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B1234506 RESEARCH AIM To investigate how the perceived persuasiveness of a speaker is influenced by the rate at which they speak

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B1234506

RESEARCH AIM

• To investigate how the perceived persuasiveness of a speaker is influenced by the rate at which they speak.
• To investigate whether perceived persuasiveness is dependent of listeners having counter or pro-attitudinal opinions towards the statements being presented.
• To determine whether the age of the speaker, and whether or not the speaker was presented as an expert, or else was member of the general public, accounted for any identified effects of rate of speech and counter- or pro-attitudinal opinions.

ANALYSIS STRATEGY

Data cleaning and variable recoding

• This process involves removing unwanted variables and ensuring the data type of the variables is in line with the metric the variable represents for instance factor variables should not be saved as characters and continuous variables should be saved as numeric.
• Missing values to be imputed using median and mode if there is any missing values in the dataset.

Descriptive statistics and Testing of model assumptions

• In the univariate analysis, I plotted histograms and bar charts for each continuous variables. These histograms will be plotted to check the distribution of the variables . • I also performed multivariate analysis on the data by plotting correlation plot to analyze the correlation score of each numerical variable with to test for multicollinearity among the independent variables. We test for multicollinearity so that we fulfill the assumption of non-multicollinearity in linear regression.

Inferential tests: Model description

A multiple linear regression model will be fitted to the data to predict persuasiveness using the . This is because our research aim is to investigate how the perceived persuasiveness of a speaker is influenced by the rate at which they speak, and whether this is dependent of listeners having counter- or pro-attitudinal opinions towards the statements being presented. Since persuasive is a continuous variable linear regression is appropriate for this analysis. Another model fitted will be a two stage least square model in order to measure if age and expert account for the effect of speech rate and the endorse variable on the persuasiveness variable.

  

Model assumptions  and diagnostics

The model assumptions that will be checked include: multicollinearity which will be checked by inspecting the correlation plot and ensuring  that no independent  variables are correlated. The model diagnostic to be used  are the p-values of the independent  variables. The p-values are expected to be less than 0.05, this is the level of  statistical significance for the model to achieve significance. We will look out for the p-values of each model , that is the linear model and the two stage least square model to ascertain that the research aims are achieved. Also we will look at the coefficients of the estimates of speech rate and endorse variables to be able to interpret the effect of these variables on persuasiveness.  

RESULTS

Data cleaning and variable recoding

• The data contained 150 observations and 5 variables. The datatypes of a variable like expert from integer into a factor variable. The data did not have any missing values.

Descriptive statistics

• The distribution of the dependent variable persuasive, and independent variable speech rate in the analysis were normally distributed while age was slightly skewed to the left as shown by their bell-shaped histograms in figure 1 and 2, whereas age in figure 3. The bar chart in figure 4 shows that variable endorse had equal proportion of participants who agreed and disagreed with the speaker. The bar chart in Figure 5 shows that most of the participants were not experts in the subject area.

Linear regression model results

The model was not statistically significant as the general p-value was greater than both 0.05 and 0.1. But looking at individual predictor’s p-values the endorse variable was statistically significant at 10% level of significance as the p-value was less than 0.1. Hence persuasiveness of a speaker increased by 5.05 when they are endorsed by pro attitudinal opinion as compared to counter opinion. 

Two stage Least square Model assumptions 

For age and expert to be considered good instruments for speech rate and endorse: - They have to be exogenous: uncorrelated with the error term, or the dependent variable persuasive. - They should be able to estimate speech rate variable and the endorse variable.

Checking for instrumental variable assumptions

• Looking at the correlation plot, the age and expert variables are uncorrelated with persuasive hence first assumption is true for both. Now for the second assumption; We will check if these variables can estimate the speech rate and endorse (altitudinal opinion) variables.
• Age passed the test as a good instrument for speech rate variable, since it achieved a 10% level of statistical significance, because its p-value was less than 0.1.

Both age and expert are not good instruments for the endorse variable. Therefore age is the only instrument and for one independent variable (speech rate).

From the instrumental regression we find that age was a good instrument for speech rate and improved its significance by lowering its p-values from previously 0.6108 to 0.145, however the standard error increased from 0.4463 to 5.141. Thus age was the only variable that accounted for some effects of rate of speech. Both age and expert variables did account for effects in attitudinal opinions.

DISCUSSION

• From the analysis endorse(attitudinal opinions) had significant impact on the perceived persuasiveness of a speaker, hence perceived persuasiveness is dependent of listeners having counter or pro-attitudinal opinions towards the statements being presented.
• The speech rate did not have significant impact on perceived persuasiveness of a speaker, however the age of a speaker can influence the speech rate of a speaker thus serving as a good instrument in estimating speech rate of a speaker.

APPENDIX

Descriptive statistics

The following plots represent univariate analysis, and they test if the continuous variables are normally distributed. Whereas for the categorical variables the frequency distribution shows the count of each level. 

 

Figure 1: Histogram of persuasive variable

 

Figure 2: Histogram of speech rate variable

 

The shape of the sp rate histogram is bell-like and this means its normally distributed.

 

Figure 3: Histogram of the variable age

 

The shape of the age histogram is skewed to the left and it’s not normally distributed.

 

Figure 4: Bar chart of variable endorse

The bar chart of the endorse variable shows that the pro and counter category were equal in terms of frequency. The number of observations with counter endorsements were same as those with pro endorsements.

 

Figure 5: Bar chart of variable expert

From the bar chart of the expert variable the 0 category had more frequency than the 1 category. This shows that there was more observations that were labeled as non - expert.

Multivariate analysis

Correlation plot to show the correlation values of the two continuous variables age and sp rate

 

Figure 6: Correlation plot of all numeric variables

Model fitting

Linear Regression of persuasiveness against speech rate and attitudinal opinion

Variable	Estimate	Std error	T-value	P-value
Sp_rate	-0.2276	6.437	8.314	5.72e-14
endorsepro	5.0517	2.6835	1.882	0.0617
Multiple R-squared:  0.02473,    Adjusted R-squared:  0.01146  F-statistic: 1.864 on 2 and Degree Freedom of 147,  p-value: 0.1588

Two stage least square regression

Instrumental variables are age and expert.

We want to find out whether the age of the speaker, and whether or not the speaker was presented as an expert, or else was member of the general public, accounted for any identified effects of rate of speech and counter- or pro-attitudinal opinions.

Model assumptions - For age and expert to be considered instruments they should be able estimate speech rate variable and the endorse variable. - They have to be exogenous: uncorrelated with the error term, or persuasiveness.

Checking model assumptions

The effect of the instruments on the speech rate: Linear regression

Variable	Estimate	Std error	T-value	P-value
Age	-0.2276	6.437	8.314	5.72e-14
Expert1	-0.47527	0.48932	-0.971	0.333
Residual         standard         error:         2.992         on         147            degrees				of         freedom
Multiple         R-squared:                   0.02912,          Adjusted          R-squared: F-statistic: 2.205 on 2 and 147 DF,  p-value: 0.1139				0.01591

The effect of the instruments on the endorse variable: Logistic regression

Variable	Estimate	Std error	T-value	P-value
Age	0.6663	0.61165	1.089	0.276
Expert1	0.27084	0.33003	0.821	0.412

Fit a two stage least square model using age as the instrument variable

Variable	Estimate	Std error	T-value	P-value
Sp_rate	7.531	5.141	1.465	0.145

 

Residual         standard         error:         28.64         on	148	degrees         of	freedom
Multiple            R-Squared:            -1.988,              Wald test: 2.146 on 1 and 148 DF,  p-value: 0.1451	Adjusted	R-squared:	-2.009