Research Class 7 Part 2

what is the symbol for Standard deviation

SD

what is the symbol for universal standard deviation

Ơ

what is the symbol for degrees of freedom

df

what does x stand for

observed score

what is N

sample size

what is X̄

mean of the sample

µ = ___ of the population or universal mean

mean

what does S stand for

sum

There are two main steps for statistical analyses…

descriptive and inferential

___ statistics is used to describe and synthesize data

Descriptive

___ statistics is used to make inferences about the population based on sample data.

Inferential

Descriptive statistics are comprised of a series of tests, based upon the level of measure of the variable, to ___ the participants’ response data, for each variable.

describe, synthesize, and organize

what are the types of descriptive statistical tests?

frequency distributions, measures of central tendency, measures of variability

which level of measure for frequency distributions?

all

which level of measure for central tendency and variability

Continuous: Interval and ratio

This is the most basic way to illustrate data. It is a method of tallying and representing how often certain scores occur in the participants’ response data, for each variable.

frequency distribution

If the data is ___, then the scores are usually grouped into class intervals or equal ranges of numbers.

continuous

Frequency distribution data are displayed as…

tables, bar charts, histograms, polygons

The type of frequency distribution display is dependent on…

level of measure

Remember that categorical data is in discrete, ___ groups. The data does not overlap across categories.

separate

Frequency distribution of categorical data presents the ___ or frequency (how often or how many times the attribute occurs)

number

Frequency distributions for categorical data includes…

A table with the N (sample size) per group

Bar chart

frequency distributions for continuous data includes….

tables, histograms, polygons

The ___ is the graph of the frequencies per point along the continuous scale

histogram

The ___ is a single dot per point along the continuous scale, centered above the score of the frequencies scale, then drawn connecting these dots.

polygon

Measures of ___ can be conducted for continuous data, interval and ratio (and those only), because interval and ratio data measure the magnitude (how much of something) of the attribute on a continuum.

central tendency

The ___ is the average, which is the most common measure for central tendency

mean

It is the most ___, but it is very sensitive to extreme scores. It is the most frequently used measure of central tendency (mean)

precise

___ is the symbol for mean.

X̄

The ___ represents the exact middle score and is not affected by extreme scores

median

The median is the value above and below which 50% of all scores fall. It is the value that divides the cases exactly in ___, otherwise known as the 50th percentile.

half

If there is an ___ number of scores, e.g., 15, then it will simply be the score at which 50% of all scores lie below that score and 50% of all scores lie above it

odd

If there is an ___ number of scores, e.g., 14, then the median is the average between the two scores (22 + 23 = 45 / 2 = 22.5)

even

The ___ is the value that occurs most frequently (unimodal). It is the most general and least precise.

mode

Sometimes, more than one number appears with equal frequency = ___ (bimodal = two modes, multi-modal = more than two modes).

multimodal

The___ is the probability distribution for data from a variable operationalized as a continuous level of measure.

normal curve

It is used to ___ the likelihood of getting scores in a given population.

estimate

Most continuous variables tend to have an ___ normal distribution, if enough samples are drawn for that variable.

approximately

A ___ is a theoretically perfect frequency polygon is a normal distribution

normal distribution

It is based on ___ observations of interval/ratio level data and creates what you probably know as the “normal curve” or “bell curve.”

repeated

The normal curve has a ___ % of scores that fall within a certain distance (% likelihood) of the mean with a symmetrical distribution

fixed

In a normal curve, two halves of distribution are mirror images of each other (skewness = ___).

zero

The normal curve is symmetrical around the mean and is unimodal: the mean, median and mode are approximately the ___.

same

In normal distributions, the curve can be divided in ___ and each half is the mirror image of the other.

half

___ is the lack of symmetry in the curve. The curve is lopsided with a non-symmetrical distribution.

Skewness

In a ___ skew, the tail is to the right of the distribution; the mean is greater than median and mode.

positive

In a ___ skew, the tail is to the left of the distribution; the mean is less than median and mode

negative

___ shows how flat or peaked the curve is. It does not refer to symmetry

Kurtosis

In a normal distribution, kurtosis = 0, which is called ___.

mesokurtic

In a ___ than normal curve, the kurtosis is called platykurtic (large negative number).

flatter

In a more ___ than normal curve, the kurtosis is called leptokurtic (large positive number)

peaked

Measures of ___, like measures of central tendency, are only for continuous data: interval and ratio.

variability

Variability measures the ___ or dispersion of the scores in the participants’ data.

spread

Variability serves two purposes

1. Describes the distribution.

2. Measures how well an individual score (or group of scores) represents the entire distribution

There are three measures of variability

1. Range

2. Variance

3. Standard deviation

The ___ is the distance between the highest value or observed score and the lowest value. Xmax – Xmin

range

However, range is completely determined by the two end points, ___ values, and ignores the other scores in the distribution

extreme

___ provides a measure of the degree to which scores in a distribution are spread out (dispersed), or clustered together.

Variance

The variance measures variability by considering the ___ between each score and the mean.

distance

It also approximates the ___ distance of any score from the mean.

average

the actual number in the variance is always very ___, so large that it seems meaningless in relation to the set of scores in your sample

large

So, if your score on a test is 85 (X) and the mean (µ) is 75.5, your ___ would be 9.5, but if your score is 65, your deviation score is –10.5.

deviation score

The deviation score = ___

X (score) – µ (average)

The ___ tells the direction from the mean, (not if the score is above or below 0) and the number gives the actual distance from the mean.

sign

next, to find the variance, you calculate the mean of the ___

deviation scores

this means for each score, it has its deviation score right

you take the deviation score from each score and you calculate the ___ of these

mean

next, you get rid of the (+ and –) signs by ___ each deviation score.

squaring

Using these values, divided by the sample size or denominator, you then compute the ___, which is called variance

mean squared deviation

Therefore, variance is the ___ of the squared deviation scores.

mean

Standard deviation = ___

√ variance

___ uses the mean of the distribution as a reference point and measures variability by considering the distance between each score and the mean

standard deviation

In other words, it ___ the average distance of any score from the mean.

approximates

SD is the ___ and the most important measure of variability.

most used

the sample is never a ___ representation of the population. There will always be some bias in the sample.

perfect

To account for the ___, which is error, in the sample, the denominator is adjusted by subtracting 1 from the sample size.

bias

Therefore, the ___ for standard deviation is :

Sample standard deviation = s = SS 
                                                   n – 1

equation

This produces a ___ SD number and makes a more unbiased estimator of the population from a sample.

larger

This is symbolized as df (degrees of freedom), so the equation is ___

df = n – 1

In descriptive statistics, sometimes the ___ do not tell you too much about what that score represents in relation to other scores, even though you have the measures of central tendency and the variability

raw scores

To understand the ___ of any raw score along a distribution of scores on a curve a little better, we first need to understand a raw score as a SD or standardized score.

location

Sometimes the ___ of the distribution is such that you wonder what the score in your sample data really represents in real life for a large population.

skew

Suppose a class wrote an exam, and the average mark was 70/100, and your mark was 76. Should you be upset or happy about your mark, in ___ to the rest of the class?

relation

___ is a statistical procedure used to make data points from different datasets comparable

Z-standardization

There are two purposes for standardized or z-scores

The first is to ___ the exact location of every score in the sample data in a distribution of all scores. For example, your grade on an exam in relation to all other grades for students in the rest of the class.

identify and describe

The second purpose of Z scores is to…

To standardize an entire distribution

Z-score transforms each X value (raw score) into a signed number above or below the mean (+ or –) so that the sign tells whether the score is ___ above (+) or below (–) the mean.

located

Z scores also transform each X value or raw score s that the number tells the ___ between the score and the mean in terms of the number of standard deviations.

distance

To calculate a raw score (what the actual score would be) from a z-score we use the following equation.

X = m + zs 

For a distribution with a mean of 75, and a standard deviation of 15, what X value corresponds to a z-score of z= –3.00?

X = μ + zσ

= 75 + z(15)

= 75 + (–3.00 x 15)

= 75 + –45

= 30

A distribution of scores has a = 50 and a SD =10, what z-score corresponds to a score of 90 in this distribution?

Z = x – x 

        SD

        

= 90 – 50 

       10

 = 4

The z-score is the number of SDs ___ the mean

above or below

If you look at the z-scores and the number of SDs away from the mean, we can consider any score that is < or > 2 standard deviations away from the mean to be considered an ___ score

extreme

These scores are happening less than ___ of the time – the idea of probability.

5%

The z-score distribution will always have a mean of ___ (this is the reference point)

0

The distribution of z-scores will always have a standard deviation of ___ (the numerical value of a z-score is the same as the number of standard deviations from the mean).

1

Z-score distribution makes it possible to ___ different scores or different individuals even though they may come from completely different distributions

compare

To determine if there are ___ multiply the sample data SD by two then add it and subtract it from the mean for that sample. (+/– the mean).

extreme scores

When an extreme score is present in the data for a variable, the ___ is the best measure of central tendency.

median