Chapter 3: Descriptive Statistics

Scattergram

________: gives a graphical representation of the relationship between 2 variables.

Mode

________: the most frequently occurring score in a sample.

Sample

________: refers to a selection of individual people or items from a population.

Kurtosis

________: a distribution is a measure of how peaked the distribution is.

Sampling Error

________: the difference between the population parameter and the sample statistic; the degree to which sample statistics differ from the equivalent population parameter.

Experimenter Bias

________: the experimenters subconsciously chose to follow people who help support their hypothesis.

x axis

The ________ contains details of each score on our variable and the y- axis represents the frequency of occurrence of those scores.

frequency histogram

The ________ is useful for discovering other important characteristics of your data.

equal whiskers

Normally distributed data: ________ coming from both edges of the box.

Population

________: consists of all possible people or items who /which have a particular characteristic.

Bimodal Distribution

________: one that has two pronounced peaks; it is suggestive of there being two distinct populations underlying the data.

Box Plots Box

________ and Whisker Plots: enable us to easily identify extreme scores as well as seeing how the scores in a sample are distributed.

frequency histogram

The ________ is a good way for us to inspect our data visually.

Frequency Histogram

________: a graphical means of representing the frequency of occurrence of each score on a variable in our sample.

Sample

refers to a selection of individual people or items from a population

Population

consists of all possible people or items who/which have a particular characteristic

Experimenter Bias

the experimenters subconsciously chose to follow people who help support their hypothesis

Parameters

descriptions of populations

Statistics

descriptions of samples

Measures of Central Tendency

give us an indication of the typical score in our sample; effectively an estimate of the middle point of our distribution of scores

Mean

the sum of all the scores in a sample divided by the number of scores in that sample

mean of the sample of the 4 scores

5, 6, 9, 2

Ranking

where we arrange a set of scores in ascending order and then assign a position number (rank) to each one

Median

the middle score/value once all scores in the sample have been put in rank order

median for the sample

2, 20, 20, 12, 12, 19, 19, 25, 20

median for the sample

2, 12, 12, 19, 19, 20, 20, 20, 25, 26

Therefore, the median in this example will be the average of the 2 scores in the 5th and 6th positions

(19 + 20) / 2 = 19.5

Mode

the most frequently occurring score in a sample

Problem with the Mean

because the mean uses all the actual scores in its calculation, it is sensitive to extreme scores

Exploratory Data Analysis (EDA)

where we explore the data that we have collected in order to describe it in more detail

Frequency Histogram

a graphical means of representing the frequency of occurrence of each score on a variable in our sample

Stem and Leaf Plots

similar to histograms but the frequency of occurrence of a particular score is represented by repeatedly writing the particular score itself rather than drawing a bar on a chart

Box Plots/Box and Whisker Plots

enable us to easily identify extreme scores as well as seeing how the scores in a sample are distributed

Outliers/Extreme Scores

those scores in our sample that are a considerable distance either higher or lower than the majority of the other scores in the sample

Normally distributed data

equal whiskers coming from both edges of the box

Negatively skewed data

no whisker coming from the top of the box

Scattergram

gives a graphical representation of the relationship between 2 variables

Normal Distribution

a distribution of scores that is peaked in the middle and tails off symmetrically on either side of the peak; the distribution is often said the be ‘bell-shaped'; for a perfectly normal distribution, the mean, median and mode will be represented by the peak of the curve

Variance or Variation of Scores

indicates the degree to which the scores on a variable are different from one another

Range

the highest score in a sample minus the lowest score

Mean Deviation

gives us an indication of how much the group as a whole differs from the sample mean; to calculate, we have to sum the individual deviations and divide by the number of scores we have

Problem with the Mean Deviation

Approximately half of the deviations from the mean will be negative deviations (the scores will be less than the mean) and half will be positive deviations (the scores will be greater than the mean)

Variance

the average squared deviation of scores in a sample from the mean

Problem with the Variance

It is based upon the squares of the deviations and thus it is not expressed in the same unites as the actual scores themselves

Standard Deviation (SD)

the degree to which the scores in a dataset deviate around the mean; it is an estimate of the average deviation of the scores from the mean; the square root of the variance

Problem with Standard Deviation

It tends to be an under estimate of the population standard deviation, therefore, we usually report a slightly modified version of the sample standard deviation when we are trying to generalize from our sample to the underlying population

Kurtosis

a distribution is a measure of how peaked the distribution is

Platykurtic

a flat distribution

Leptokurtic

a very peaked distribution

Mesokurtic

a distribution between the two extremes

Skewed Distributions

those where the peak is shifted away from the center of the distribution and there is an extended tail on one of the sides of the peak

Negatively Skewed Distribution

the peak has been shifted to the right towards the high numbers of the scale and the tail is pointing to the low number (or even pointing to the negative numbers)

Positively Skewed Distribution

the peak shifted left, towards the low numbers, and has the tailed extended towards the high numbers

Bimodal Distribution

one that has two pronounced peaks; it is suggestive of there being two distinct populations underlying the data