Chapter 4: Probability, Sampling, and Distributions

Advantage

________: there is a probability associated with each particular score from the distribution.

confidence intervals

Examining ________ gives us a fair idea of the pattern of means in the populations.

Inferential Statistics

________: techniques employed to draw conclusions from your data.

Central Limit Theorem

________: states that as the size of the samples we select increases, the nearer to the population mean will be the mean of the sample means and the closer to normal will be the distribution of the sample means.

Conditional Probability

________: the probability of a particular event happening if another event (or set of conditions) has also happened)

Probability

________: refers to the likelihood of a particular event of interest occurring.

Point Estimate

________: a single figure of an unknown number.

confidence intervals

We can calculate ________ for a number of different statistics, including the actual size of a difference between two means, correlation coefficients, and t- statistics.

point estimate

Where a(n) ________ exists, it is usually possible to calculate an interval estimate.

Probability

refers to the likelihood of a particular event of interest occurring

Example

tossing a coin with one desired outcome (heads) and two possible outcomes (heads or tails) = 1 ÷ 2 = 0.5 [in percentage = 0.5 * 100 = 50%]

Conditional Probability

the probability of a particular event happening if another event (or set of conditions) has also happened)

Inferential Statistics

techniques employed to draw conclusions from your data

Standard Normal Distribution (SND)

the distribution of z-scores; normally shaped probability distribution which has a mean (as well as median and mode) of zero and a standard deviation of 1

z-scores

aka standardized scores; you can convert any score from a sample into this by subtracting the sample mean from the score and then dividing by the standard deviation

z-scores are expressed in standard deviation units

that is, the z-score tells us how many standard deviations above or below the mean our score is

Probability Distribution

a mathematical distribution of scores where we know the probabilities associated with the occurrence of every score in the distribution'; we know that the probability is of randomly selecting a particular score or set of scores from the distribution

Advantage

there is a probability associated with each particular score from the distribution

Example

You decided to take a course in pottery and weightlifting

Sampling Distribution

a hypothetical distribution

Sampling Distribution of the Mean

if you plotted the sample means of many samples from one particular population

Central Limit Theorem

states that as the size of the samples we select increases, the nearer to the population mean will be the mean of the sample means and the closer to normal will be the distribution of the sample means

Point Estimate

a single figure of an unknown number

Interval Estimate

range within which we think the unknown number will fall

Confidence Interval

a statistically determined interval estimate of a population parameter

Standard Error

refers to the standard deviation of a particular sampling distribution; in the context of the sampling distribution of the mean, it is the standard deviation of all of the sample means

Formula

standard deviation of the sample divided by the square root of the sample size

Error Bar Chart

a graphical representation of confidence intervals around the mean