Swearing is a common, almost reflexive, response to pain. Whether you knock your shin into the edge of a coffee table or smash your thumb with a hammer, most of us respond with a streak of obscenities. One question, however, is whether swearing has any effect on the amount of pain that you feel. To address this issue, Stephens, Atkins, and Kingston (2009) conducted an experiment comparing swearing with other responses to pain. In the study, participants were asked to place one hand in icy cold water for as long as they could bear the pain. Half of the participants were told to repeat their favorite swear word over and over for as long as their hands were in the water. The other half repeated a neutral word. The researchers recorded how long each participant was able to tolerate the ice water. After a brief rest, the two groups switched words and repeated the ice water plunge. Thus, all the participants experienced both conditions (swearing and neutral) with half swearing on their first plunge and half on their second. The data in the following table are representative of the results obtained in the study and represent the reports of pain level of n = 9 participants. Complete the following table and find M and SS for each group of scores and for the differences. Participant Neutral Word X₁ Swearing X₂ Difference D = X₂ – X₁ A 9 7 B 9 8 C 9 5 D 4 5 E 10 8 F 9 4 G 6 5 H 10 10 I 6 2 ∑ M = M = M = SS = SS = SS = Assume that the data are from an independent-measures study using two separate samples, each with n = 9 participants. Compute the pooled variance and the estimated standard error for the mean difference. (Use three decimal places.) s2pp2 = sM1 – M2M1 – M2 = Compute the independent measures t statistic. Using α = .05, is there a significant difference between the two sets of scores? t Distribution Degrees of Freedom = 11 -3.0-2.0-1.00.01.02.03.0x t-critical = ± t = 1.85 Fail to reject H₀. The mean difference is significant. Fail to reject H₀. The mean difference is not significant. Reject H₀. The mean difference is significant. Reject H₀. The mean difference is not significant. Now assume that the data are from a repeated-measures study using the same sample of n =9 participants in both treatment conditions. Compute the variance for the sample of difference scores and the estimated standard error for the mean difference. (Hint: You should find that the repeated-measures design substantially reduces the variance and the standard error.) s² = sMDMD = 1.080 Compute the repeated measures t statistic. Using α = .05, is there a significant difference between the two sets of scores? t-critical = t = Fail to reject H₀. The mean difference is significant. Reject H₀. The mean difference is not significant. Reject H₀. The mean difference is significant. Fail to reject H₀. The mean difference is not significant.

Swearing is a common, almost reflexive, response to pain. Whether you knock your shin into the edge of a coffee table or smash your thumb with a hammer, most of us respond with a streak of obscenities. One question, however, is whether swearing has any effect on the amount of pain that you feel. To address this issue, Stephens, Atkins, and Kingston (2009) conducted an experiment comparing swearing with other responses to pain. In the study, participants were asked to place one hand in icy cold water for as long as they could bear the pain. Half of the participants were told to repeat their favorite swear word over and over for as long as their hands were in the water. The other half repeated a neutral word. The researchers recorded how long each participant was able to tolerate the ice water. After a brief rest, the two groups switched words and repeated the ice water plunge. Thus, all the participants experienced both conditions (swearing and neutral) with half swearing on their first plunge and half on their second. The data in the following table are representative of the results obtained in the study and represent the reports of pain level of n = 9 participants. Complete the following table and find M and SS for each group of scores and for the differences. Participant Neutral Word X₁ Swearing X₂ Difference D = X₂ – X₁ A 9 7 B 9 8 C 9 5 D 4 5 E 10 8 F 9 4 G 6 5 H 10 10 I 6 2 ∑ M = M = M = SS = SS = SS = Assume that the data are from an independent-measures study using two separate samples, each with n = 9 participants. Compute the pooled variance and the estimated standard error for the mean difference. (Use three decimal places.) s2pp2 = sM1 – M2M1 – M2 = Compute the independent measures t statistic. Using α = .05, is there a significant difference between the two sets of scores? t Distribution Degrees of Freedom = 11 -3.0-2.0-1.00.01.02.03.0x t-critical = ± t = 1.85 Fail to reject H₀. The mean difference is significant. Fail to reject H₀. The mean difference is not significant. Reject H₀. The mean difference is significant. Reject H₀. The mean difference is not significant. Now assume that the data are from a repeated-measures study using the same sample of n =9 participants in both treatment conditions. Compute the variance for the sample of difference scores and the estimated standard error for the mean difference. (Hint: You should find that the repeated-measures design substantially reduces the variance and the standard error.) s² = sMDMD = 1.080 Compute the repeated measures t statistic. Using α = .05, is there a significant difference between the two sets of scores? t-critical = t = Fail to reject H₀. The mean difference is significant. Reject H₀. The mean difference is not significant. Reject H₀. The mean difference is significant. Fail to reject H₀. The mean difference is not significant.

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Complete the following table and find M and SS for each group of scores and for the differences.

Participant	Neutral Word X₁	Swearing X₂	Difference D = X₂ – X₁
A	9	7
B	9	8
C	9	5
D	4	5
E	10	8
F	9	4
G	6	5
H	10	10
I	6	2
	∑
	M =	M =	M =
	SS =	SS =	SS =

Assume that the data are from an independent-measures study using two separate samples, each with n = 9 participants. Compute the pooled variance and the estimated standard error for the mean difference. (Use three decimal places.)

s2pp2	=
sM1 – M2M1 – M2	=

Compute the independent measures t statistic. Using α = .05, is there a significant difference between the two sets of scores?

t Distribution

Degrees of Freedom = 11

-3.0-2.0-1.00.01.02.03.0x

t-critical	=	±
t	=	1.85

Fail to reject H₀. The mean difference is significant.

Fail to reject H₀. The mean difference is not significant.

Reject H₀. The mean difference is significant.

Reject H₀. The mean difference is not significant.

Now assume that the data are from a repeated-measures study using the same sample of n =9 participants in both treatment conditions. Compute the variance for the sample of difference scores and the estimated standard error for the mean difference. (Hint: You should find that the repeated-measures design substantially reduces the variance and the standard error.)

s²	=
sMDMD	=	1.080

Compute the repeated measures t statistic. Using α = .05, is there a significant difference between the two sets of scores?

t-critical	=
t	=

Fail to reject H₀. The mean difference is significant.

Reject H₀. The mean difference is not significant.

Reject H₀. The mean difference is significant.

Fail to reject H₀. The mean difference is not significant.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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