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ura esearc et o o ogyura esearc et o o ogy

PGP ABM IIPGP ABM II

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Data Pre arationData Pre aration

CodebookCodebook

Deciding on the data formatDeciding on the data format Data entryData entry

Data cleaningData cleaning

Handling missing dataHandling missing data

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Data Anal sisData Anal sis

UnivariateUnivariate DescriptiveDescriptive

InferentialInferential

BivariateBivariate

InferentialInferential

MultivariateMultivariate

DescriptiveDescriptive

InferentialInferential

To a large extent depends on level of measurementTo a large extent depends on level of measurement

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Univariate Descri tive StatisticsUnivariate Descri tive Statistics

Fre uenc distributionFre uenc distribution

Measures of central tendencyMeasures of central tendency ModeMode

MedianMedian

MeanMean Measures of dispersionMeasures of dispersion

RangeRange

Average absolute deviationAverage absolute deviation Variance & Standard deviationVariance & Standard deviation

rr uu

Standardized ScoresStandardized Scores

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Univariate Descri tive StatisticsUnivariate Descri tive Statistics

How many observations occur in each responseHow many observations occur in each response

category of the variable. FD is a table of thecategory of the variable. FD is a table of theoutcomes, or response categories, of a variableoutcomes, or response categories, of a variable

and the number of times each outcome isand the number of times each outcome is..

Relative FDRelative FD

PercentPercent

Cumulative frequencyCumulative frequency

Cumulative percentCumulative percent

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Univariate Descri tive StatisticsUnivariate Descri tive StatisticsFrequency distributionFrequency distribution

Statistics

Interest in Movies

1504

13

Valid

Missing

N

Interest in Movies

Frequency Percent Valid Percent

Cumulative

Percent

467 30.8 31.1 31.1872 57.5 58.0 89.0

165 10.9 11.0 100.0

1504 99.1 100.0

Great InterestSome Interest

No Interest

Total

Valid

13 .9

1517 100.0

NAMissing

Total

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Univariate Descri tive StatisticsUnivariate Descri tive Statistics

Grouped data is the data that have been collapsedGrouped data is the data that have been collapsed

into a smaller number of categories. Constructing ainto a smaller number of categories. Constructing afrequency distribution for a continuous variablefrequency distribution for a continuous variable

first requires grouped data.first requires grouped data.

The process of grouping continuous variables fromThe process of grouping continuous variables fromman initial values into fewer cate ories is calledman initial values into fewer cate ories is called

recoding.recoding.

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Univariate Descri tive StatisticsUnivariate Descri tive StatisticsHighest Year of School Completed

Cumulative

Grouped DistributionGrouped Distribution

2 .1 .1 .15 .3 .3 .5

5 .3 .3 .8

6 .4 .4 1.2

03

4

5

Valid

Frequency Percent Valid Percent Percent

Statistics

12 .8 .8 2.0

25 1.6 1.7 3.6

68 4.5 4.5 8.1

56 3.7 3.7 11.9

73 4.8 4.8 16.7

6

7

8

9

10

1510

7

Valid

Missing

N. . .

461 30.4 30.5 52.8

130 8.6 8.6 61.5

175 11.5 11.6 73.0

73 4.8 4.8 77.9

12

13

14

15

. . .

43 2.8 2.8 93.6

45 3.0 3.0 96.6

22 1.5 1.5 98.0

30 2.0 2.0 100.0

17

18

19

20

Total . .

7 .5

1517 100.0

NAMissing

Total

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Univariate Descri tive StatisticsUnivariate Descri tive StatisticsGrouped DistributionGrouped Distribution

Statistics Highest years of School ing - Recoded

Highest Year of School Com

1510

7

Valid

Missing

N

18 1.2 1.2 1.2

234 15.4 15.5 16.7924 60.9 61.2 77.9

1 (0-5)

2 (6-10)3 11-15

Valid

Frequency Percent Valid Percent

Cumulative

Percent

334 22.0 22.1 100.0

1510 99.5 100.0

7 .5

1517 100.0

4 (16-20)

Total

SystemMissing

Total

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Univariate Descri tive StatisticsUnivariate Descri tive Statistics

The category among the K categories in aThe category among the K categories in a

observations.observations.

A distribution may be bimodal.A distribution may be bimodal.

Mode is central tendency statistic applicable toMode is central tendency statistic applicable tonominal, ordinal, & interval variables.nominal, ordinal, & interval variables.

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Univariate Descri tive StatisticsUnivariate Descri tive Statistics

The median is the outcome that divides an orderedThe median is the outcome that divides an ordered

have scores above the median value and half willhave scores above the median value and half will

have scores below the median.have scores below the median. For a grouped frequency distribution the median isFor a grouped frequency distribution the median is

the value of that category at which the cumulativethe value of that category at which the cumulative

Mode is central tendency statistic applicable toMode is central tendency statistic applicable toordinal & interval variablesordinal & interval variables

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Univariate Descri tive StatisticsUnivariate Descri tive Statistics

The arithmetic average of a set of data in which the valuesThe arithmetic average of a set of data in which the valuesof all observations are added together and divided by theof all observations are added together and divided by the

..

Y

Y i=

Mean of grouped frequency distribution:Mean of grouped frequency distribution:k

NY i

ii

== 1

fi =The frequency of cases with score Yi

K =The no. of categories in the distribution

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Univariate Descri tive StatisticsUnivariate Descri tive Statistics

The difference between the largest and smallestThe difference between the largest and smallestscores in a distribution.scores in a distribution.

The mean of the absolute values of the differenceThe mean of the absolute values of the difference

between a set of continuous measures and theirbetween a set of continuous measures and their

mean.mean.di

AADMM

=

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Univariate Descri tive StatisticsUnivariate Descri tive Statistics

Variance is the mean squared deviation of aVariance is the mean squared deviation of a

continuous distribution.continuous distribution.N

2

2 i 1Y

(Yi Y)

S =

=

Standard deviation is the square root of theStandard deviation is the square root of the

2

YY SS =

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Univariate Descri tive StatisticsUnivariate Descri tive Statistics

Is the outcome or score below which a givenIs the outcome or score below which a givenpercentage of the observations falls.percentage of the observations falls.

e me ian is t e 50e me ian is t e 50 percenti e.percenti e.

Quantiles:Quantiles: v s on o o serva ons n o groups w nownv s on o o serva ons n o groups w nown

proportions in each group.proportions in each group.

Percentiles divide observations into 100 equalPercentiles divide observations into 100 equal

groupsgroups Quartiles divide the observations into 4 equalQuartiles divide the observations into 4 equal

groups, and Deciles into 10 equal groupsgroups, and Deciles into 10 equal groups

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Univariate Descri tive StatisticsUnivariate Descri tive Statistics

DecilesDecilesa s cs

Highest Year of School Completed

1510ValidN

9.00

11.00

12.00

10

20

25

Percentiles

12.00

12.00

12.00

13.00

30

40

50

60

14.00

15.00

16.00

70

75

80

.

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Univariate Descri tive StatisticsUnivariate Descri tive Statistics

A transformation of the scores of a continuousA transformation of the scores of a continuous

frequency distribution by subtracting the meanfrequency distribution by subtracting the meanfrom each outcome and dividing by thefrom each outcome and dividing by thestandard deviation.standard deviation.

..

Mean of Z scores equals zero and variance andMean of Z scores equals zero and variance andstandard deviation e ual 1.standard deviation e ual 1.

ii

)Y(YZ

=

y

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INFERENTIAL ANALYSISINFERENTIAL ANALYSIS

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Inferential Analysis: From Sample toInferential Analysis: From Sample to

studying the characteristics of a samplestudying the characteristics of a sample..

Major objective is to draw inferencesMajor objective is to draw inferences

sample was drawn.sample was drawn.

amp e s a s c s use or es ma on oamp e s a s c s use or es ma on othe population parameterthe population parameter

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Po ulation and Sam le descri tionsPo ulation and Sam le descri tions

NameName Sample StatisticSample Statistic Population ParametersPopulation Parameters

MeanMeanN

YY

i=

=

==k

1i

iiY )p(YYE(Y)

VarianceVariance

1N

)Y(Yi

S

N

1i

2

2

Y

=

=

=

==k

1i

i

2

ii

2

y

2 )p(Y)(Y)E(Y

StandardStandardDeviationDeviation

2

YY SS =2

YY =

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Inferential StatisticsInferential Statistics

Making interval estimatesMaking interval estimates

Let us first clarify some basic concepts

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Basic Probabilit Conce tsBasic Probabilit Conce ts

,,

each of which has an associatedeach of which has an associated..

In deck of cardsIn deck of cards

Probabilit of randoml drawin a card from theProbabilit of randoml drawin a card from theheart suit is 13/52 or (0.25).heart suit is 13/52 or (0.25).

Probability of randomly drawing an ace of spadesProbability of randomly drawing an ace of spades

s . .s . .If an outcome cannot occur it has a probability ofIf an outcome cannot occur it has a probability of

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Basic Probabilit Conce tsBasic Probabilit Conce ts

A probability distribution for a continuous variable,A probability distribution for a continuous variable,

with no interruptions or spaces between thewith no interruptions or spaces between theoutcomes of the variable.outcomes of the variable.

p(Y)

P(a Yb) =

a b Y

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Normal Distribution & Confidence IntervalsNormal Distribution & Confidence Intervals. . . .. . . .

Mean = 3.75S.D. = 0.25

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Sam lin DistributionSam lin Distribution

If all possible random samples ofIf all possible random samples ofNNare drawnare drawn

from any population with meanfrom any population with mean and varianceand variance

22yy, then as, then as NNgrows large, these sample meansgrows large, these sample means

approach aapproach a normal distributionnormal distribution, with mean, with meanyy

andand22 yy ..

he h othetical distribution of all ossiblehe h othetical distribution of all ossible

(infinite) means for samples of size(infinite) means for samples of size NNis called theis called thesampling distributionsampling distribution of sample means.of sample means.

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Sampling DistributionSampling Distribution (Source: http://trochim.human.cornell.edu/kb/sampstat.htm)(Source: http://trochim.human.cornell.edu/kb/sampstat.htm)

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Sampling DistributionSampling Distribution

Standard deviation of the sampling distribution is referredStandard deviation of the sampling distribution is referredto as the Standard Error. It indicates distribution pattern ofto as the Standard Error. It indicates distribution pattern of

..

N

YY

=

Sampling Error:Sampling Error: Standard error in the sam lin context is called Sam linStandard error in the sam lin context is called Sam lin

Error.Error.

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Confidence IntervalsConfidence Intervals

but know the distribution of the samplebut know the distribution of the sample

our sample and calculate our sample and calculate standard errorstandard error..

the sampling distribution in order tothe sampling distribution in order to

population parameter.population parameter.

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Confidence IntervalsConfidence Intervals (Source: http://trochim.human.cornell.edu/kb/sampstat.htm(Source: http://trochim.human.cornell.edu/kb/sampstat.htm

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Inferential StatisticsInferential Statistics

Making interval estimatesMaking interval estimates

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Significance Tests:Significance Tests: Nominal & Ordinal VariablesNominal & Ordinal Variables

Government should provide electricity free of costto the farmers

Agree Disagree

Population assumption of no differencePopulation assumption of no difference 50%50% 50%50%

Sam le observationSam le observation 47%47% 53%53%

The sample is unrepresentative. The discrepancy in our assumption andsample observation is due to sampling error.

Our assumption (null hypothesis) of equal split in the population is

incorrect.

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Significance Tests:Significance Tests: Nominal & Ordinal VariablesNominal & Ordinal Variables

Binomial test for dichotomous variablesBinomial test for dichotomous variables

Binomial test of statistical significance is the estimate ofBinomial test of statistical significance is the estimate ofthe likelihood of obtaining a random sample in whichthe likelihood of obtaining a random sample in whichsampling error produced a difference between categoriessampling error produced a difference between categories

as big as we have observed (as big as we have observed (53/4753/47).). The figure obtained in this test range from 0.00 to 1.00The figure obtained in this test range from 0.00 to 1.00

and are calledand are called significance levelssignificance levels..

,,

that observed percentage differences reflect realthat observed percentage differences reflect realdifferences in the population.differences in the population.

population proportions.population proportions.

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Significance Tests:Significance Tests: Nominal & Ordinal VariablesNominal & Ordinal Variables

One sam le chiOne sam le chi--s uare tests uare test

Is used for testing differences across the categories of a variableIs used for testing differences across the categories of a variablewith three or more categories.with three or more categories.

Farmers Orientation towards Farming Business Subsistence Others

.. .. ..

Sample observation (332)Sample observation (332) 33.1%33.1% 37.0%37.0% 29.8%29.8%

ChiChi--square 2.6 (p=0.27)square 2.6 (p=0.27)

There is a 27% chance that the difference across categories are due toThere is a 27% chance that the difference across categories are due tosamp ing error. T ere ore continue wit t esamp ing error. T ere ore continue wit t e null hypothesisnull hypothesist at eac va uet at eac va ueorientation is equally prevalent.orientation is equally prevalent.

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Interval Estimates:Interval Estimates: Nominal & Ordinal VariablesNominal & Ordinal Variables

pattern will hold in the population, intervalpattern will hold in the population, intervalestimate procedures calculate the likely marginestimate procedures calculate the likely marginor error in the sample figures.or error in the sample figures.

Suppose in a survey 35% of the respondentsSuppose in a survey 35% of the respondentsview view farmingfarming as a as a way of lifeway of life. What is the. What is thelikely margin of error of this estimate? How closelikely margin of error of this estimate? How close

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Interval Estimates:Interval Estimates: Nominal & Ordinal VariablesNominal & Ordinal Variables

Com uteCom ute standard errorstandard error of the binomial:of the binomial:

PQSB =

SB = Std. error for the binomial distributionP = Per cent in the category of interest

Q = Per cent in the remaining category(ies).

Confidence interval = PSB

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Si nificance Tests:Si nificance Tests: Interval VariablesInterval Variables

--

significance can be used for interval data.significance can be used for interval data.

limit our analysis to examination oflimit our analysis to examination of

..

We can test whether the sample meanWe can test whether the sample mean

population mean.population mean.

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Si nificance Tests:Si nificance Tests: Interval VariablesInterval Variables

--

Average Annual income

People)People)

..

Known population meanKnown population mean Rs. 38922Rs. 38922

known population meanknown population mean

TT--test significance leveltest significance level 0.0000.000

people and that of the general population ispeople and that of the general population issufficiently large for a sample of this sizesufficiently large for a sample of this sizethat it almost certainly reflects a realthat it almost certainly reflects a realpopulation difference rather than being duepopulation difference rather than being dueto sampling errorto sampling error

Source: de vaus (2002)

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Interval Estimates:Interval Estimates: Interval VariablesInterval Variables

Usin the same eneral lo ic as with nominalUsin the same eneral lo ic as with nominal

and ordinal variables we estimate the marginand ordinal variables we estimate the marginof error. However, in place of percentages,of error. However, in place of percentages,

means.means.

N

sSM =

SM = Std. error of the mean= .

N = No. of cases in the sample

Confidence interval = PSM

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Bivariate Analysis:Bivariate Analysis: Nominal & Ordinal VariablesNominal & Ordinal Variables

BivariateBivariate anal sis rovides a s stematic wa ofanal sis rovides a s stematic wa of

measuring whether two variables are associatedmeasuring whether two variables are associated(related).(related).

UsingUsing univariateunivariate analysis we establishedanalysis we establishedvariation among people;variation among people; bivariatebivariate analysisanalysis

..

If two variables are associated then knowing aIf two variables are associated then knowing a

improves our prediction about otherimproves our prediction about othercharacteristics of that person.characteristics of that person.

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Bivariate Analysis:Bivariate Analysis: Nominal & Ordinal VariablesNominal & Ordinal Variables

Frequency Distributions

Importance of Crop Insurance

Cumulative

StatisticsImportance of Crop Insurance

836 46.4 46.4 46.4

574 31.9 31.9 78.2

132 7.3 7.3 85.6

62 3.4 3.4 89.0

198 11.0 11.0 100.0

VERY IMPORTANT

FAIRLY IMPORTANT

OF LITTLE IMPORTANCE

OF NO IMPORTANCE

DONT KNOW

Valid

Frequency Percent Valid Percent Percent

1802

0

2.01

2.00

1

Valid

Missing

N

Mean

Median

Mode

SEX

1802 100.0 100.0Total1.290Std. Deviation

SEX1802

0

2

Valid

Missing

N

Mode

842 46.7 46.7 46.7

960 53.3 53.3 100.0

1802 100.0 100.0

MALE

FEMALE

Total

Valid

Frequency Percent Valid Percent

Cumulative

Percent

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Bivariate Analysis:Bivariate Analysis: Nominal & Ordinal VariablesNominal & Ordinal Variables

CrossCross--tabulationstabulations

Importance of Crop Insurance * SEX

Independent Var.Count or cell freq.

Count

MALE FEMALE

SEX

Total

432 404 836

241 333 574

54 78 132

VERY IMPORTANT

FAIRLY IMPORTANT

OF LITTLE IMPORTANCE

Dependent Var.

89 109 198842 960 1802

DONT KNOWTotal

Row Marginals

Bivariate Analysis:Bivariate Analysis: Nominal & Ordinal VariablesNominal & Ordinal Variables

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*

Bivariate Analysis:Bivariate Analysis: Nominal & Ordinal VariablesNominal & Ordinal Variables

u

432 404 836

51.7% 48.3% 100.0%

Count

% within CROP

IINSURANCE

IMPORTANCE

VERY IMPORTANT

MALE FEMALE

SEX

Total

51.3% 42.1% 46.4%

24.0% 22.4% 46.4%

241 333 574

42.0% 58.0% 100.0%

% within SEX

% of Total

Count

% within CROP

IINSURANCE

IMPORTANCE

% within SEX

FAIRLY IMPORTANT

Column percent

Row percent

. . .

13.4% 18.5% 31.9%

54 78 132

40.9% 59.1% 100.0%

6.4% 8.1% 7.3%

% of Total

Count

% within CROP

IINSURANCE

IMPORTANCE

% within SEX

OF LITTLE IMPORTANCETotal percent

. . .

26 36 62

41.9% 58.1% 100.0%

3.1% 3.8% 3.4%

1.4% 2.0% 3.4%

Count

% within CROP

IINSURANCE

TOIMPORTANCE

% within SEX

% of Total

OF NO IMPORTANCE

1 1

44.9% 55.1% 100.0%

10.6% 11.4% 11.0%

4.9% 6.0% 11.0%

842 960 1802

oun

% within CROP

IINSURANCE

TOIMPORTANCE

% within SEX

% of Total

Count

Total

46.7% 53.3% 100.0%

100.0% 100.0% 100.0%

46.7% 53.3% 100.0%

% within CROP

IINSURANCE

TOIMPORTANCE

% within SEX

% of Total

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Bivariate Analysis:Bivariate Analysis: Nominal & Ordinal VariablesNominal & Ordinal Variables

CrossCross--tabulationstabulations

CROP INSURANCE IMPORTANCE* SEX Crosstabulation

SEX

432 404 836

51.3% 42.1% 46.4%

241 333 574

28.6% 34.7% 31.9%

Count

% within SEX

Count

% within SEX

1

2

o a

54 78 132

6.4% 8.1% 7.3%

26 36 62

3.1% 3.8% 3.4%

Count

% within SEX

Count

% within SEX

3

4

89 109 198

10.6% 11.4% 11.0%

842 960 1802

100.0% 100.0% 100.0%

Count

% within SEX

Count

% within SEX

5

Total

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Bivariate Analysis:Bivariate Analysis: Nominal & Ordinal VariablesNominal & Ordinal Variables

--

independent, the formula for the expectedindependent, the formula for the expectedfrequency in rowfrequency in row iiand columnand columnjjis:is:

))(f(ff .ji.=)

marginalrowiin thetotalthef

columnjthe&rowitheincelltheoffrequencyexpectedthef

N

th

i.

thth

ij

=

=)

tableentirefor thesizesampleortotal,grandtheNmarginalcolumnjin thetotalthef

th

.j

=

=

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Bivariate Analysis:Bivariate Analysis: Nominal & Ordinal VariablesNominal & Ordinal Variables

The chiThe chi--square test statistic summarizes the differences across thesquare test statistic summarizes the differences across thecells between the observed frequencies and the expectedcells between the observed frequencies and the expected

frequencies. Chifrequencies. Chi--square is calculated by the formula:square is calculated by the formula:R C )2O(E

= =

=1i 1j ijE

Eij

= The expected frequency in the ith row, jthcolumn under independence.= .

C = The number columns in the cross-tabulation.R = The number of rows in the cross tabulation

-

at the relevant degrees of freedom. If the computed chi-squarestatistic is greater than the critical value at an acceptablesignificance level, reject the null hypothesis

df = (R-1)(C-1)

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Bivariate Analysis:Bivariate Analysis: Nominal & Ordinal VariablesNominal & Ordinal VariablesHow often go market * SEX Crosstabulation

432 404 836Count1

MALE FEMALE

SEX

Total

. . .

51.3% 42.1% 46.4%

241 333 574

268.2 305.8 574.0

28.6% 34.7% 31.9%

54 78 132

% within SEX

Count

Expected Count

% within SEX

Count

2

3

61.7 70.3 132.0

6.4% 8.1% 7.3%

26 36 62

29.0 33.0 62.0

3.1% 3.8% 3.4%

89 109 198

xpec e oun

% within SEX

Count

Expected Count

% within SEX

Count

4

5

92.5 105.5 198.0

10.6% 11.4% 11.0%

842 960 1802

842.0 960.0 1802.0

100.0% 100.0% 100.0%

Expected Count

% within SEX

Count

Expected Count

% within SEX

Total

Chi-Square Tests

16.022a 4 .003

16.047 4 .003

Pearson Chi-Square

Likelihood Ratio

Value df

Asymp. Sig.

(2-sided)

5.753 1 .016

1802

- -

Association

N of Valid Cases

0 cells (.0%) have expected count less than 5. The

minimum expected count is 28.97.

a.

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Bivariate Analysis:Bivariate Analysis: Interval VariablesInterval Variables

apply methods of nominal or ordinalapply methods of nominal or ordinal..

Colla se the cate ories orColla se the cate ories or Use techniques that can handle a large number ofUse techniques that can handle a large number of

numeric valuesnumeric values

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Bivariate Anal sis:Bivariate Anal sis: Interval VariablesInterval Variables

Cannot use powerful statistical toolsCannot use powerful statistical tools

,

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Bivariate Anal sis:Bivariate Anal sis: Interval VariablesInterval Variables

De endent: interval Inde endent: dichotomousDe endent: interval Inde endent: dichotomous

Comparison ofComparison of MeansMeans: t: t--testtest

ase rocess ng ummary

N Percent N Percent N Percent

Included Excluded Total

Cases

40081 65.9% 20708 34.1% 60789 100.0%

Amount spent on

nature related activity *

Sex of the respondent

Amount spent on nature related activity

992.42 19560 3659.611

Sex of the respondent

Male

Mean N Std. Deviation

464.21 20521 2260.503

721.98 40081 3036.691

Female

Total

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Bivariate Anal sis:Bivariate Anal sis: Interval VariablesInterval Variables

De endent: interval Inde endent: dichotomousDe endent: interval Inde endent: dichotomous

Comparison ofComparison of MeansMeans: t: t--testtest

19560 992.42 3659.611 26.167

Sex of the respondent

MaleAmount spent on

N Mean Std. Deviation

Std. Error

Mean

. . .ema e

Independent Samples Test

Levene's Test for

F Sig.

Equality of

Variances

t df Sig. (2-tailed)

Mean

Difference

Std. Error

Difference Lower Upper

95% Confidence

Interval of the

Difference

t-test for Equality of Means

456.503 .000 17.473 40079 .000 528.20 30.230 468.952 587.457

17.286 32300.106 .000 528.20 30.557 468.312 588.097

assumed

Equal variances

not assumed

nature related activity

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Bivariate Anal sis:Bivariate Anal sis: Interval VariablesInterval Variables

Pearsons Correlation coefficientPearsons Correlation coefficient

Correlations

Amount spent

1 -.032**

. .000

Pearson Correlation

Sig. (2-tailed)

Weekly earnings

ee y

earnings

on na ure

related activity

-.032** 1.000 .

40081 40081

Pearson CorrelationSig. (2-tailed)

N

Amount spent onnature related activity

** orre a on s s gn can a e . eve - a e ..

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Bivariate Anal sis:Bivariate Anal sis: Interval VariablesInterval Variables

Dependent: interval, Independent: intervalDependent: interval, Independent: interval

Correlations

Pearsons Correlation coefficientPearsons Correlation coefficient

1 -.032** .022Pearson CorrelationWeekly earnings

Weekly

earnings

Amount spent

on nature

related activity

Total spent on

membership

fees, donation

. .000 .215

60789 40081 3317

-.032** 1 .109**

.000 . .000

Sig. (2-tailed)

N

Pearson Correlation

Sig. (2-tailed)

Amount spent on

nature related activity

40081 40081 3317

.022 .109** 1

.215 .000 .

N

Pearson Correlation

Sig. (2-tailed)

N

Total spent on

membership fees,

donation

3317 3317 3317

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