Research Methodology in CSD - Normal Distributions and Z-Statistics

distribution

pattern of scores

normal distribution

in (what kind of distribution?), many variables in communication disorders are continuously distributed as opposed to being placed into distinct categories

individual groups

distribution provides information about __ cases as well as information about __ of scores

bar graphs

distributions for categorical variables are shown in (what type of graph?)

line graphs and histograms

distributions for continuous variables are shown in (what type of graph?)

normal distribution

theoretical distribution providing a model for evaluating distributions of many real life variables

1. unimodal/symmetrical 2. continuous 3. asymptotic

3 important characteristics of normal distribution

asymptotic

when the curved line gets closer to horizontal axis as it moves away from the center

means SDs

different variables have different __ and __

approximate, comparable, units

distributions may __ the normal distribution, but they are not __ because of their different __ of measurement

transformed

all normal distributions are __ to fit the standard normal distribution

1. mean SD 2. mean = 0 SD = 1

1. all normal distributions can be converted into a common distribution with the same __ and __

2. What do these each equal?

z statistic

mean = 0 and SD = 1 is the ___

proportion same

the __ of scores in a given area under the bell-shaped curve is always the __

68%

area between -1 and +1 SD always includes ___ of total distribution of scores

95%

area between -2 and +2 SD always includes ___ of total distribution of scores

99%

area between -3 and +3 SD always includes ___ of total distribution of scores

probability of outcome

information of standard scores and the SD's distance from mean is important in determining ____

standard unit

single score in a distribution of scores in standard normal distribution

z score

another name for standard unit

standard unit

another name for z score

individual location

z score/standard unit is a measure of ___

individual location

measures of ___ tell us where individual scores are located within a distribution of scores

score mean

z score tells us how far the SD corresponding value of X (__) lies above/below the __

comparisons variables

z score allows us to make __ between different __

transformed standard score

when z scores are changed into a distribution of standard scores with a mean of 100 and SD equal to 15 units

negative values and decimals

what do z scores include that make them difficult to report, making them misleading?

transformed standard scores

Because z scores contain values/decimals that can be misleading, they are converted to __

100 15

transformed standard scores (what z scores were converted into) have a mean = (1) and an SD that = (2) units

bell-shaped, symmetrical

skewed distributions are not __ or __

negatively skewed distributions

have more scores with larger values toward the right tail

positively skewed distributions

have more scores with larger values toward the left tail

kurtosis

measure of peakedness for symmetrical distributions

a measure of peakedness for symmetrical distributions

what is kurtosis?

fat/thin normal

kurtosis is a measure of how __/__ the tails of a distribution are relative to a __ distribution

distributions

all variables and statistics have __

1. is not 2. distributions

1. the mean of one set of scores (is/is not) the same as the mean of another set of scores

2. this means that all statistics have __

1. values 2. repeatedly 3. populations

the distribution of a sample statistic indicates how often different (1) of that statistic should occur if samples of the same size are collected (2) from the same (3)

probability distributions

provide information about the chance occurrence of a particular outcome for a particular distribution of scores

1. chance 2. outcome 3. distribution

probability distributions provide information about the (1) occurrence of a particular (2) for a particular (3) of scores

distribution probabilities

when __ of sample mean is known, it is easy to compute __

sample means

we do NOT typically know the distribution of __

no

do we typically know the distribution of sample means?

central limit theorem

since we typically do not know the distribution of sample means, what do we use?

population

mean of the distribution of sample means = the mean of the __

less

distribution of sample means is (more/less) variable than the population

smaller

SD of sample means is __ than SD of population

standard error of the mean

SD of sample mean is known as

SD of sample mean

standard error of the mean (SEM) is also known as

parameters

we do not typically have the __ of the population available, which we need to have to determine standard error of the mean (SEM)/SD of sample mean

central limit theorem

distribution of sample means will be approximately normal if the sample if large enough

distribution of sample means will be approximately normal if that sample is large enough

what does the central limit theorem state?

>30

according to the central limit theorem, what would be considered a large sample?

1. yes 2. it has a large sample

1. can the sampling distribution be approximately normal even if the variables are not normally distributed?

2. why/why not?

1. population 2. sample

If characteristics of a target population are unknown, [1] parameters can be estimated from [2] parameters

SD of the sample

Standard error of the mean is estimated from __

interval estimation

the establishment of a range of values that we can say with confidence contain the population parameter

confidence interval

range of values is the __

critical value

when constructing a confidence interval, what is chosen?

2

critical value for a 95% confidence interval equals ___

the level of confidence chosen by the researcher

what does the critical value depend on?

1. bell shaped 2. symmetrical 3. centered on the mean

what three things make t distributions similar to z statistics?

distribution

in t distributions, __ changes as sample size changes

sample size

in t distributions, distribution changes as __ changes

t distribution

(type of distribution) distribution changes as sample size changes

small

research in CSD often involves [small/large] samples

because sample size is less than 30

why do students in CSD depend on t distributions to test hypotheses?

1. mean 2. individuals

*from google* The t-distribution is typically used to study the [1] of a population, rather than to study [2] within a population (z statistics).