Chapter 1. Single-Sample t Test: What’s a Signature Worth?

1.1 Single-Sample t Test: What’s a Signature Worth?

SINGLE-SAMPLE t TEST: WHAT’S A SIGNATURE WORTH?
What’s a Signature Worth?
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You must read each slide, and complete any questions on the slide, in sequence.

Welcome

What’s a Signature Worth?

Authors:

Kelly M. Goedert, Seton Hall University

Susan A. Nolan, Seton Hall University

Kaylise D. Algrim, Seton Hall University

Before the internet age, signatures didn’t just sign off on your decisions. They also showed off your style, provided reassurance to others, and legally proved you were really you. Now, e-signatures and other digital types of identity verification are faster and easier for many types of transactions. Does this matter in any meaningful way?

A series of studies looked at the psychological difference between e-signatures and handwritten signatures (Chou, 2015). In an objective way, digital signatures verify the same things as handwritten signatures; however, subjectively, they may not hold the same meaning. Researchers hypothesized that the potentially less meaningful nature of e-signatures may mean that e-signatures might lead to cheating and dishonesty in ways that handwritten signatures do not (Chou, 2015).

Female ice hockey player signing autograph for fan
Hero Images/DigitalVision/Getty Images

Question 1.1

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1.2

Let’s explore one of the studies that pitted e-signatures against hand-written signatures. Participants rolled a pair of 12-sided dice and self-reported their scores to the experimenters (Chou, 2015). Each participant’s score translated into raffle tickets for a $50 prize. So, rolling two ones meant two raffle tickets and rolling two twelves meant 24 raffle tickets. The experimenters didn’t see what they rolled – an ideal opportunity to cheat! How did signatures fit in? The experimenters randomly assigned research participants to one of two groups: Before rolling the dice, participants in one group verified that they understood the rules by signing their name by hand, whereas participants in the second group confirmed their identity with a version of an e-signature.

Jerome Wilson / Alamy Stock Photo

Question 1.2

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Correct! The expected average if no one is cheating is 13. Here’s a shortcut to get that solution. If you average the lowest and highest scores, 2 and 24, you’ll get 13. [(2 + 24)/2 = 13].
Actually, the expected average if no one is cheating is 13. Here’s a shortcut to get that solution: If you take the average of the lowest and highest scores, 2 and 24, you’ll get 13. [(2 + 24)/2 = 13].

1.3

Assuming no one is cheating, participants in both groups should have rolled an average of 13 for a pair of 12-sided dice. This average of 13 is the population mean in this example, assuming no cheating. The researchers conducted two single-sample t tests – one for each group comparing its mean to the expected mean (the population mean) of 13. Here are the results:

Hand-signature condition:

(M = 12.89, SD = 3.98), t(27) = –0.14, p = 0.88


E-signature condition:

(M = 14.97, SD = 5.05), t(30) = 2.17, p = 0.03

Question 1.3

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Correct! Only the sample mean for those who provided e-signatures was statistically significantly higher than the expected mean of 13.
Actually, only the sample mean for those who provided e-signatures was statistically significantly higher than the expected mean of 13.

1.4

Hand-signature condition:

(M = 12.89, SD = 3.98), t(27) = –0.14, p = 0.88


E-signature condition:

(M = 14.97, SD = 5.05), t(30) = 2.17, p = 0.03

Question 1.4

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Correct! Only the p value for those who provided an e-signature was lower than the alpha level of 0.05.
Actually, only the p value for those who provided an e-signature was lower than the alpha level of 0.05.

1.5

Hand-signature condition:

(M = 12.89, SD = 3.98), t(27) = –0.14, p = 0.88


E-signature condition:

(M = 14.97, SD = 5.05), t(30) = 2.17, p = 0.03

Question 1.5

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Correct! We compared the data from each sample in the experiment to an expected statistical mean score for the population.
Actually, we compared the data from each sample in the experiment to an expected statistical mean score for the population.

1.6

Hand-signature condition:

(M = 12.89, SD = 3.98), t(27) = –0.14, p = 0.88


E-signature condition:

(M = 14.97, SD = 5.05), t(30) = 2.17, p = 0.03

Question 1.6

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Correct! For the group in which participants signed by hand, the mean was lower than the population mean, but not statistically significant, so those results were inconclusive. We cannot accept the null hypothesis.
Actually, for the group in which participants signed by hand, the mean was lower than the population mean, but not statistically significant, so those results were inconclusive. We cannot accept the null hypothesis.

1.7

Hand-signature condition:

(M = 12.89, SD = 3.98), t(27) = –0.14, p = 0.88


E-signature condition:

(M = 14.97, SD = 5.05), t(30) = 2.17, p = 0.03

Question 1.7

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Correct! For the group in which participants provided an e-signature, the mean was statistically significantly higher than the population mean of 13, so we have evidence of cheating.
Actually, for the group in which participants provided an e-signature, the mean was statistically significantly higher than the population mean of 13, so we have evidence of cheating.

1.8

Hand-signature condition:

(M = 12.89, SD = 3.98), t(27) = –0.14, p = 0.88


E-signature condition:

(M = 14.97, SD = 5.05), t(30) = 2.17, p = 0.03

Question 1.8

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Correct! We only have evidence that those in the e-signature group cheated.
Actually, we only have evidence that those in the e-signature group cheated.

1.9

Hand-signature condition:

(M = 12.89, SD = 3.98), t(27) = –0.14, p = 0.88


E-signature condition:

(M = 14.97, SD = 5.05), t(30) = 2.17, p = 0.03

Question 1.9

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Correct! We would need to know the effect size – in this case, Cohen’s d – in order to know the size, or importance, of the effect.
Actually, we would need to know the effect size – in this case, Cohen’s d – in order to know the size, or importance, of the effect.

1.10

Hand-signature condition:

(M = 12.89, SD = 3.98), t(27) = –0.14, p = 0.88


E-signature condition:

(M = 14.97, SD = 5.05), t(30) = 2.17, p = 0.03

Question 1.10

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
Correct! We have more nuanced information about the means from an interval estimate such as a confidence interval than from the point estimate of the mean.
Actually, we have more nuanced information about the means from an interval estimate such as a confidence interval than from the point estimate of the mean.

1.11

agreed with the hypotheses
disagreed with the hypothesis

The bottom line: We have evidence that e-signatures, but not handwritten signatures, don’t seem to bind people to their word. Earlier you said that you [decision] that e-signatures lead to cheating and handwritten signatures don’t. Now you know: If you’re in a position to get signatures, opt for the old-school kind.

REFERENCES

Chou, E. Y. (2015). What’s in a name? The toll e-signatures take on individual honesty. Journal of Experimental Social Psychology, 61 84–95. https://doi.org/10.1016/j.jesp.2015.07.010