Descriptive Evaluation

Dependent (Response) Variable – the results of your operational definition will be data --

data represent variables, the valueshave a “life” and a “meaning”

Scales of Measurement – determines information available and how we

can treat the data nominal - names, purely categorical, qualitativeordinal - quantitative, but often with categoriesinterval - quantitative, equal interval ratio - quantitative, equal interval, absolute zero

Dependent Variable

Stay or Leave Abusive Relationship

Treatment Outcome –worse, no change, better

Letter Grade Received in Course

Rated attractiveness on 11 point scalevery unattractive (0) to very attractive (11)

Minutes to Complete a Task

Dependent Variable (from manuscript reviewed)

– time want to spend with a blind date

0 minutes

15 minutes

30 minutes

60 minutes

120 minutes

Underlying dimension is time – which is on what scale?

How would you ‘treat’ this variable, based on their format – what scale?

Describing Data sets - organize and summarize

organize “internal organization/structure”

summarize by reducing to indices

Options will depend partially on Scale of Measurement

Organize Tables and Graphs -

Frequency Table - simple count of all valuesBar Graph - best if small number of possible valuesHistogram - will group when many values Stem & Leaf - groups, but retains more of valuesBox plots - gross summary

Rating on 9-point scale, Definitely No (1) to (9) Definitely Yes

“Is person likely to have a relapse?”

Scores of 0 and 10 not possible

What do these data say?

Scores of 650 possible – but there are none

What do these data say?

Now have ‘groupings’, not individual scores, since so many possible values.Can ‘see’ the organization of the data, but have lost some information.

Rate – How upset would you be if you found out your partner had been sexually unfaithful

On a 9 point scale – Not at all (1) to (9) Extremely

What do these data say?

Summarize- to describe sample or compare samples

Central Tendency – “typical” value in the set

mode – most frequent

median – central value in ordered set

mean – mathematical midpoint

M = (x)/df ?

Appropriateness/Advantages/Disadvantages of each

Variability – differences within the data set

range – difference between highest - lowest

inter-quartile range – uses median

distance between 25th and 75th percentile scores (middle 50%)

variance – mean squared deviation from mean

(MS) (x-M)2/df

standard deviation – “mean” deviation from mean (RMS)

Note that Variance and Standard Deviation are means

(typical values)

How well can these “Summary Statistics” describe the data set?

If you can assume a “Normal” Distribution of the data, you can ‘reconstruct’ the data set from the two ‘descriptive statistics’

(and you know calculus)

If the shape is not ‘normal’, but is relatively ‘smooth’,can increase accuracy of reconstruction usingother descriptive statistics.

Less Common Descriptive Statistics

Skewness – symmetry of the two tails

Kurtosis – ‘peakedness’ of the distribution

Data from four questions of a survey on which participants rated their views on a 9-point scale from “Definitely No” (1) to “Definitely Yes” (9).

x x xx x x x

x x x x _________________________

1 2 3 4 5 6 7 8 9

x x x x x

x x x x x x_________________

1 2 3 4 5 6 7 8 9

xx

x x x x x x

x x x___________________________

1 2 3 4 5 6 7 8 9

xx x x

x x x x x x x________

1 2 3 4 5 6 7 8 9

Population- behavior or data of interest

Sample – behavior or data set available (selected from population – how?

subject to sampling error)

Organize – picture and describe the complete data set

Summarize – reduce data set to the ‘typical’ characteristics, characterize qualities of

the entire set (statistic)

Generalize – draw inferences about the population (parameter)

What can sample reveal about population –

Generality of the information from the sample

Based on the sample Mean, the Population Mean is ….

point estimation – use sample Mean as estimate of ‘true’ population Mean – signal, ignores noise

Assume assess attitudes toward War

Totally Oppose 1 2 3 4 5 6 7 8 9 10 11 Totally support

Collect data from a sample, and find M = 6

What inference would you make about the attitude in the Population?

What can sample reveal about population –

Generality of the information from the sample

Based on the sample Mean, the Population Mean is ….

point estimation – use sample Mean as estimate of ‘true’ population Mean

interval estimation – use sample Mean and sample SD to estimate range (based on SE) within which the population mean is ‘likely’ to fall

Confidence Intervals (at some %)

• The population from which these samples were drawn has a range of possible scores from 1 to 11, with a mean score of 6.

• Sample Size• 5 10 30 100 1000• Sample 1 4.2 4.6 6.2 5.7 6.1• 2 5.0 4.9 6.2 5.9 5.9• 3 5.8 5.0 6.1 6.1 6.1• 4 5.8 5.3 6.1 6.0 5.9• 5 6.2 6.1 6.1 5.7 6.2• 6 6.2 6.3 5.9 5.7 6.0• 7 6.2 6.4 5.9 6.2 6.1• 8 6.4 6.5 6.2 5.8 6.1• 9 6.4 6.6 5.6 6.0 6.0• 10 8.0 7.0 5.8 5.8 6.1

• Mean of 10 6.02 5.87 6.01 5.89 6.05• samples•• std error of mean .98 .84 .20 .17 .08

• 95% conf 4.10-7.94 4.22-7.52 5.62-6.40 5.56-6.22 5.89-6.21 intervals

• + 1.96 sem

Descriptive Statistics can also be used to characterize individuals within the data set

Standardized scores assess relative position of an individual

z score = (x – M)/SD

individual deviation from mean typical deviation from mean for the group

resulting set of z scores will have:

mean of set of z scores = 0 variance and standard deviation = 1shape of distribution of z’s will

match shape of raw scores

How would you feel about an exam z-score of +2.0?

Standard Normal Distribution – normal distribution of z scores (popular with statisticians)

if scores are from a normal distribution,

has useful properties

many stats tests are based on this because it has fixed properties

simpler, predictable

is it ‘realistic’ to assume normal distributions?

(sampling distributions)

To ‘truly’ know the Population parameter – best estimate

Need to draw repeated samples from the population

Sampling Distribution –

theoretical distribution of a statistic

based on some sample size (n),

assuming ALL POSSIBLE random samples

of size n are drawn

Central Limit Theorem – as sample size increases,

distribution of ‘statistic’ approaches a normal distribution

For example

sampling dist of mean will become normal as sample size increases, no matter what the shape of the distribution of actual scores.

mean of distribution will have mean equal to the ‘true’ mean of the raw scores

standard error is the measure of variability of the statistic (across samples)

‘comparable’ to the standard deviationof individual scores

Based upon this distribution, can get idea about likely accuracy of sample estimates of population parameters

with large samples (30+), Sampling Distribution Mean + 1.65 std error

will include 90% of sample meansSampling Distribution Mean + 1.96 std error

will include 95% of sample meansSampling Distribution Mean + 2.58 std error

will include 99% of sample means

Where values are based on z scores (1.65, 1.96, 2.58)*with smaller sample, use t-value for the sample size

to determine cut-offs for %

Exploratory Data Analysis –are data ‘appropriate’ for analyses

What ‘assumptions’ must be met for analysis?

Examine the data for errors and anomalies

are data ‘non-normally’ distributed

are there outliers

are there missing data

Interpreting Skewness and Kurtosis in SPSS

reported as ‘z-score’ equivalents

determining degree of deviation from normal

Dealing with Missing Data

Why is it missing?

Comparing those with missing data to those without

Replacing missing data?

Impact of missing data in SPSS

pairwise vs. listwise analyses