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103-450: In a classic experiment investigating the effectiveness of the DITF technique, researchers separated participants into three groups. In group 1, experimenters asked participants to volunteer to counsel juvenile delinquents for two hours a week for two years (large request). After their refusal, the group was asked to chaperone juvenile delinquents on a one-day trip to the zoo (small request). Group 2

206-410: A + bX and Y to c + dY , where a , b , c , and d are constants ( b and d being positive). This is true of some correlation statistics as well as their population analogues. Some correlation statistics, such as the rank correlation coefficient, are also invariant to monotone transformations of the marginal distributions of X and/or Y . Most correlation measures are sensitive to

309-449: A screenshot of 50 different locations. After refusal, the experimenter gave the smaller request, which was to take one screenshot. In the FITD condition, the experimenter started with the smaller request and then gave the moderate one. The control condition involved only the smaller request. For half of the participants, the experimenter's avatar was dark-skinned and for the other half the avatar

412-409: A causal relationship between the variables. This dictum should not be taken to mean that correlations cannot indicate the potential existence of causal relations. However, the causes underlying the correlation, if any, may be indirect and unknown, and high correlations also overlap with identity relations ( tautologies ), where no causal process exists. Consequently, a correlation between two variables

515-442: A correlation coefficient is not enough to define the dependence structure between random variables. The correlation coefficient completely defines the dependence structure only in very particular cases, for example when the distribution is a multivariate normal distribution . (See diagram above.) In the case of elliptical distributions it characterizes the (hyper-)ellipses of equal density; however, it does not completely characterize

618-414: A correlation matrix by a diagram where the "remarkable" correlations are represented by a solid line (positive correlation), or a dotted line (negative correlation). In some applications (e.g., building data models from only partially observed data) one wants to find the "nearest" correlation matrix to an "approximate" correlation matrix (e.g., a matrix which typically lacks semi-definite positiveness due to

721-460: A large, moderate, or small request initially. The large request involved 10 hours of volunteering for several weeks, the moderate request involved a $ 30.00 donation, and the small request involved a donation of any amount. The confederate gave the smaller request after an initial large or moderate one. Participants then filled out a questionnaire that asked about the respondent's perceived obligation to comply, perceptions of negotiation and/or helping in

824-531: A major role, including the interface of cognition with overt behavior, affect, and motivation. Interpersonal Relations and Group Processes focuses on psychological and structural features of interaction in dyads and groups. Personality Processes and Individual Differences publishes research on all aspects of personality psychology. It includes studies of individual differences and basic processes in behavior, emotions, coping, health, motivation, and other phenomena that reflect personality. The journal has implemented

927-415: A mathematical property of probabilistic independence . In informal parlance, correlation is synonymous with dependence . However, when used in a technical sense, correlation refers to any of several specific types of mathematical relationship between the conditional expectation of one variable given the other is not constant as the conditioning variable changes ; broadly correlation in this specific sense

1030-406: A metacommunicative statement, and one with only a smaller request and excluding a metacommunicative statement. For all of the groups a confederate asked participants to fill out a questionnaire about campus activities. The large request required a few hours, while the smaller one required 20 minutes. In the groups that started with a large request, the confederate followed up with the smaller one after

1133-446: A mild day based on the correlation between electricity demand and weather. In this example, there is a causal relationship , because extreme weather causes people to use more electricity for heating or cooling. However, in general, the presence of a correlation is not sufficient to infer the presence of a causal relationship (i.e., correlation does not imply causation ). Formally, random variables are dependent if they do not satisfy

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1236-424: A mountain dialect, a DITF condition with both an emphasis on concession and credibility, and a control condition in which the experimenter only made the smaller second request. Results show increased compliance for the second request in all of the DITF conditions compared to the control. The DITF condition with an emphasis on concession and credibility had the largest increase in compliance. The researchers suggest that

1339-717: A negative or positive correlation if there is any sort of relationship between the variables of our data set. The population correlation coefficient ρ X , Y {\displaystyle \rho _{X,Y}} between two random variables X {\displaystyle X} and Y {\displaystyle Y} with expected values μ X {\displaystyle \mu _{X}} and μ Y {\displaystyle \mu _{Y}} and standard deviations σ X {\displaystyle \sigma _{X}} and σ Y {\displaystyle \sigma _{Y}}

1442-409: A page with a picture and several links to outside charitable organizations. In the DITF condition, the homepage asked participants to help the children in the photographs. The link redirected participants to a page that asked them to spend several hours a week finding people to donate to the site. There were links to respond to the question on the page. After a refusal, the participants were redirected to

1545-416: A person does not belong to and might perceive negatively. This study employed two different types of confederates, in-group confederates who dressed and acted like college students and out-group confederates who dressed and acted more formally. The in-group confederates introduced themselves as university students, while the out-group confederates introduced themselves as private business school students. All of

1648-557: A possible causal relationship, but cannot indicate what the causal relationship, if any, might be. The Pearson correlation coefficient indicates the strength of a linear relationship between two variables, but its value generally does not completely characterize their relationship. In particular, if the conditional mean of Y {\displaystyle Y} given X {\displaystyle X} , denoted E ⁡ ( Y ∣ X ) {\displaystyle \operatorname {E} (Y\mid X)} ,

1751-410: A refusal. The requests with metacommunication included a sentence stating, "This is kind of awkward. There is something else I'd like to ask of you, but tell me if even this seems inappropriate between strangers" prior to filling out the 20-minute questionnaire (p. 92). Results show significantly greater compliance to requests that included the metacommunicative statement. The researchers suggest that

1854-421: A response that requires metacommunication. For example, a person may use metacommunication to indicate that it is inappropriate that a stranger make such an extreme request. This study included four different groups: one starting with a large request and including a metacommunicative statement, one starting with a large request and excluding a metacommunicative statement, one with only a smaller request and including

1957-618: A series of n {\displaystyle n} measurements of the pair ( X i , Y i ) {\displaystyle (X_{i},Y_{i})} indexed by i = 1 , … , n {\displaystyle i=1,\ldots ,n} , the sample correlation coefficient can be used to estimate the population Pearson correlation ρ X , Y {\displaystyle \rho _{X,Y}} between X {\displaystyle X} and Y {\displaystyle Y} . The sample correlation coefficient

2060-411: A straight line. Although in the extreme cases of perfect rank correlation the two coefficients are both equal (being both +1 or both −1), this is not generally the case, and so values of the two coefficients cannot meaningfully be compared. For example, for the three pairs (1, 1) (2, 3) (3, 2) Spearman's coefficient is 1/2, while Kendall's coefficient is 1/3. The information given by

2163-418: A study investigating the effectiveness of the FITD and DITF techniques in a virtual world, researchers found that both techniques worked to increase compliance. The study occurred in a virtual world called " There.com ", where users create avatars to interact with other users' avatars. In the DITF condition, the experimenter approached another user's avatar and asked for a moderate request, which involved taking

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2266-599: A theory or test multiple competing hypotheses. Some researchers see the multiple-experiments requirement as an excessive burden that delays the publication of valuable work, but this requirement also helps maintain the impression that research that is published in JPSP has been thoroughly vetted and is less likely to be the result of a type I error or an unexplored confound . The journal is divided into three independently edited sections. Attitudes and Social Cognition addresses those domains of social behavior in which cognition plays

2369-506: A value of zero implies independence. This led some authors to recommend their routine usage, particularly of Distance correlation . Another alternative measure is the Randomized Dependence Coefficient. The RDC is a computationally efficient, copula -based measure of dependence between multivariate random variables and is invariant with respect to non-linear scalings of random variables. One important disadvantage of

2472-875: Is 0. However, because the correlation coefficient detects only linear dependencies between two variables, the converse is not necessarily true. A correlation coefficient of 0 does not imply that the variables are independent . X , Y  independent ⇒ ρ X , Y = 0 ( X , Y  uncorrelated ) ρ X , Y = 0 ( X , Y  uncorrelated ) ⇏ X , Y  independent {\displaystyle {\begin{aligned}X,Y{\text{ independent}}\quad &\Rightarrow \quad \rho _{X,Y}=0\quad (X,Y{\text{ uncorrelated}})\\\rho _{X,Y}=0\quad (X,Y{\text{ uncorrelated}})\quad &\nRightarrow \quad X,Y{\text{ independent}}\end{aligned}}} For example, suppose

2575-449: Is 0.7544, indicating that the points are far from lying on a straight line. In the same way if y {\displaystyle y} always decreases when x {\displaystyle x} increases , the rank correlation coefficients will be −1, while the Pearson product-moment correlation coefficient may or may not be close to −1, depending on how close the points are to

2678-492: Is a corollary of the Cauchy–Schwarz inequality that the absolute value of the Pearson correlation coefficient is not bigger than 1. Therefore, the value of a correlation coefficient ranges between −1 and +1. The correlation coefficient is +1 in the case of a perfect direct (increasing) linear relationship (correlation), −1 in the case of a perfect inverse (decreasing) linear relationship ( anti-correlation ), and some value in

2781-672: Is a monthly peer-reviewed scientific journal published by the American Psychological Association that was established in 1965. It covers the fields of social and personality psychology . The editors-in-chief are Shinobu Kitayama ( University of Michigan ; Attitudes and Social Cognition Section ), Colin Wayne Leach ( Barnard College ; Interpersonal Relations and Group Processes Section ), and Richard E. Lucas ( Michigan State University ; Personality Processes and Individual Differences Section ). The journal's focus

2884-410: Is consideration of the copula between them, while the coefficient of determination generalizes the correlation coefficient to multiple regression . The degree of dependence between variables X and Y does not depend on the scale on which the variables are expressed. That is, if we are analyzing the relationship between X and Y , most correlation measures are unaffected by transforming X to

2987-448: Is defined as where x ¯ {\displaystyle {\overline {x}}} and y ¯ {\displaystyle {\overline {y}}} are the sample means of X {\displaystyle X} and Y {\displaystyle Y} , and s x {\displaystyle s_{x}} and s y {\displaystyle s_{y}} are

3090-845: Is defined as: ρ X , Y = corr ⁡ ( X , Y ) = cov ⁡ ( X , Y ) σ X σ Y = E ⁡ [ ( X − μ X ) ( Y − μ Y ) ] σ X σ Y , if   σ X σ Y > 0. {\displaystyle \rho _{X,Y}=\operatorname {corr} (X,Y)={\operatorname {cov} (X,Y) \over \sigma _{X}\sigma _{Y}}={\operatorname {E} [(X-\mu _{X})(Y-\mu _{Y})] \over \sigma _{X}\sigma _{Y}},\quad {\text{if}}\ \sigma _{X}\sigma _{Y}>0.} where E {\displaystyle \operatorname {E} }

3193-495: Is designed to use the sensitivity to the range in order to pick out correlations between fast components of time series . By reducing the range of values in a controlled manner, the correlations on long time scale are filtered out and only the correlations on short time scales are revealed. The correlation matrix of n {\displaystyle n} random variables X 1 , … , X n {\displaystyle X_{1},\ldots ,X_{n}}

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3296-401: Is effective because of reciprocal concessions or social responsibility . The reciprocal concessions explanation is more common and involves reciprocity , or the need for a respondent to comply to the smaller second request because the persuader is compromising from the initial request. The social responsibility explanation involves internal standards of the importance of helping others that make

3399-426: Is not a sufficient condition to establish a causal relationship (in either direction). A correlation between age and height in children is fairly causally transparent, but a correlation between mood and health in people is less so. Does improved mood lead to improved health, or does good health lead to good mood, or both? Or does some other factor underlie both? In other words, a correlation can be taken as evidence for

3502-460: Is not linear in X {\displaystyle X} , the correlation coefficient will not fully determine the form of E ⁡ ( Y ∣ X ) {\displaystyle \operatorname {E} (Y\mid X)} . The adjacent image shows scatter plots of Anscombe's quartet , a set of four different pairs of variables created by Francis Anscombe . The four y {\displaystyle y} variables have

3605-412: Is on empirical research reports; however, specialized theoretical, methodological, and review papers are also published. For example, the journal's most highly cited paper, cited over 90,000 times, is a statistical methods paper discussing mediation and moderation. Articles typically involve a lengthy introduction and literature review, followed by several related studies that explore different aspects of

3708-406: Is the n × n {\displaystyle n\times n} matrix C {\displaystyle C} whose ( i , j ) {\displaystyle (i,j)} entry is Thus the diagonal entries are all identically one . If the measures of correlation used are product-moment coefficients, the correlation matrix is the same as the covariance matrix of

3811-516: Is the Pearson product-moment correlation coefficient (PPMCC), or "Pearson's correlation coefficient", commonly called simply "the correlation coefficient". It is obtained by taking the ratio of the covariance of the two variables in question of our numerical dataset, normalized to the square root of their variances. Mathematically, one simply divides the covariance of the two variables by the product of their standard deviations . Karl Pearson developed

3914-1087: Is the expected value operator, cov {\displaystyle \operatorname {cov} } means covariance , and corr {\displaystyle \operatorname {corr} } is a widely used alternative notation for the correlation coefficient. The Pearson correlation is defined only if both standard deviations are finite and positive. An alternative formula purely in terms of moments is: ρ X , Y = E ⁡ ( X Y ) − E ⁡ ( X ) E ⁡ ( Y ) E ⁡ ( X 2 ) − E ⁡ ( X ) 2 ⋅ E ⁡ ( Y 2 ) − E ⁡ ( Y ) 2 {\displaystyle \rho _{X,Y}={\operatorname {E} (XY)-\operatorname {E} (X)\operatorname {E} (Y) \over {\sqrt {\operatorname {E} (X^{2})-\operatorname {E} (X)^{2}}}\cdot {\sqrt {\operatorname {E} (Y^{2})-\operatorname {E} (Y)^{2}}}}} It

4017-450: Is the sole explanation for the effectiveness of the DITF technique. In a study looking at the DITF technique, researchers found that DITF requests that required metacommunication in the responses had higher rates of compliance than requests that did not. The researchers define metacommunication as establishing social boundaries. This is important because the DITF technique often involves strangers making extreme requests, which might elicit

4120-567: Is used when E ( Y | X = x ) {\displaystyle E(Y|X=x)} is related to x {\displaystyle x} in some manner (such as linearly, monotonically, or perhaps according to some particular functional form such as logarithmic). Essentially, correlation is the measure of how two or more variables are related to one another. There are several correlation coefficients , often denoted ρ {\displaystyle \rho } or r {\displaystyle r} , measuring

4223-405: Is zero; they are uncorrelated . However, in the special case when X {\displaystyle X} and Y {\displaystyle Y} are jointly normal , uncorrelatedness is equivalent to independence. Even though uncorrelated data does not necessarily imply independence, one can check if random variables are independent if their mutual information is 0. Given

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4326-402: The uncorrected sample standard deviations of X {\displaystyle X} and Y {\displaystyle Y} . If x {\displaystyle x} and y {\displaystyle y} are results of measurements that contain measurement error, the realistic limits on the correlation coefficient are not −1 to +1 but a smaller range. For

4429-829: The Newton's method for computing the nearest correlation matrix ) results obtained in the subsequent years. Similarly for two stochastic processes { X t } t ∈ T {\displaystyle \left\{X_{t}\right\}_{t\in {\mathcal {T}}}} and { Y t } t ∈ T {\displaystyle \left\{Y_{t}\right\}_{t\in {\mathcal {T}}}} : If they are independent, then they are uncorrelated. The opposite of this statement might not be true. Even if two variables are uncorrelated, they might not be independent to each other. The conventional dictum that " correlation does not imply causation " means that correlation cannot be used by itself to infer

4532-439: The Pearson product-moment correlation coefficient , and are best seen as measures of a different type of association, rather than as an alternative measure of the population correlation coefficient. To illustrate the nature of rank correlation, and its difference from linear correlation, consider the following four pairs of numbers ( x , y ) {\displaystyle (x,y)} : As we go from each pair to

4635-448: The coefficient of multiple determination , a measure of goodness of fit in multiple regression . In statistical modelling , correlation matrices representing the relationships between variables are categorized into different correlation structures, which are distinguished by factors such as the number of parameters required to estimate them. For example, in an exchangeable correlation matrix, all pairs of variables are modeled as having

4738-412: The corrected sample standard deviations of X {\displaystyle X} and Y {\displaystyle Y} . Equivalent expressions for r x y {\displaystyle r_{xy}} are where s x ′ {\displaystyle s'_{x}} and s y ′ {\displaystyle s'_{y}} are

4841-444: The open interval ( − 1 , 1 ) {\displaystyle (-1,1)} in all other cases, indicating the degree of linear dependence between the variables. As it approaches zero there is less of a relationship (closer to uncorrelated). The closer the coefficient is to either −1 or 1, the stronger the correlation between the variables. If the variables are independent , Pearson's correlation coefficient

4944-401: The standardized random variables X i / σ ( X i ) {\displaystyle X_{i}/\sigma (X_{i})} for i = 1 , … , n {\displaystyle i=1,\dots ,n} . This applies both to the matrix of population correlations (in which case σ {\displaystyle \sigma } is

5047-504: The Austrian Alps. The experimenter rotated between five conditions: a DITF condition in which the experimenter first tried to sell two pounds of cheese at eight euros and then one pound of cheese at four euros, a DITF condition with an emphasis on concession in which the experimenter said that two pounds was probably too much anyway, a DITF condition with an emphasis on credibility of the experimenter, who wore traditional clothes and spoke in

5150-401: The DITF and FITD techniques indicated that there were no significant differences in effectiveness of the two techniques. Overall, they both produced similar rates of compliance across many studies that employed comparable target requests. In a set of studies about compliance methods, the researcher found evidence for the effectiveness of the " foot-in-the-face " (FITF) technique, which combines

5253-455: The DITF and FITD techniques. The FITF technique involves two moderately difficult requests that are equally demanding. Study 1 : Confederates asked one group of participants to read temperature and another to read air pressure. Regardless of whether the participants complied with the first request, they were given a second one. One group read temperature first and the other air pressure. Results show that participants were more likely to agree to

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5356-422: The DITF technique could be useful in other retail settings. Researchers investigated the DITF technique in a restaurant setting and found that it is effective if there is no delay between the first and second requests. Waitresses were instructed to ask randomly selected restaurant patrons whether they wanted dessert at the end of their meals. If the participant refused, the waitress then either immediately asked if

5459-412: The DITF technique was most effective. The study had three groups of 2nd grade participants: the FITD, DITF, and control groups. The FITD group was asked by one teacher to do an easy 15-question worksheet and then asked 15 minutes later by another teacher to complete a 20-question worksheet. The DITF group was initially asked to complete a 100-question worksheet. After refusal, the group was asked to do 20 of

5562-505: The Future" controversy ). The journal refused to publish refuting replications performed by Ritchie 's team, in relation to an earlier article they published in 2010 that suggested that psychic abilities may have been involved (backward causality). Non-fiction author Malcolm Gladwell writes frequently about findings that are reported in the journal. Gladwell, upon being asked where he would like to be buried, replied "I'd like to be buried in

5665-761: The Transparency and Openness Promotion (TOP) Guidelines. The TOP Guidelines provide structure to research planning and reporting and aim to make research more transparent, accessible, and reproducible. The journal is abstracted and indexed in: According to the Journal Citation Reports , the journal has a 2023 impact factor of 6.4. JPSP is one of the journals analyzed in the Open Science Collaboration's Reproducibility Project after JPSP's publication of questionable research for mental time travel (Bem, 2011) (see: replication crisis ; "Feeling

5768-450: The alternative, more general measures is that, when used to test whether two variables are associated, they tend to have lower power compared to Pearson's correlation when the data follow a multivariate normal distribution. This is an implication of the No free lunch theorem theorem. To detect all kinds of relationships, these measures have to sacrifice power on other relationships, particularly for

5871-412: The assumption of normality. The second one (top right) is not distributed normally; while an obvious relationship between the two variables can be observed, it is not linear. In this case the Pearson correlation coefficient does not indicate that there is an exact functional relationship: only the extent to which that relationship can be approximated by a linear relationship. In the third case (bottom left),

5974-402: The case of a linear model with a single independent variable, the coefficient of determination (R squared) is the square of r x y {\displaystyle r_{xy}} , Pearson's product-moment coefficient. Consider the joint probability distribution of X and Y given in the table below. For this joint distribution, the marginal distributions are: This yields

6077-467: The coefficient from a similar but slightly different idea by Francis Galton . A Pearson product-moment correlation coefficient attempts to establish a line of best fit through a dataset of two variables by essentially laying out the expected values and the resulting Pearson's correlation coefficient indicates how far away the actual dataset is from the expected values. Depending on the sign of our Pearson's correlation coefficient, we can end up with either

6180-495: The correlation-like range ⁠ [ − 1 , 1 ] {\displaystyle [-1,1]} ⁠ . The odds ratio is generalized by the logistic model to model cases where the dependent variables are discrete and there may be one or more independent variables. The correlation ratio , entropy -based mutual information , total correlation , dual total correlation and polychoric correlation are all also capable of detecting more general dependencies, as

6283-507: The current-periodicals room, maybe next to the unbound volumes of the Journal of Personality and Social Psychology (my favorite journal)." Correlation and dependence In statistics , correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data . Although in the broadest sense, "correlation" may indicate any type of association, in statistics it usually refers to

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6386-647: The degree of correlation. The most common of these is the Pearson correlation coefficient , which is sensitive only to a linear relationship between two variables (which may be present even when one variable is a nonlinear function of the other). Other correlation coefficients – such as Spearman's rank correlation – have been developed to be more robust than Pearson's, that is, more sensitive to nonlinear relationships. Mutual information can also be applied to measure dependence between two variables. The most familiar measure of dependence between two quantities

6489-515: The degree to which a pair of variables are linearly related. Familiar examples of dependent phenomena include the correlation between the height of parents and their offspring, and the correlation between the price of a good and the quantity the consumers are willing to purchase, as it is depicted in the so-called demand curve . Correlations are useful because they can indicate a predictive relationship that can be exploited in practice. For example, an electrical utility may produce less power on

6592-424: The dependence structure (for example, a multivariate t-distribution 's degrees of freedom determine the level of tail dependence). For continuous variables, multiple alternative measures of dependence were introduced to address the deficiency of Pearson's correlation that it can be zero for dependent random variables (see and reference references therein for an overview). They all share the important property that

6695-656: The experiment. As the participant was leaving, the experimenter asked the participant to record meals for the next three months as a part of a larger study on health. After refusal, the experimenter then made a second smaller request for the participant to record their meals for four days. There was a control condition that only received the second smaller request. Participants were assigned to one of four groups: high guilt induction and high guilt reduction, high guilt induction and low guilt reduction, low guilt induction and high guilt reduction, and low guilt induction and low guilt reduction. The high guilt induction statement indicated that

6798-430: The explanations work together in the DITF effect. In a similar study looking at differences between friends and strangers using the DITF technique, the DITF technique was more effective in increasing compliance for friends than strangers, which is contrary to other research findings. The researcher explains the results as evidence for the importance of self-presentation when friends use the DITF technique. They suggest that

6901-770: The explicit statement regarding social boundaries makes participants comply to avoid engaging in metacommunicative conflict. Research investigating reverse psychology showed that participants used the DITF technique in their everyday lives. They also use other reverse psychology tactics, such as FITD. There were two studies that looked at participants' own experiences using reverse psychology, which these researchers refer to as strategic self-anti conformity . The first study consisted of an open-ended questionnaire that asked participants about instances in which they used strategic self-anticonformity. The second study asked about specific instances of different types of strategic self-anti-conformity, like DITF and FITD. Findings indicate that most of

7004-404: The female confederate only made the second smaller request. The DITF technique yielded significantly more behavioral compliance than the control, which shows that the DITF technique works for more than just verbal agreement. A study looking at the DITF technique in retail found that it was very effective in increasing sales. In this study the experimenter sold cheese to people walking past a hut in

7107-422: The first, while another group was given the second request two to three days after the first. The requests were to complete a questionnaire or to tape record a section out of a book. Findings indicate that the delay between requests was more effective for participants who complied to the first request, while the immediate request was more effective for those who rejected the first request. Study 3 : This study used

7210-430: The first. Researchers measured both verbal and behavioral compliance to the smaller second request. Findings indicate a significant increase in both types of compliance for the high guilt induction, high guilt reduction condition. There was no DITF effect for the other conditions because compliance to the second request was the same as compliance for the control condition. According to the researcher, this suggests that guilt

7313-416: The following expectations and variances: Therefore: Rank correlation coefficients, such as Spearman's rank correlation coefficient and Kendall's rank correlation coefficient (τ) measure the extent to which, as one variable increases, the other variable tends to increase, without requiring that increase to be represented by a linear relationship. If, as the one variable increases, the other decreases ,

7416-626: The important special case of a linear relationship with Gaussian marginals, for which Pearson's correlation is optimal. Another problem concerns interpretation. While Person's correlation can be interpreted for all values, the alternative measures can generally only be interpreted meaningfully at the extremes. For two binary variables , the odds ratio measures their dependence, and takes range non-negative numbers, possibly infinity: ⁠ [ 0 , + ∞ ] {\displaystyle [0,+\infty ]} ⁠ . Related statistics such as Yule's Y and Yule's Q normalize this to

7519-414: The initial request. These three studies provide evidence to support the effectiveness of the FITD technique because it increased compliance in all three experiments. The researcher suggests that the FITD technique may be preferable to DITF because it does not place as much pressure on people to comply. Journal of Personality and Social Psychology The Journal of Personality and Social Psychology

7622-450: The latter case. Several techniques have been developed that attempt to correct for range restriction in one or both variables, and are commonly used in meta-analysis; the most common are Thorndike's case II and case III equations. Various correlation measures in use may be undefined for certain joint distributions of X and Y . For example, the Pearson correlation coefficient is defined in terms of moments , and hence will be undefined if

7725-406: The male announced loudly that he was leaving to buy a part for his bicycle. After he left the female confederate expressed aloud that the male did not pay and asked the participant sitting near her to pay the total bill. In the DITF condition, the female confederate asked if the participant would pay part of the bill after a refusal to pay the total bill from every participant. In the control condition

7828-404: The manner in which X and Y are sampled. Dependencies tend to be stronger if viewed over a wider range of values. Thus, if we consider the correlation coefficient between the heights of fathers and their sons over all adult males, and compare it to the same correlation coefficient calculated when the fathers are selected to be between 165 cm and 170 cm in height, the correlation will be weaker in

7931-466: The moments are undefined. Measures of dependence based on quantiles are always defined. Sample-based statistics intended to estimate population measures of dependence may or may not have desirable statistical properties such as being unbiased , or asymptotically consistent , based on the spatial structure of the population from which the data were sampled. Sensitivity to the data distribution can be used to an advantage. For example, scaled correlation

8034-516: The next pair x {\displaystyle x} increases, and so does y {\displaystyle y} . This relationship is perfect, in the sense that an increase in x {\displaystyle x} is always accompanied by an increase in y {\displaystyle y} . This means that we have a perfect rank correlation, and both Spearman's and Kendall's correlation coefficients are 1, whereas in this example Pearson product-moment correlation coefficient

8137-469: The participant wanted tea or coffee or waited three minutes to ask. Findings indicate increased compliance to the second request for the immediate condition but not the delayed one. The researchers suggest that these results have significant implications for the restaurant industry, particularly the importance of servers' timing when the restaurant is busy. In a study looking at compliance techniques for children to complete academic work, researchers found that

8240-401: The participants could provide examples of their own use of reverse psychology tactics and that a likely explanation for this is a need for social reassurance. A study looking at behavioral, not just verbal, compliance to donate money found that the DITF technique was effective. The study involved male and female confederates who ordered lemonade at a restaurant and engaged in conversation before

8343-554: The participants in this study went to the same university as the in-group confederates. The confederates either made a large request then a smaller one, a smaller request alone, or offered the participant a choice of both requests. Results show greater compliance to the second smaller request for the in-group confederates compared to out-group confederates, but there was still a DITF effect in the out-group context. Participants were most likely to comply to requests from those within their social groups, yet they still had increased compliance to

8446-405: The population standard deviation), and to the matrix of sample correlations (in which case σ {\displaystyle \sigma } denotes the sample standard deviation). Consequently, each is necessarily a positive-semidefinite matrix . Moreover, the correlation matrix is strictly positive definite if no variable can have all its values exactly generated as a linear function of

8549-409: The questions. The control group was asked to complete a 20-question worksheet. The researchers looked at compliance as well as students' mathematical ability, quality of work, and amount of help needed. Results show that the DITF technique was effective in increasing compliance rates compared to the FITD and control conditions. The DITF group also needed less adult help to complete the worksheet. Overall,

8652-463: The random variable X {\displaystyle X} is symmetrically distributed about zero, and Y = X 2 {\displaystyle Y=X^{2}} . Then Y {\displaystyle Y} is completely determined by X {\displaystyle X} , so that X {\displaystyle X} and Y {\displaystyle Y} are perfectly dependent, but their correlation

8755-406: The rank correlation coefficients will be negative. It is common to regard these rank correlation coefficients as alternatives to Pearson's coefficient, used either to reduce the amount of calculation or to make the coefficient less sensitive to non-normality in distributions. However, this view has little mathematical basis, as rank correlation coefficients measure a different type of relationship than

8858-428: The rejection of the first request would have negative effects on the study, while the low guilt induction statement indicated that the rejection of the first request would not really have negative effects on the study. The high guilt reduction statement indicated that the second request would be equally helpful as the first, while the low guilt reduction statement indicated that the second request would not be as helpful as

8961-455: The researchers suggest that DITF can be a useful technique to get students to do their academic work. Research on the DITF effect in internet fundraising indicates that the DITF technique works in an electronic context. This study looked at donations for children victims of mine injuries. The homepage of the website provided pictures of children with injuries. In the control condition, the homepage asked for donations and redirected participants to

9064-518: The respondent feel they must comply to the second smaller request. Other explanations of the DITF effect involve maintaining a positive self-presentation and reducing guilt . Two studies comparing reciprocal concessions with social responsibility explanations found evidence for social responsibility related to helping. In the first study, participants read DITF scenarios and then rated whether certain terms were relevant to these situations or not. These terms either referred to helping or to bargaining. In

9167-399: The respondents' need to present themselves well to their friends motivates compliance to the second request. Research on the influence of guilt indicates that it plays an important role in the effectiveness of the DITF technique. Participants began the study by filling out a questionnaire related to demographics and health. The experimenter then told the participant he or she was finished with

9270-440: The same correlation, so all non-diagonal elements of the matrix are equal to each other. On the other hand, an autoregressive matrix is often used when variables represent a time series, since correlations are likely to be greater when measurements are closer in time. Other examples include independent, unstructured, M-dependent, and Toeplitz . In exploratory data analysis , the iconography of correlations consists in replacing

9373-404: The same mean (7.5), variance (4.12), correlation (0.816) and regression line ( y = 3 + 0.5 x {\textstyle y=3+0.5x} ). However, as can be seen on the plots, the distribution of the variables is very different. The first one (top left) seems to be distributed normally, and corresponds to what one would expect when considering two variables correlated and following

9476-406: The same page as the control group, which had links to outside charities. The researcher measured numbers of clicks on these links, not actual donations. Results show that participants in the DITF condition were more willing to click on the outside links than those in the control condition. The researcher highlights that these results indicate DITF technique can be effective in electronic contexts. In

9579-400: The same requests from the study 2. Confederates made the second request immediately to participants who rejected the first but waited two to three days for those who complied with the first request. Results show that overall there was significantly greater compliance to the second request and that participants who agreed to the first were more likely to agree to the second than those who rejected

9682-410: The second request following the first than the second request in isolation, regardless of whether it was to read the temperature or air pressure. There were participants who complied with both requests, but there were also participants who complied to the second, but not the first request. Study 2 : This study was very similar to the first, except one group was given the second request immediately after

9785-465: The second study, participants rated the similarity of a DITF interaction to four other situations: helping a friend, negotiating with a friend, helping a stranger, and negotiating with a stranger. The DITF scenarios used in both studies were taken from previous research and shown to be very effective in influencing compliance. Overall, findings indicate that participants felt DITF interactions were more closely related to helping than bargaining. This supports

9888-539: The situation, and whether the respondent was friends with the confederate. Results show that participants were more likely to comply for friends than strangers, the DITF technique had greater compliance overall than a small request alone, and the DITF technique had larger increases in compliance for strangers. Findings regarding social responsibility and reciprocal concessions were inconclusive, with high correlations between perceptions of negotiation and guilt as well as guilt and obligation. The researchers suggest that both of

9991-448: The small request was also significantly larger for group 1 than group 3, which demonstrates that mere exposure to the more extreme task does not affect compliance as significantly. A 2020 study published in the Journal of Personality and Social Psychology replicated the findings of Cialdini's original 1975 experiment. An important topic in DITF research involves whether the DITF technique

10094-639: The smaller second request for people outside of their social groups. The researchers suggest that this is evidence for reciprocal concessions because the influence of social group and the DITF effect work independently of each other, therefore, there must be another explanation for DITF that does not involve in-group-out-group biases. The researchers fail to mention the social responsibility explanation, however. Another study comparing reciprocal concessions with social responsibility found neither explanation to be sufficient. This study employed confederates who asked for donations door-to-door. Participants were either given

10197-446: The social responsibility explanation of the DITF technique because social responsibility is related to helping one's self, while reciprocal concessions is related to negotiating. Research investigating reciprocal concessions and in-group-out-group biases found both reciprocal concessions and in-group context to be important in the DITF technique. In-groups are groups that a person feels that they belong to, while out-groups are ones that

10300-459: The values of the others. The correlation matrix is symmetric because the correlation between X i {\displaystyle X_{i}} and X j {\displaystyle X_{j}} is the same as the correlation between X j {\displaystyle X_{j}} and X i {\displaystyle X_{i}} . A correlation matrix appears, for example, in one formula for

10403-543: The way it has been computed). In 2002, Higham formalized the notion of nearness using the Frobenius norm and provided a method for computing the nearest correlation matrix using the Dykstra's projection algorithm , of which an implementation is available as an online Web API. This sparked interest in the subject, with new theoretical (e.g., computing the nearest correlation matrix with factor structure ) and numerical (e.g. usage

10506-400: Was given only the small request. In group 3, the experimenter described the large request but asked the participants to perform the small request. 50% of the participants in group 1 agreed to the small request, compared to 17% in group 2 and 25% in group 3. Because compliance for the small request was significantly larger for group 1 than group 2, the DITF technique was successful. Compliance for

10609-450: Was light-skinned. Findings indicate that both the FITD and DITF techniques increased compliance to the second request compared to the control condition, although the DITF technique was less effective for the dark-skinned avatar. There was no skin color effect for the FITD condition. The researchers suggest that these results illustrate social carryover from real-life to the virtual world. A meta-analysis of findings from 22 studies comparing

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