Hypothesis testingHypothesis testing

Intermediate Food Security Analysis TrainingRome, July 2010Rome, July 2010

Hypothesis testing

Hypothesis testing involves:1. defining research questions and2. assessing whether changes in an independent

variable are associated with changes in the dependent variable by conducting a statistical test

Dependent and independent variablesDependent and independent variables Dependent variables are the outcome variables Independent variables are the predictive/

explanatory variables

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Examples…

Research question: Is educational level of the mother related to birthweight?

What is the dependent and independent variable?

Research question: Is access to roads related to educational level of mothers?

Now?

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Tests statistics To test hypotheses, we rely on test

statistics…

Test statistics are simply the result of a particular statistical test

The most common include:The most common include:

1. T-tests calculate T-statistics

2. ANOVAs calculate F-statistics

3. Correlations calculate the pearson correlation coefficient

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Significant test statistic Is the relationship observed by chance, or because there

actually is a relationship between the variables???

This probability is referred to as a p-value and is expressed a decimal percent (ie. p=0.05)

If the probability of obtaining the value of our test statistic by chance is less than 5% then we generally accept the experimental hypothesis as true: there is an effect on the population

Ex: if p=0.1-- What does this mean? Do we accept the experimental hypothesis?

This probability is also referred to as significance level (sig.)

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Hypothesis testing Part 1: Hypothesis testing Part 1: Continuous variablesContinuous variables

Topics to be covered in this presentation

T- test One way analysis of variance (ANOVA) Correlation

By the end of this session, the participant should be able to:

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Hypothesis testing…WFP tests a variety of hypothesis…

Some of the most common include:

1. Looking at differences between groups of people (comparisons of means)

Ex. Are different livelihood groups more likely to have different levels food consumption??

2. Looking at the relationship between two variables…

Ex. Is asset wealth associated with food consumption??

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How to assess differences in two means statistically

T-tests

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T-testA test using the t-statistic that establishes whether two means differ significantly.

Independent means t-test:Independent means t-test: It is used in situations in which there are two

experimental conditions and different participants have been used in each condition.

Dependent or paired means t-test:Dependent or paired means t-test: This test is used when there are two

experimental conditions and the same participants took part in both conditions of experiment.

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Independent T-tests works well if:

continuous variables

groups to compare are composed of different people

within each group, variable’s values are normally distributed

there is the same level of homogeneity in the 2 groups.

T-test: assumptions

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Normal distribution

Normal distributions are perfect symmetrical around the mean (mean is equal to zero)

Values close to the mean (zero) have higher frequency.

Values very far from the mean are less likely to occur (lower frequency)

Variance

Variance measures how cases are similar on a specific variable (level of homogeneity)

V = sum of all the squared distances from the Mean / N

Variance is low → cases are very similar to the mean of the distribution (and to each other). The group of cases is therefore homogeneous (on this variable)

Variance is high → cases tend to be very far from the mean (and different from each other). The group of cases is therefore heterogeneous (on this variable)

Homogeneity of Variance

T-test works well if the two groups have the same homogeneity (variance) on the variable. If one group is very homogeneous and the another is not, T-test fails.

The independent t-test

The independent t-test compares two means, when those means have come from different groups of people;

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To conduct an independent t-test in SPSS

1. Click on “Analyze” drop down menu2. Click on “Compare Means”3. Click on “Independent- Sample T-Test…”4. Move the independent and dependent

variable into proper boxes5. Click “OK”

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T-test: SPSS procedure

Drag the variables into the proper boxes

define values for the independent variable

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One note of caution about independent t-testsIt is important to ensure that the assumption of homogeneity of variance is met:

To do so:

Look at the column labelled Levene’s Test for Equality of Variance.

If the Sig. value is less than .05 then the assumption of homogeneity of variance has been broken and you should look at the row in the table labelled Equal variances not assumed.

If the Sig. value of Levene’s test is bigger than .05 then you should look at the row in the table labelled Equal variances assumed.

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T-test: SPSS output

Look at the Levene’s Test …

If the Sig. value of the test is less than .05, groups have different variance. Read the row “Equal variances not assumed”

If the Sig. value of test is bigger than .05, read the row labelled “Equal variances assumed”

Independent Samples Test

.004 .950 -.791 1147 .429 -1.47311 1.86149 -5.12542 2.17921

-.791 1140.469 .429 -1.47311 1.86261 -5.12764 2.18143

Equal variancesassumed

Equal variancesnot assumed

coping strategies indexF Sig.

Levene's Test forEquality of Variances

t df Sig. (2-tailed)Mean

DifferenceStd. ErrorDifference Lower Upper

95% ConfidenceInterval of the

Difference

t-test for Equality of Means

Group Statistics

581 40.9019 30.70829 1.27399

568 42.3750 32.38332 1.35877

beneficiary householdas per CP records1

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coping strategies indexN Mean Std. Deviation

Std. ErrorMean

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What to do if we want to statistically compare differences in three means?

Analysis of variance

(ANOVA)

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Analysis of Variance (ANOVA) ANOVAs test tells us if there are any

difference among the different means but not how (or which) means differ.

ANOVAs are similar to t-tests and in fact an ANOVA conducted to compare two means will give the same answer as a t-test.

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Calculating an ANOVA

ANOVA formulas: calculating an ANOVA by hand is complicated and knowing the formulas are not necessary…

Instead, we will rely on SPSS to calculate ANOVAs…

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Example of One-Way ANOVAs

Report

WAZNEW

-1.3147 736 1.32604

-1.0176 3247 1.21521

-.5525 907 1.25238

-.1921 172 1.33764

-.9494 5062 1.27035

Mother's education level

No education

Primary

Secondary

Higher

Total

Mean N Std. Deviation

ANOVA

WAZNEW

354.567 3 118.189 76.507 .000

7812.148 5057 1.545

8166.715 5060

Between Groups

Within Groups

Total

Sum of Squares df Mean Square F Sig.

Research question: Do mean child malnutrition (GAM) rates differ according to mother’s educational level (none, primary, or secondary/ higher)?

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To calculate one-way ANOVAs in SPSSIn SPSS, one-way ANOVAs are run using the

following steps:

Click on “Analyze” drop down menu

1. Click on “Compare Means”

2. Click on “One-Way ANOVA…”

3. Move the independent and dependent variable into proper boxes

4. Click “OK”

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ANOVA: SPSS procedure

1. Analyze; compare means; one-way ANOVA

2. Drag the independent and dependent variable into proper boxes

3. Ask for the descriptive

4. Click on ok

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ANOVA: SPSS output

ANOVA

coping strategies index

25600.110 10 2560.011 2.609 .004

1116564 1138 981.163

1142164 1148

Between Groups

Within Groups

Total

Sum ofSquares df Mean Square F Sig.

Along with the mean for each group, ANOVA produces the F-statistic. It tells us if there are differences between the means. It does not tell which means are different.

Look at the F’s value and at the Sig. level

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Determining where differences existIn addition to determining that differences exist among the means, you may want to know which means differ.

There is one type of test for comparing means:

Post hoc tests are run after the experiment has been conducted (if you don’t have specific hypothesis).

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ANOVA post hoc testsOnce you have determined that differences exist among the means, post hoc range tests and pairwise multiple comparisons can determine which means differ.

Tukeys post hoc test is the amongst the most popular and are adequate for our purposes…so we will focus on this test…

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To calculate Tukeys test in SPSSIn SPSS, Tukeys post hoc tests are run using the

following steps:1. Click on “Analyze” drop down menu2. Click on “Compare Means”3. Click on “One-Way ANOVA…”4. Move the independent and dependent variable into

proper boxes5. Click on “Post Hoc…”6. Check box beside “Tukey”7. Click “Continue”8. Click “OK”

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Determining where differences exist in SPSS

Once you have determined that differences exist among the means → you may want to know which means differ…

Different types of tests exist for pairwise multiple comparisons

Pairwise comparisons: SPSS outputOnce you have decided which post-hoc test is appropriate

Look at the column “mean difference” to know the difference between each pair

Look at the column Sig.: if the value is less than .05 then the means of the two pairs are significantly different

Multiple Comparisons

Dependent Variable: coping strategies index

Tukey HSD

8.5403* 1.6796 .000 4.599 12.481

22.5906* 2.7341 .000 16.175 29.006

-8.5403* 1.6796 .000 -12.481 -4.599

14.0503* 2.5873 .000 7.979 20.121

-22.5906* 2.7341 .000 -29.006 -16.175

-14.0503* 2.5873 .000 -20.121 -7.979

(J) asset wealthasset medium

asset rich

asset poor

asset rich

asset poor

asset medium

(I) asset wealthasset poor

asset medium

asset rich

MeanDifference

(I-J) Std. Error Sig. Lower Bound Upper Bound

95% Confidence Interval

The mean difference is significant at the .05 level.*. 34

Now what if we would like to measure how well two variables are associated with one another?

Correlations

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Correlations

T-tests and ANOVAs measure differences between means

Correlations explain the strength of the linear relationship between two variables…

Pearson correlation coefficients (r) are the test statistics used to statistically measure correlations

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Types of correlations

Positive correlations: Two variables are positively correlated if increases (or decreases) in one variable results in increases (or decreases) in the other variable.

Negative correlations: Two variables are negatively correlated if one increases (or decreases) and the other decreases (on increases).

No correlations: Two variables are not correlated if there is no linear relationship between them.

Strong negative correlation

No correlation Strong positive correlation

-1--------------------------0---------------------------1

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Illustrating types of correlations

Perfect positive correlation

Test statistic= 1

Positive correlation

Test statistics>0 and <1

Perfect negative correlation

Test statistic= -1

Negative correlation

Test statistic<0 and >-138

Example for the Kenya Data

Correlation between children’s weight and height…

Cases w eighted by CHWEIGHT

Weight of child

3002001000

He

igh

t o

f ch

ild

1400

1200

1000

800

600

400

200

Is this a positive or negative correlation??

In what range would the test statistics fall?

To calculate a Pearson’s correlation coefficient in SPSSIn SPSS, correlations are run using the following

steps:1. Click on “Analyze” drop down menu2. Click on “Correlate”3. Click on “Bivariate…”4. Move the variables that you are interested

in assessing the correlation between into the box on the right

5. Click “OK”

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example in SPSS…

Correlations

1 .932**

.000

10 10

.932** 1

.000

10 10

Pearson Correlation

Sig. (2-tailed)

N

Pearson Correlation

Sig. (2-tailed)

N

wealth

FCS

wealth FCS

Correlation is significant at the 0.01 level(2-tailed).

**.

Using SPSS we get Pearson’s correlation (0.932)

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1. Lets refresh briefly, what does a correlation of 0.932 mean??

2. What does *** mean?

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Summary

Check out pg 171 of CFSVA manual for an overview of the test

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