hui bian office for faculty excellence fall 2011 -...

Hui Bian

Office for Faculty Excellence

Fall 2011

• Purpose of data screening

•To find wrong entries

•To find extreme responses or outliers

•To see if data meet the statistical

assumptions of analysis you are going to

use.

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• Distribution diagnosis

• Frequency tables

• Histograms and bar graphs

• Stem-and-leaf plots

• Box plots

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• Frequencies procedure provides statistics and

graphical display to describe your variables.

• Frequency tables can give you: frequency

counts, percentages, cumulative percentages,

mean, median, mode, sum, standard deviation,

variance. Skewness and kurtosis, etc.

• Assumptions

• Tabulations and percentages are useful for categorical data.

•Mean and standard deviation are based on normal theory and are appropriate for quantitative variables.

• Robust statistics, such as median, percentiles, and quartiles are appropriate for quantitative variables that may or may not meet the assumption of normality.

• Example: what are the distributions of

demographic variables? Such as age,

gender, and grade (Q1, Q2, Q3).

• First recode Q1 into Q1r because we want

real ages for the participants.

• How to recode Q1?

• Recode Q1 into Q1r

• Obtain frequency table: Analyze > Descriptive Statistics >

Frequencies

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• Click Statistics to get this window

• Click Charts to get this window

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• Frequency statistics

• Frequency statistics

• Skewness and kurtosis are statistics that characterize

the shape and symmetry of the distribution

• Skewness: a measure of the asymmetry of a

distribution. The normal distribution is symmetric and

has a skewness value of zero.

• Positive skewness: a long right tail.

• Negative skewness: a long left tail.

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• Skewness

• Kurtosis: a measure of the extent to which

observations cluster around a central point. For a

normal distribution, the value of the kurtosis statistic is

zero.

• Leptokurtic data values are more peaked (positive

kurtosis) than normal distribution.

• Platykurtic data values are flatter and more

dispersed along the X axis (negative kurtosis) than

normal distribution.

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• Unacceptable level of skewness and kurtosis:

departure from normality

• Some use: ± 0.5

• Some use: ± 1.00

•As a guideline, a skewness value more than twice its

standard error is taken to indicate a departure from

symmetry (from SPSS help menu).

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• Frequency tables of Q2 and Q3

• From frequency table of Q3, we decide that we do

not want Ungraded or Other grade group in our data

analysis.

• Then, we need to recode Q3.

• How to recode Q3 into Q3r

• Keep four levels (9th - 12th ).

• Recode the fifth level (Ungraded or Other grade) into system

missing.

• Run frequency for Q3r.

• Recode Q3 into Q3r

• Histogram

1. It is plotted along an

equal interval scale. The

height of each bar is the

count of values of a

variable.

2. It shows the shape,

center, and spread of

the distribution.

3. A normal curve helps

you judge whether the

data are normally

distributed.

• Example: Frequency of Q41(frequency of drinking)

• The Explore procedure produces summary statistics

and graphical displays, either for all of your cases

or separately for groups of cases. Reasons of using

Explore procedure:

• Data screening

• Outlier identification

• Description

• Assumption checking

• Characterizing differences among subpopulations

(groups of cases).

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• Exploring the data can help

• to determine whether the statistical techniques that

you are considering for data analysis are

appropriate.

• the exploration may indicate that you need to

transform the data if the technique requires a normal

distribution.

• or you may decide that you need nonparametric

tests.

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• Statistics: Mean, median, standard error, variance, standard

deviation , range, skewness, kurtosis, and confidence interval for

the means, the Kolmogorov-Smirnov statistic with a Lilliefors

significance level for testing normality, and the Shapiro-Wilk

statistic. Boxplots, stem-and-leaf plots, histograms, normality

plots, and spread-versus-level plots with Levene tests and

transformations.

• Data: quantitative variables or categorical variables with a

reasonable number of distinct categories.

• Assumptions: the distribution of your data does not have to be

symmetric or normal.

• Example: let’s explore Q41 again, by Q2 (gender).

• Obtain Explore: Analyze > Descriptive Statistics >

Explore

• Click Statistics to get this window

• Click Plots to get this window

Descriptives

Q2 What is your sex Statistic Std. Error

Q41 How many days drink

alcohol 30 days

Female Mean 1.76 .013

95% Confidence Interval for

Mean

Lower Bound 1.73

Upper Bound 1.79

5% Trimmed Mean 1.63

Median 1.00

Variance 1.230

Std. Deviation 1.109

Minimum 1

Maximum 7

Range 6

Interquartile Range 1

Skewness 1.647 .029

Kurtosis 2.501 .058

Male Mean 1.85 .015

95% Confidence Interval for

Mean

Lower Bound 1.83

Upper Bound 1.88

5% Trimmed Mean 1.69

Median 1.00

Variance 1.732

Std. Deviation 1.316

Minimum 1

Maximum 7

Range 6

Interquartile Range 1

Skewness 1.726 .028

Kurtosis 2.624 .055

• Test of normality

The normality

assumption is not

satisfied.

• Stem-and-Leaf Plots: use the original data values to

display the distribution's shape.

Female Male

• Stem-and-Leaf Plots

•Normal Q-Q Plots:

• The straight line in the plot represents expected values

when the data are normally distributed.

• A normal distribution is indicated if the data points

fall on or very near the diagonal line.

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• Normal Q-Q Plot of Q41among Females

• Normal Q-Q Plot of Q41among Males

• Why use box plots?

• Provide some indication of the data's symmetry and

skewness.

•We can detect outliers.

• By using a boxplot for each categorical variable

side-by-side on the same graph, one quickly can

compare data sets.

• Box plots

•A boxplot splits the data set into quartiles.

•Calculate the median and the quartiles (the lower

quartile is the 25th percentile and the upper quartile

is the 75th percentile).

• For 25th percentile, 25% of the data values are

below it.

• The box represents the middle 50% of the data--the

"body" of the data.

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Median

Smallest

value

Highest

value

25th

percentile

No outliers

Response

variable

• Box plots of Q41 by gender

Median

• Box Position:

• The location of the box within two outer lines can provide insight on the normality of the sample's distribution.

•When the box is not centered between the outer lines, the sample may be positively or negatively skewed.

• If the box is shifted significantly to the low end, it is positively skewed; if the box is shifted significantly to the high end, it is negatively skewed.

• Box Size

• The size of the box can provide an estimate of the

kurtosis.

•A very thin box relative to the outer lines indicates a

distribution with a thinner peak.

•A wider box relative to the outer lines indicates a

wider peak. The wider the box, the more U-shaped

the distribution becomes.

• If there is a violation of statistical assumptions, you

might need a data transformation to correct this

matter.

•Concern: interpretation problem

• Log transformation, square root, logarithm, inverse,

reflect and square root, reflect and logarithm, and

reflect and inverse

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• The Crosstabs procedure forms two-way and multiway

tables and provides a variety of tests and measures

of association for two-way tables.

• Crosstabs’ statistics and measures of association are

computed for two-way tables only.

• Example 1: the association (independence) of gender

(Q2) and physical activity (Q80r).

•Q2 has two levels: female and male

•Q80r has four levels: 0 days, 1-2 days, 3-5 days,

and more than 5 days

• Obtain Crosstabs: Analyze > Descriptive Statistics >

Crosstabs

• Click Statistics to get this window

• Click Cell to get this window

• Crosstabs statistics (SPSS): Chi-square

• For tables with two rows and two columns, select Chi-

square to calculate the Pearson chi-square, the

likelihood-ratio chi-square, Fisher’s exact test, and

Yates’ corrected chi-square.

• For 2 × 2 tables, Fisher’s exact test is computed

when columns in a larger table has a cell with an

expected frequency of less than 5 (more than 20%).

•Yates’ corrected chi-square is computed for all other

2 × 2 tables.

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• Crosstabs: Chi-square

• For tables with any number of rows and columns,

select Chi-square to calculate the Pearson chi-square

and the likelihood-ratio chi-square.

•When both table variables are quantitative, Chi-

square yields the linear-by-linear association test.

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• Q80r by Q2

• Chi-square results

• Nominal. For nominal data (no intrinsic order, such as

Catholic, Protestant, and Jewish), you can select Contingency

coefficient, Phi (coefficient) and Cramer’s V, Lambda

(symmetric and asymmetric lambdas and Goodman and

Kruskal’s tau), and Uncertainty coefficient.

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• Ordinal. For tables in which both rows and columns contain

ordered values, select Gamma (zero-order for 2-way tables

and conditional for 3-way to 10-way tables), Kendall’s tau-b,

and Kendall’s tau-c.

• For predicting column categories from row categories, select

Somers’ d.

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• Nominal by Interval. When one variable is

categorical and the other is quantitative, select Eta.

The categorical variable must be coded numerically.

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• Kappa. Cohen's kappa measures the agreement

between the evaluations of two raters when both are

rating the same object (interrater reliability).

A value of 1 indicates perfect agreement.

A value of 0 indicates that agreement is no better

than chance.

Kappa is available only for tables in which both

variables use the same category values and both

variables have the same number of categories.

• Example 2. Whether Q24 (ever consider suicide) and

Q25 (ever make suicide plan) agree each other.

• Sometimes, one measure is from an objective test and

another is self-report measure.

• We need to get Kappa statistic.

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• Example 2: SPSS output

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• Kappa statistics

Kappa = 0.589 with p < 0.001. This measure of agreement, while

statistically significant, is only marginally convincing. As a rule of

thumb values of Kappa from 0.40 to 0.59 are considered moderate,

0.60 to 0.79 substantial, and 0.80 outstanding. Most statisticians

prefer for Kappa values to be at least 0.6 and most often higher than

0.7 before claiming a good level of agreement.

• Risk. For 2 x 2 tables, a measure of the strength of

the association between the presence of a factor and

the occurrence of an event.

• relative risk (RR) is the risk of an event (or of

developing a disease) relative to exposure. Relative

risk is a ratio of the probability of the event occurring

in the exposed group versus a non-exposed group.

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• Example 3: examine the effect of thinking

about suicide on suicide behavior. We have two

groups: Q24, thinking about suicide (yes) and

not thinking about suicide (no). Then, they plan

suicide, Q25 (yes/no).

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• Risk

• Relative Risk: is the risk of making suicide plan relative

to thinking about suicide. Relative risk is a ratio of the

probability of making plan (yes) in the thinking about

suicide group versus a non-thinking about suicide

group.

Relative

risk

• RR = (1274/2231)/(483/13926)= 16.46

• It means the risk of making plan for people thinking about suicide is more than 16 times that of people non-thinking about suicide.

• Odds ratio is a way of comparing whether the probability of making suicide plan is the same for thinking and non-thinking groups.

• Odds ratio = (1274/957)/(483/13443)=37.05

• This odds ratio illustrates that making plan is far more likely in the thinking group.

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• Bivariate correlation is about the association of two

variables.

Research question is like: whether two variables

are related to each other.

Bivariate correlation statistic: Pearson product-

moment coefficient (Pearson correlation: r).

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• Before calculating a correlation coefficient, screen

your data for outliers and evidence of a linear

relationship.

• Pearson’s correlation coefficient is a measure of linear

association.

• Two variables can be perfectly related, but if the

relationship is not linear, Pearson’s correlation

coefficient is not an appropriate statistic for measuring

their association.

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• Data. Use symmetric quantitative variables for

Pearson’s correlation coefficient and quantitative

variables or variables with ordered categories for

Spearman’s rho and Kendall’s tau-b.

• Assumptions. Pearson’s correlation coefficient

assumes that each pair of variables is bivariate

normal.

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• Correlation Coefficients. For quantitative, normally

distributed variables, choose the Pearson correlation

coefficient.

• If your data are not normally distributed or have

ordered categories, choose Kendall’s tau-b or

Spearman, which measure the association between

rank orders.

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• Example: Correlation between Q3r and Q80

• Go to Analyze > Correlate > Bivariate

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• SPSS output

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• Correlation coefficients range in value from –1 (a

perfect negative relationship) and +1 (a perfect

positive relationship).

• A value of 0 indicates no linear relationship. When

interpreting your results, be careful not to draw any

cause-and-effect conclusions due to a significant

correlation.

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Pearson correlation: -.064

Kendall’s tau-b : -.051

Question: the coefficients are small but significant, why?

• For large samples, it is easy to achieve significance,

and one must pay attention to the strength of the

correlation to determine if the relationship explains

very much.

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• Partial correlation coefficients describe the linear

relationship between two variables while controlling

for the effects of one or more additional variables.

• Correlations are measures of linear association

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• Example: Is there a relationship between Q39 and

Q80 while controlling Q81?

•Analyze > Correlate > Partial

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• SPSS output

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T test

One-Sample T test

Independent-Samples T test

Paired-Samples T test

One-way ANOVA

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• One-Samples T Test: this procedure tests whether the

mean of a single variable differs from a specified

constant.

• Example: we want to know whether the mean of

Q80 is different from 5 days (we use 5-day as cut-

off)

• Recode Q80 into 0 = 0 days, 1 = 1 day, 2 = 2

days … 7= 7 days.

•Go to Analyze > Compare Means > One-Samples T

Test

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SPSS output

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Independent-Samples T test

The Independent-Samples T Test procedure

compares means for two groups of cases.

Example: whether there is a difference in Q80

between males and females.

Go to Analyze > Compare Means > Independent-

Samples T Test

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Independent-Samples T test

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Independent-Samples T test: SPSS output

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• Paired-Samples T Test: This procedure compares the means of

two variables for a single group.

• The procedure computes the differences between values of the

two variables for each case and tests whether the average

differs from 0.

• Each subject has two measures, often called before and after

measures. An alternative design for which this test is used is a

matched-pairs or case-control study, in which each record in the

data file contains the response for one person and also for his

or her matched control subject.

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• Paired-Sample T Test

•Use combined data set from the example of Merging data sets.

•We want to know if there is a difference in a05 (school performance) across the time after intervention.

•We focus on one group. So we need to select cases from group 1.

•Go to Analyze > Compare Means > Paired-Sample T Test

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• Paired-Sample T Test:

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• Paired-Sample T Test: SPSS output

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