Essay about Non-parametric Statistics

Submitted By Caged-Lioness
Words: 1024
Pages: 5
Open Document
Week 3

p-values
• The calculated probability values corresponding to a particular test statistic given some set of circumstances
– Sample size
– Degrees of freedom
– Etc

• Calculated for us by SPSS
• P<0.05 generally considered significant
– Corresponds to alpha level

χ and
Other Non-Parametric Tests
2

Parametric vs Non-Parametric
Tests
• Parametric tests
– used when making a generalization about at least one parameter (population measure)
– Generally requires
• Normal distribution
• At least one interval level data
– Or that “approaches” interval level

– More powerful than non-parametric tests

Parametric vs Non-Parametric
Tests
• Non-Parametric Tests
– Don’t test hypotheses about population parameters – Don’t require normal distributions
– May be used for all levels of measurement
• Nominal to ratio

Chi-squared (χ ) Test
2

• The basic non-parametric test
• A test of independence
– Are two categorical variables independent? or – Is there a relationship between two categorical variables?

Chi-squared (χ ) Hypotheses
2

• Ho: there is no relationship between categorical variables
• H1: there is a relationship between categorical variables

χ2 Assumptions and
Requirements
• May be used when:
– Both IV and DV are nominal
• Ordinal sometimes if few categories
• Interval or ratio data is sometimes grouped to form nominal or ordinal variables
– Age in years into {0-15, 16-25, 26-35}

•
•
•
•
•

Assumes random and independent sampling
Each subject must qualify for ONE cell
No assumptions made about distribution shape
No assumptions about homogeneity
Expected frequency for each cell must be >0

χ Contingency Table
2

In SPSS: Crosstabs subject has diabetes * subject had stroke Crosstabulation
Count

subject has diabetes Total

no yes subject had stroke no yes
67
10
15
8
82
18

Total
77
23
100

The 2×2 table is the simplest but… can go to n1×n2

Calculating χ

2

(Oij - Eij)2
2 =  -------------- with df = (r-1)(c-1)
Eij
Where,
Oij = Observed cell frequencies
Eij = Expected cell frequencies =

Row Count x Column Count
--------------------------------------Total Count (N)

χ Distribution
2

• One-tailed
• Skewed to the right
• Similar to F distribution Calculating χ

2

subject has diabetes * subject had stroke Crosstabulation
Count

subject has diabetes no yes Total

E11
E12
E21
E22

=
=
=
=

(77X82)/100
(77X18)/100
(23X82)/100
(23X18)/100

subject had stroke no yes
67
10
15
8
82
18

=
=
=
=

63.1
13.9
18.9
4.1

Total
77
23
100

*Remember: This can be expanded to almost any reasonably sized table.

In Our Example…
(Oij - Eij)2
2 = 
Eij
(67 – 63.1)2 + (10 – 13.9)2 + (15 – 18.9)2 + (8 - 4.1)2
=

=5.8
63.1

13.9

18.9

4.1

with df = (R - 1)(C - 1) = (2 - 1)(2 - 1) = 1
General rule of thumb for 2X2 table with 1 df: χ2>4 is significant

SPSS Chi-Square Results
Chi-Square Tests

Pearson Chi-Square
Continuity Correctiona
Likelihood Ratio
Fisher's Exact Test
Linear-by-Linear
Association
N of Valid Cases

Value
5.700b
4.319
5.093
5.643

df
1
1
1
1

Asymp. Sig.
(2-sided)
.017
.038
.024

Exact Sig.
(2-sided)

Exact Sig.
(1-sided)

.028

.023

.018

100

a. Computed only for a 2x2 table
b. 1 cells (25.0%) have expected count less than 5. The minimum expected count is 4.
14.

Fisher’s Exact Test
• Used when an expected value is <5
– Takes into account small sizes

• Can be used only with 2×2 table
– Sometime necessary to collapse cells if χ2 cannot be adequately calculated
– If cells are not collapsed, χ2 can provide estimate but NOT actual significance

Yates’ Correction
• Yates’ correction for continuity
• Used in 2X2 tables, generally when any expected cell frequency is <10
– Do not apply when expected frequencies are small • Some disagreement about its use
– Reduces power

• Provides more conservative estimate
– Sometimes desirable, particularly with small numbers Yates’ Correction χ2 = ∑

(|O-E| - 0.5)2
E

Other Non-Parametric Tests
• Used when DV is nominal or ordinal OR
• When the assumptions for more
Show More

Related Documents: Essay about Non-parametric Statistics

Spearman: Non-parametric Statistics and Differences Categorical Essay

11/20/13 Spearman’s Rho 6  Another non-parametric test  Different from anything you’ve done yet SPEARMAN’S RHO 25.11.13 GOLDSMITHS |PS51008C: DESIGN AND ANALYSIS OF PSYCHOLOGICAL INVESTIGATIONS Dr Keon West Spearman’s Rho Spearman’s Rho 7 8 Test Investigate IV (Cat / Cont) DV (Cat / Cont) Within/ Between Formula critical Test Chi-square test Chi-square test MannWhitney U Differences Categorical Either (ppts…

Words 1009 - Pages 5

qbus revision Essay

relationship between two variables A measure of linear relationship: sample covariance and Pearson Coefficient of correlation (scale free) :Data Analysis > Correlation 2. Perform parametric and non-parametric tests for the coefficient of correlation Parametric Test: T-test, Data Analysis Plus > Correlation (Pearson) Non-Parametric Test: Z-test, Data Analysis Plus > Correlation (Spearman) 3. Understand the concept of simple linear regression analysis A statistical process to construst a relationship between…

Words 1686 - Pages 7

Parametric Test Assignment

Ans.1 In research statistics, we have 2 categories of tests for the purpose of data analysis and interpretation- one group is based on means and the other group is based on medians. Based on the outcomes of these tests, we accept or reject the hypotheses. The tests which are based on means of the groups are called parametric tests and the tests which are based on medians of the groups are called as non-parametric tests. Let us discuss them in detail. Parametric tests Parametric tests are used when…

Words 1074 - Pages 5

Pt2520 Unit 3 Assignment 2

Why would you calculate t-tests? Answer: - it allows you to compare statistics from 2 data populations and there means. This help to see if the 2 data population are significantly different from each other. A null hypothesis is used to test the difference between the 2 data populations and usually follow a normal distribution curve but the variances are unknown and are assumed to be equal. The test can then look at the t-statistic and t-distribution to determine a p-value that will validate or dispute…

Words 792 - Pages 4

Essay on Statistical Inference(lecture a)

Statistical Inference Lecture 01a ANU - RSFAS Semester 1, 2015 1 / 20 What is Statistics? Statistics is the Science of Data or Data Science 2 / 20 Our Increasingly Quantitative World The world is becoming quantitative. More and more professions, from the everyday to the exotic, depend on data and numerical reasoning. Data are not just numbers, but numbers that carry information about a specific setting and need to be interpreted in that setting. With this growth in the use of data comes…

Words 957 - Pages 4

Essay on Applied Managerial Dision Making

Applied Managerial Decision Making MGMT600-1301B-03 Phase 3 individual project Rocklyn Kee Colorado Technical University Online Professor Donald Pratl March 11, 2013 There are 500 employees in the sales force of Company W that are spread out over Southeast, Northeast, West, and Central regions. The company has recently incorporated a new software program in and attempt to monitor how many sales are generated by each employee. It is expected that each month each region should sell the same…

Words 925 - Pages 4

Essay on Exercises 2014 15 MAIN Topic 7 Chi Squa

appropriate chi-squared test (see example 4 in the notes) test the hypothesis that the population has a normal distribution. Compare the result obtained with an alternative test for normality (the Shapiro-Wilk test) in SPSS: Use Analyze-Descriptive Statistics-Explore Move Score to Dependent List Click Plots Tick Normality tests with plots Click Continue, Click OK. The p-value is shown in the Tests or Normality output table under Shapiro-Wilk as Sig. Note: Initially it may be useful to create a histogram…

Words 822 - Pages 4

Shaikh Farhan Essay

on 12/18/2009 and ended 05/16/2010. Table 1 presents the basic statistics for this data. Table 2 presents the mean statistics per day-of-the-week and shows the mean statistics of seasonality and holiday. Table 1 Basic Statistics for Coin-In and Promo-Play For 12/18/09 Through 05/16/10 Mean Maximum Minimum Standard Deviation Coin-In $2,297,821 $4,026,877 $1,251,546 $592,194 Promo $19,451 $61,144 $3,729 $11,803 Table 2 Mean Statistics Per Day-of-the Week For Coin-In and Promo-Play For 12/18/09 Through…

Words 1202 - Pages 5

Shaikh Farhan Essay

on 12/18/2009 and ended 05/16/2010. Table 1 presents the basic statistics for this data. Table 2 presents the mean statistics per day-of-the-week and shows the mean statistics of seasonality and holiday. Table 1 Basic Statistics for Coin-In and Promo-Play For 12/18/09 Through 05/16/10 Mean Maximum Minimum Standard Deviation Coin-In $2,297,821 $4,026,877 $1,251,546 $592,194 Promo $19,451 $61,144 $3,729 $11,803 Table 2 Mean Statistics Per Day-of-the Week For Coin-In and Promo-Play For 12/18/09 Through…

Words 1206 - Pages 5

Preparing To Conduct Business Research: Part III

Preparing to Conduct Business Research: Part III The dilemma facing XYZ Employment is the cost of providing Workman’s Compensation Insurance and the costly nature of its claims. All companies that have employee require this costly, yet necessary standard. It is provided to protect hard working employees in difficult circumstances. While most times it is a legitimate claim, fraud does occur. XYZ would like to eliminate the preventable claims and fraudulent collections. XYZ is making all efforts…

Words 2358 - Pages 10