statistics 4040 flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

Primary data

Data collected directly by the investigator for the specific current investigation. Sources include surveys, experiments, and direct observation, giving control over definitions and accuracy but costing more time and money.

Secondary data

Data originally gathered by another party for a different purpose, reused in a new study. It is quick and cheap but may be outdated, inconsistently defined, or unavailable in the detail required.

Census versus sample

A census measures every population member, eliminating sampling error but costly and slow. A sample studies a subset, is faster and cheaper, but results carry sampling error and depend on selection quality.

Leading question

A questionnaire item worded so that it suggests or encourages a particular answer. It introduces response bias, so neutral wording is required for valid measurement.

Frequency density

The height of a histogram bar, calculated as frequency divided by class width. Using frequency density makes bar area proportional to frequency, allowing unequal class widths to be compared fairly.

Cumulative frequency curve

A graph of cumulative frequency against upper class boundary. The median is read at n/2 and quartiles at n/4 and 3n/4, enabling estimation of the interquartile range.

Pie chart angle formula

Each sector angle equals the category frequency divided by the total frequency, multiplied by 360 degrees. All sector angles must sum to 360 degrees for a complete circle.

Stem-and-leaf key

A statement showing how digits are split, such as 3|5 means 35. The key is essential because the display retains original values but the place value is otherwise ambiguous.

Median

The middle value of data arranged in order, or the mean of the two middle values when n is even. It is resistant to extreme values and suits skewed distributions.

Sample standard deviation

The square root of the sum of squared deviations from the mean divided by n minus one. The divisor n minus one corrects bias, and the result is in the original units.

Interquartile range

The difference between the upper quartile and lower quartile, Q3 minus Q1. It measures spread of the middle half of the data and ignores extreme values.

Effect of coding

If y equals (x minus a) divided by b, then the mean of x equals a plus b times the mean of y, and the standard deviation of x equals b times the standard deviation of y.

Addition rule

For events A and B, the probability of A or B equals P(A) plus P(B) minus P(A and B). The subtraction avoids double-counting outcomes in both events.

Conditional probability

The probability of A given B equals the probability of both A and B divided by the probability of B, provided B has nonzero probability. It restricts attention to the reduced sample space B.

Mutually exclusive events

Two events that cannot both occur in the same trial, so their intersection has probability zero. Their union probability is the sum of their individual probabilities.

Independent events

Two events where the occurrence of one does not change the probability of the other. Formally the probability of both equals the product of the individual probabilities.

Tree diagram multiplication

Along any branch, multiply the probabilities of successive stages to obtain that path's outcome probability. Add the probabilities of all paths that satisfy the required event.

Correlation coefficient

A number between minus one and plus one measuring the strength and direction of linear association. Values near zero indicate weak linear association, not necessarily no relationship.

Least-squares regression line

The line y equals a plus bx minimising the sum of squared vertical deviations. Here b equals the covariance of x and y divided by the variance of x, and a equals y-bar minus b times x-bar.

Extrapolation

Predicting the response variable for an x value outside the observed data range. Such predictions are unreliable because the fitted relationship may not continue beyond the measured region.

Coefficient of determination

The square of the correlation coefficient, giving the proportion of total variation in the response explained by the regression on the explanatory variable. It ranges from zero to one.

Moving average

An average of consecutive values over a fixed window, used to smooth fluctuations and reveal trend. A window equal to the seasonal period removes seasonal effects.

Centred moving average

A moving average adjusted so it aligns with an actual time point. It is required when the period is even, such as four-quarter data, because ordinary averages fall between periods.

Laspeyres price index

A weighted price index using base-year quantities: the sum of current prices times base quantities, divided by the sum of base prices times base quantities, multiplied by 100.

Seasonal variation

The regular pattern repeating within each year. In the additive model it is estimated as actual value minus trend; in the multiplicative model as actual divided by trend times 100.

Stratified sampling

The population is divided into strata that are internally similar, then random samples are drawn from each stratum. It reduces sampling variance and guarantees representation of every stratum.

Standard error of mean

The standard deviation of the sampling distribution of the sample mean, equal to the population standard deviation divided by the square root of the sample size. It decreases as n grows.

Central limit theorem

For sufficiently large sample sizes, the sampling distribution of the sample mean is approximately normal regardless of the shape of the population distribution. This underpins large-sample inference.

Confidence interval

A range of plausible values for a population parameter, built so that a stated percentage of such intervals would contain the true parameter across repeated sampling.

Type I error

Rejecting a null hypothesis that is actually true. Its probability equals the significance level chosen, commonly five per cent, and is reduced by using a smaller significance level.

Type II error

Failing to reject a null hypothesis that is actually false. Its probability decreases as the sample size, effect size, or significance level increases.

p-value

The probability, assuming the null hypothesis is true, of obtaining a test statistic at least as extreme as the observed value. The null is rejected when it falls below the significance level.