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# Bivariate Investigations.

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Bivariate Procedures I Overview. Chi-square testT-testCorrelation. Chi-Square Test. Connections between ostensible variablesTypes:2x2 chi-squareGender by Political Party2x3 chi-squareGender by Dosage (Hi versus Med. Versus Low). Beginning stage: The Crosstab Table. Example:Gender (IV)MalesFemalesDemocrat120Party (DV)Republican102Total1122.
Transcripts
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﻿Bivariate Analyses

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Bivariate Procedures I Overview Chi-square test T-test Correlation

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Chi-Square Test Relationships between ostensible variables Types: 2x2 chi-square Gender by Political Party 2x3 chi-square Gender by Dosage (Hi versus Med. Versus Low)

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Starting Point: The Crosstab Table Example: Gender (IV) Males Females Democrat 1 20 Party (DV) Republican 10 2 Total 11 22

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Column Percentages Gender (IV) Males Females Democrat 9% 91% Party (DV) Republican 91% 9% Total 100% 100%

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Row Percentages Gender (IV) Males Females Total Democrat 5% 95% 100% Party (DV) Republican 83% 17% 100%

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Full Crosstab Table Males Females Total Democrat 1 20 21 5% 95% 9% 91% 64% Republican 10 2 12 83% 17% 91% 9% 36% Total 11 22 33 33% 67% 100%

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Research Question and Hypothesis Research Question: Is sexual orientation identified with gathering alliance? Speculation: Men are more probable than ladies to be Republicans Null theory: There is no connection amongst sex and gathering

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Testing the Hypothesis Eyeballing the table: Seems to be a relationship Is it noteworthy? On the other hand, would it be able to be only a chance finding? Rationale: Is the finding sufficiently distinctive from the invalid? Chi-square answers this inquiry What components would it consider?

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Factors Taken into Consideration Factors: 1. Size of the distinction 2. Test size Biased coin illustration Magnitude of distinction: 60% heads versus 99% heads Sample size: 10 flips versus 100 flips versus 1 million flips

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Chi-square Chi-Square begins with the frequencies: Compare watched frequencies with frequencies we expect under the invalid theory

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What might the Frequencies be if there was No Relationship? Males Females Total Democrat 21 Republican 12 Total 11 22 33

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Expected Frequencies (Null) Males Females Total Democrat 7 14 21 Republican 4 8 12 Total 11 22 33

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Comparing the Observed and Expected Cell Frequencies Formula:

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Calculating the Expected Frequency Simple equation for expected cell frequencies Row all out x segment absolute/Total N 21 x 11/33 = 7 21 x 22/33 = 14 12 x 11/33 = 4 12 x 22/33 = 8

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Observed and Expected Cell Frequencies Males Females Total Democrat 1 7 20 14 21 Republican 10 4 2 8 12 Total 11 22 33

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Plugging into the Formula O - E Square Square/E Cell A = 1-7 = - 6 36 36/7 = 5.1 Cell B = 20-14 = 6 36 36/14 = 2.6 Cell C = 10-4 = 6 36 36/4 = 9 Cell D = 2-8 = - 6 36 36/8 = 4.5 Sum = 21.2 Chi-square = 21.2

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Is the chi-square critical? Importance of the chi-square: Great contrasts amongst watched and anticipated that lead would greater chi-square How huge does it need to be for centrality? Relies on upon the "degrees of flexibility" Formula for degrees of opportunity: (Rows – 1) x (Columns – 1)

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Chi-square Degrees of Freedom 2 x 2 chi-square = 1 3 x 3 = ? 4 x 3 = ?

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df P = 0.05 P = 0.01 P = 0.001 1 3.84 6.64 10.83 2 5.99 9.21 13.82 3 7.82 11.35 16.27 4 9.49 13.28 18.47 5 11.07 15.09 20.52 6 12.59 16.81 22.46 7 14.07 18.48 24.32 8 15.51 20.09 26.13 9 16.92 21.67 27.88 10 18.31 23.21 29.59 Chi-square Critical Values * If chi-square is > than basic worth, relationship is noteworthy

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Chi-Square Computer Printout

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Chi-Square Computer Printout

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Multiple Chi-square Exact same methodology as 2 variable X 2 Used for more than 2 variables E.g., 2 x 2 x 2 X 2 Gender x Hair shading x eye shading

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Multiple chi-square case

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Multiple chi-square illustration

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The T-test Groups T-test Comparing the method for two ostensible gatherings E.g., Gender and IQ E.g., Experimental versus Control bunch Pairs T-test Comparing the method for two variables Comparing the mean of a variable at two focuses in time

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Logic of the T-test A T-test considers three things: 1. The gathering implies 2. The scattering of individual scores around the mean for every gathering (sd) 3. The span of the gatherings

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Difference in the Means The more remote separated the methods are: The more certain we are that the two gathering means are diverse Distance between the methods goes in the numerator of the t-test recipe

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Why Dispersion Matters Small fluctuations Large changes

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Size of the Groups Larger gatherings imply that we are more positive about the gathering implies IQ case: Women: mean = 103 Men: mean = 97 If our example was 5 men and 5 ladies, we are not that sure If our specimen was 5 million men and 5 million ladies, we are significantly more sure

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The four t-test formulae 1. Coordinated examples with unequal fluctuations 2. Coordinated examples with equivalent fluctuations 3. Free specimens with unequal changes 4. Autonomous specimens with equivalent fluctuations

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All four formulae have the same Numerator X1 - X2 (bunch one mean - bunch two mean) What separates the four formulae is their denominator is "standard blunder of the distinction of the signifies" every equation has an alternate standard mistake

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Independent example with unequal differences recipe Standard mistake equation (denominator):

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T-test Value Look up the T-esteem in a T-table (use supreme quality ) First decide the degrees of opportunity ex. df = (N1 - 1) + (N2 - 1) 40 + 30 = 70 For 70 df at the .05 level =1.67 ex. 5.91 > 1.67: Reject the invalid (means are distinctive)

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Groups t-test printout illustration

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Pairs t-test case

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Pearson Correlation Coefficient (r ) Characteristics of correlational connections: 1. Quality 2. Noteworthiness 3. Directionality 4. Curvilinearity

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Strength of Correlation: Strong, feeble and non-connections Nature of such relations can be seen in disperse charts Scatter outline One variable on x pivot and the other on the y-hub of a diagram Plot every case as per its x and y values

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Scatterplot: Strong relationship B O K R E A D I N G Years of Education

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Scatterplot: Weak relationship I N C O M E Years of Education

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Scatterplot: No relationship S P O R T S I N T E R E S T Years of Education

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Strength increments… As the focuses all the more nearly comply with a straight line Drawing the best fitting line between the focuses: "the relapse line" Minimizes the separation of the focuses from the line: "slightest squares" Minimizing the deviations from the line

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Significance of the relationship Whether we are sure that a watched relationship is "genuine" or because of chance What is the probability of getting results this way if the invalid theory were valid? Contrast watched comes about with expected under the invalid If under 5% chance, dismiss the invalid theory

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Directionality of the relationship Correlational relationship can be sure or negative Positive relationship High scores on variable X are connected with high scores on variable Y Negative relationship High scores on variable X are connected with low scores on variable Y

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Positive relationship case B O K R E A D I N G Years of Education

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Negative relationship case R A C I A L P R E J U D I C E Years of Education

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Curvilinear connections Positive and negative connections are "straight-line" or "straight" connections Relationships can likewise be solid and curvilinear too Points comply with a bended line

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Curvilinear relationship illustration F A M I L Y S I Z E SES

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Curvilinear connections Linear measurements (e.g. connection coefficient, relapse) can veil a critical curvilinear relationship Correlation coefficient would demonstrate no relationship

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Pearson Correlation Coefficient Correlation coefficient Numerical articulation of: Strength and Direction of straight-line relationship Varies amongst –1 and 1

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Correlation coefficient results - 1 is an impeccable adverse relationship - .7 is a solid pessimistic relationship - .4 is a moderate antagonistic relationship - .1 is a feeble contrary relationship 0 is no relationship .1 is a frail constructive relationship .4 is a moderate constructive relationship .7 is a solid constructive relationship 1 is an immaculate constructive relationship

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Pearson\'s r (connection coefficient) Used for interim or proportion variables Reflects the degree to which cases have comparative z-scores on variables X and Y Positive relationship—z-scores have the same sign Negative relationship—z-scores have the inverse sign

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Positive relationship z-scores Person Xz Yz A 1.06 1.11 B .56 .65 C .03 -.01 D -.42 -.55 E -1.23 -1.09

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Negative relationship z-scores Person Xz Yz A 1.06 -1.22 B .56 -.51 C .03 -.06 D -.42 .66 E -1.23 1.33

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Conceptual equation for Pearson\'s r Multiply every cases z-score Sum the items Divide by N

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Significance of Pearson\'s r Pearson\'s r lets us know the quality and course Significance is dictated by changing over the r perfectly proportion and finding it in a t table Null: r = .00 How distinctive is the thing that we see from invalid? Under .05?

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Computer Printout

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