Bernard Ch. 6

frequency polygon

histogram that emphasizes the shape of the distribution of a set of points. (See page 150 for term and 152 for graph)

z-score (a.k.a. standard score)

number of standard deviations (in increments of 1/100th of a standard deviation) from the mean in a normal distribution. (See Appendix A for a complete table. It goes from 0.0 sd to 3.09 sd.)

standard deviation (formula)

sd = squareroot[(sumof(score-mean)^2) / (n-1)] (n = number of scores) "The standard deviation is the square root of the sum of all the squared differences between every score in a set of scores and the mean, divided by the number of scores minus 1" (page 149)

exponential distribution

the graph of this probability distribution is y = e^x (refer to page 147). E.g. Someone is playing basketball. If you plot the number of minutes she shoots basketballs on the x-axis and number of hoops made from the foul line on the y-axis, there will be an exponential relationship between the two variables. As time passes, it becomes increasingly more likely that she will make a shot.

bimodal distribution

(Refer to page 147 for a visual of this graph.) E.g. Age is represented on the x-axis, and interest in watching tv is represented on the y-axis. Some age groups are more interested in watching tv than others; therefore, more than one mode will be seen on the plotted graph. If only two modes are seen, then the graph has a bimodal distribution. If more than two modes are seen, then the graph has a multimodal distribution.

skewed distribution

(Refer to page 147 for a visual of this graph.) There are two types: negative and positive. -A negatively skewed distribution has a long tail going off to the right (with its mode being near the left of the graph). -A positively skewed distribution has a long tail going off to the left (with its mode being near the right of the graph).

probability distribution

-uniform distribution -exponential distribution -bimodal distribution -multimodal distibution -skewed distribution -symmetrical distribution

according to the central limit theorem, the problem with only using one sample is...

...the value of the sample could be significantly different from the value of the true mean. The more samples that are taken, the more likely it is that the mean of those samples will approximate the true mean.

sds and percentages of areas under the curve (of normal distribution)

1 sd = 68.26% of area under the curve (around the mean) = 68.26% of all scores in the normal distribution 2 sd = 95.44% of area under the curve (around the mean) = 95.44% of all scores in the normal distribution 3 sd = 99.70% of area under the curve (around the mean) = 99.70% of all scores in the normal distribution

central limit theorem

1) mean and sd of sample means will approximate the true mean and sd of the population. 2) distribution of sample means with approximate a normal distribution

calculating the confidence interval

It is determined by relating the standard error of the mean to the percentage of area under the curve at each sd. E.g. if standard error is 800, then the confidence interval of 1 sd (around the mean = 68.26% of the area under the curve) is 800. The confidence interval of 2 sd (around the mean = 95.44% of the area under the curve) is 1,600 (twice the previous value).

standard deviation (definition)

Measure of variance of the scores from the mean in a normal distribution.

standard error of the mean (definition)

Standard deviation of a sampling distribution of means. This value tells us how similar the sample mean and the mean of the population are.

symmetrical distribution

There are three types: 1) leptokurtic: "thin bulge"; has a small standard deviation 2) platykurtic: "flat bulge"; has a large standard deviation 3) normal distribution: bell-curved; the standard

sampling distribution

list of means in a sample (see page 150). (According to Koppel, this doesn't exist outside of theory.)

cumulative mean

sum of means within a sample (see page 150)

normal distribution

the bell-shaped curve. (Refer to page 148.) It has a mean of 0 and a standard deviation of 1.

uniform distribution

the characteristic shape of this graph is a rectangle (refer to page 147). Each unit of the given population has an equal chance of being selected. E.g. flipping a coin and getting a tails has a uniform probability of 0.50.