Narrative Study 2 - Spring Analysis
dcz
march 2019
Study Description
Pretest-posttest design
Independent Variables
IV1 - Script Content (0 = Advice; 1 = Story)
IV2 - Stats Evidence (0 = Control; 1 = Stats)
Mediators
Transportation - (Green & Brock 2000)
Counter-argue - (Same as Study 1)
Dependent Vars
Preference for Structured Interview (Time 1 & Time 2)
1. Descriptive Statistics
Sample Characteristics
describe(select(df.clean, AGE, SEX))## vars n mean sd median trimmed mad min max range skew kurtosis
## AGE 1 197 39.74 10.35 38 39.00 10.38 18 68 50 0.61 -0.29
## SEX 2 197 1.47 0.50 1 1.47 0.00 1 2 1 0.11 -2.00
## se
## AGE 0.74
## SEX 0.04 # Hiring Experience Q1
table(df.clean$EXPERIENCE_1)##
## 1 2 3 4 5 8
## 13 27 79 50 23 5 # Hiring Experience Q2
table(df.clean$EXPERIENCE_2)##
## 1 2 3 4 5 8
## 17 40 88 45 6 1 # Hiring Experience Q3
table(df.clean$EXPERIENCE_3)##
## 1 2 3 4 5
## 16 40 84 43 14 # Company Type
table(df.clean$`Company type`)##
## Large private Other Publicly listed Small
## 45 26 37 61
## SME
## 21 # Employ Status
table(df.clean$`Employment Status`)##
## Full-Time Part-Time
## 163 31 # Industry
table(df.clean$Industry)##
## Agriculture, Forestry, Fishing and Hunting
## 1
## Art/Design
## 4
## Arts, Entertainment, and Recreation
## 6
## Broadcasting
## 1
## College, University, and Adult Education
## 14
## Computer and Electronics Manufacturing
## 5
## Construction
## 9
## Finance and Insurance
## 9
## Government and Public Administration
## 13
## Graphic Design
## 3
## Grocery
## 2
## Health Care and Social Assistance
## 15
## Hotel and Food Services
## 4
## Information Services and Data Processing
## 12
## Legal Services
## 7
## Market Research
## 1
## Military
## 2
## Other Education Industry
## 9
## Other Industry / None of the above
## 20
## Other Manufacturing
## 8
## Primary/Secondary (K-12) Education
## 5
## Product Development
## 2
## Publishing
## 2
## Retail
## 11
## Scientific or Technical Services
## 6
## Software
## 8
## Telecommunications
## 3
## Transportation and Warehousing
## 2
## Utilities
## 2
## Wholesale
## 4 # Highest educatin
table(df.clean$`Highest education level`)##
## College/A levels Doctorate degree (PhD/MD/other)
## 36 11
## Graduate degree (MA/MSc/MPhil/other) No formal qualifications
## 51 1
## Secondary school/GCSE Undergraduate degree (BA/BSc/other)
## 10 85 # Work groups
table(df.clean$Workgroups)##
## I sometimes work as part of a group and sometimes alone
## 89
## I work alone
## 17
## I work as part of a large group 10+
## 27
## I work as part of a small group 2-10
## 58
## Not applicable
## 3 # Ethnicity
table(df.clean$RACE)##
## 1 2 4 6 14
## 177 6 6 5 2 # Nationality
table(df.clean$Nationality)##
## Canada Dominican Republic Germany
## 9 1 2
## Greece Iran Ireland
## 1 1 1
## Lithuania Malaysia Portugal
## 1 1 1
## Spain Uganda United Kingdom
## 9 1 108
## United States
## 58Correlation Matrix
2. Psychometrics
CFA
Testing the measurement model of interview attitudes
## lavaan 0.6-3 ended normally after 27 iterations
##
## Optimization method NLMINB
## Number of free parameters 8
##
## Used Total
## Number of observations 196 197
##
## Estimator ML
## Model Fit Test Statistic 10.611
## Degrees of freedom 2
## P-value (Chi-square) 0.005
##
## Model test baseline model:
##
## Minimum Function Test Statistic 1064.777
## Degrees of freedom 6
## P-value 0.000
##
## User model versus baseline model:
##
## Comparative Fit Index (CFI) 0.992
## Tucker-Lewis Index (TLI) 0.976
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -696.508
## Loglikelihood unrestricted model (H1) -691.202
##
## Number of free parameters 8
## Akaike (AIC) 1409.015
## Bayesian (BIC) 1435.240
## Sample-size adjusted Bayesian (BIC) 1409.897
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.148
## 90 Percent Confidence Interval 0.069 0.241
## P-value RMSEA <= 0.05 0.023
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.009
##
## Parameter Estimates:
##
## Information Expected
## Information saturated (h1) model Structured
## Standard Errors Standard
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## attitudePost =~
## GENERALINTENT_ 1.000
## GENERALINTENT_ 1.008 0.034 29.468 0.000
## GENERALINTENT_ 1.003 0.036 28.131 0.000
## GENERALINTENT_ 1.041 0.036 29.170 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .GENERALINTENT_ 0.097 0.016 6.270 0.000
## .GENERALINTENT_ 0.148 0.020 7.484 0.000
## .GENERALINTENT_ 0.172 0.022 7.855 0.000
## .GENERALINTENT_ 0.164 0.022 7.573 0.000
## attitudePost 1.153 0.126 9.115 0.000Scale Reliabilities
## Warning in alpha(dplyr::select(df.clean, TRANSPORTATION_1:TRANSPORTATION_10), : Some items were negatively correlated with total scale and were automatically reversed.
## This is indicated by a negative sign for the variable name.##
## Reliability analysis
## Call: alpha(x = dplyr::select(df.clean, TRANSPORTATION_1:TRANSPORTATION_10),
## na.rm = T, check.keys = T)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.76 0.76 0.79 0.26 3.2 0.026 3.4 0.56 0.26
##
## lower alpha upper 95% confidence boundaries
## 0.7 0.76 0.81
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r
## TRANSPORTATION_1 0.72 0.73 0.74 0.25 2.7 0.030 0.019
## TRANSPORTATION_3 0.71 0.72 0.74 0.24 2.6 0.031 0.020
## TRANSPORTATION_4 0.72 0.72 0.75 0.25 2.6 0.031 0.022
## TRANSPORTATION_5- 0.74 0.75 0.78 0.27 3.0 0.028 0.030
## TRANSPORTATION_6 0.71 0.73 0.76 0.25 2.7 0.031 0.029
## TRANSPORTATION_7 0.74 0.76 0.77 0.28 3.1 0.028 0.023
## TRANSPORTATION_8 0.76 0.76 0.79 0.29 3.2 0.026 0.024
## TRANSPORTATION_9- 0.76 0.76 0.79 0.29 3.2 0.026 0.023
## TRANSPORTATION_10 0.72 0.73 0.77 0.26 2.8 0.030 0.031
## med.r
## TRANSPORTATION_1 0.27
## TRANSPORTATION_3 0.25
## TRANSPORTATION_4 0.25
## TRANSPORTATION_5- 0.27
## TRANSPORTATION_6 0.25
## TRANSPORTATION_7 0.27
## TRANSPORTATION_8 0.28
## TRANSPORTATION_9- 0.28
## TRANSPORTATION_10 0.23
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## TRANSPORTATION_1 197 0.63 0.67 0.66 0.52 4.2 0.79
## TRANSPORTATION_3 197 0.67 0.70 0.69 0.56 4.1 0.86
## TRANSPORTATION_4 197 0.66 0.69 0.66 0.55 4.2 0.85
## TRANSPORTATION_5- 196 0.54 0.53 0.42 0.38 2.9 1.02
## TRANSPORTATION_6 197 0.68 0.66 0.60 0.54 3.5 1.07
## TRANSPORTATION_7 197 0.51 0.50 0.41 0.36 1.9 0.94
## TRANSPORTATION_8 196 0.49 0.47 0.36 0.30 2.5 1.08
## TRANSPORTATION_9- 196 0.45 0.46 0.35 0.28 4.0 0.99
## TRANSPORTATION_10 197 0.65 0.63 0.55 0.50 3.4 1.03
##
## Non missing response frequency for each item
## 1 2 3 4 5 miss
## TRANSPORTATION_1 0.00 0.05 0.07 0.47 0.41 0.00
## TRANSPORTATION_3 0.01 0.06 0.11 0.47 0.35 0.00
## TRANSPORTATION_4 0.01 0.03 0.13 0.42 0.41 0.00
## TRANSPORTATION_5 0.06 0.24 0.34 0.30 0.07 0.01
## TRANSPORTATION_6 0.04 0.14 0.27 0.35 0.20 0.00
## TRANSPORTATION_7 0.43 0.32 0.19 0.06 0.01 0.00
## TRANSPORTATION_8 0.20 0.32 0.25 0.21 0.02 0.01
## TRANSPORTATION_9 0.36 0.39 0.15 0.09 0.01 0.01
## TRANSPORTATION_10 0.05 0.17 0.26 0.42 0.11 0.00##
## Reliability analysis
## Call: alpha(x = dplyr::select(df.clean, COUNTER_1:COUNTER_3), na.rm = T,
## check.keys = T)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.81 0.82 0.76 0.6 4.4 0.023 2.4 1 0.61
##
## lower alpha upper 95% confidence boundaries
## 0.77 0.81 0.86
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## COUNTER_1 0.81 0.82 0.69 0.69 4.4 0.026 NA 0.69
## COUNTER_2 0.65 0.66 0.49 0.49 1.9 0.049 NA 0.49
## COUNTER_3 0.76 0.76 0.61 0.61 3.1 0.035 NA 0.61
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## COUNTER_1 197 0.81 0.82 0.66 0.59 2.0 1.1
## COUNTER_2 197 0.89 0.90 0.84 0.75 2.4 1.1
## COUNTER_3 194 0.86 0.85 0.74 0.66 2.7 1.3
##
## Non missing response frequency for each item
## 1 2 3 4 5 miss
## COUNTER_1 0.40 0.35 0.09 0.14 0.02 0.00
## COUNTER_2 0.24 0.33 0.20 0.20 0.03 0.00
## COUNTER_3 0.22 0.28 0.18 0.25 0.08 0.02## Warning in alpha(dplyr::select(df.clean, CREDIBLE_1:CREDIBLE_5), check.keys = T, : Some items were negatively correlated with total scale and were automatically reversed.
## This is indicated by a negative sign for the variable name.##
## Reliability analysis
## Call: alpha(x = dplyr::select(df.clean, CREDIBLE_1:CREDIBLE_5), na.rm = T,
## check.keys = T)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.86 0.86 0.83 0.55 6 0.016 4.2 0.61 0.58
##
## lower alpha upper 95% confidence boundaries
## 0.82 0.86 0.89
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r
## CREDIBLE_1 0.82 0.82 0.78 0.54 4.7 0.021 0.00513
## CREDIBLE_2 0.81 0.81 0.77 0.52 4.4 0.022 0.00703
## CREDIBLE_3 0.82 0.82 0.78 0.53 4.5 0.021 0.00675
## CREDIBLE_4- 0.86 0.86 0.82 0.60 6.1 0.016 0.00047
## CREDIBLE_5 0.82 0.82 0.78 0.53 4.6 0.021 0.00972
## med.r
## CREDIBLE_1 0.54
## CREDIBLE_2 0.53
## CREDIBLE_3 0.53
## CREDIBLE_4- 0.61
## CREDIBLE_5 0.55
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## CREDIBLE_1 197 0.81 0.81 0.75 0.68 4.3 0.76
## CREDIBLE_2 197 0.83 0.83 0.78 0.72 4.2 0.77
## CREDIBLE_3 197 0.82 0.82 0.76 0.70 4.2 0.76
## CREDIBLE_4- 197 0.72 0.71 0.59 0.55 4.3 0.81
## CREDIBLE_5 197 0.81 0.82 0.76 0.70 3.9 0.75
##
## Non missing response frequency for each item
## 1 2 3 4 5 miss
## CREDIBLE_1 0.00 0.03 0.10 0.44 0.44 0
## CREDIBLE_2 0.00 0.02 0.18 0.43 0.38 0
## CREDIBLE_3 0.01 0.02 0.10 0.47 0.41 0
## CREDIBLE_4 0.45 0.40 0.12 0.04 0.00 0
## CREDIBLE_5 0.00 0.02 0.25 0.50 0.23 0##
## Reliability analysis
## Call: alpha(x = dplyr::select(df.clean, GENERALINTENT_PRE_1:GENERALINTENT_PRE_4),
## na.rm = T, check.keys = T)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.97 0.97 0.96 0.89 31 0.0036 3.3 1.3 0.89
##
## lower alpha upper 95% confidence boundaries
## 0.96 0.97 0.98
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se
## GENERALINTENT_PRE_1 0.96 0.96 0.94 0.89 24 0.0050
## GENERALINTENT_PRE_2 0.96 0.96 0.94 0.88 22 0.0054
## GENERALINTENT_PRE_3 0.96 0.96 0.94 0.88 23 0.0053
## GENERALINTENT_PRE_4 0.96 0.96 0.95 0.90 26 0.0047
## var.r med.r
## GENERALINTENT_PRE_1 0.00012 0.89
## GENERALINTENT_PRE_2 0.00033 0.88
## GENERALINTENT_PRE_3 0.00075 0.88
## GENERALINTENT_PRE_4 0.00028 0.89
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## GENERALINTENT_PRE_1 197 0.95 0.96 0.94 0.92 3.3 1.3
## GENERALINTENT_PRE_2 197 0.96 0.96 0.95 0.93 3.2 1.3
## GENERALINTENT_PRE_3 196 0.96 0.96 0.94 0.93 3.2 1.3
## GENERALINTENT_PRE_4 197 0.95 0.95 0.93 0.91 3.2 1.4
##
## Non missing response frequency for each item
## 1 2 3 4 5 miss
## GENERALINTENT_PRE_1 0.06 0.29 0.10 0.35 0.20 0.00
## GENERALINTENT_PRE_2 0.10 0.27 0.12 0.30 0.21 0.00
## GENERALINTENT_PRE_3 0.10 0.30 0.11 0.28 0.22 0.01
## GENERALINTENT_PRE_4 0.13 0.27 0.10 0.28 0.22 0.00##
## Reliability analysis
## Call: alpha(x = dplyr::select(df.clean, GENERALINTENT_POST_1:GENERALINTENT_POST_4),
## na.rm = T, check.keys = T)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.97 0.97 0.96 0.89 33 0.0035 3.8 1.1 0.89
##
## lower alpha upper 95% confidence boundaries
## 0.96 0.97 0.98
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se
## GENERALINTENT_POST_1 0.96 0.96 0.94 0.88 22 0.0053
## GENERALINTENT_POST_2 0.96 0.96 0.94 0.89 25 0.0047
## GENERALINTENT_POST_3 0.96 0.96 0.95 0.90 26 0.0046
## GENERALINTENT_POST_4 0.96 0.96 0.94 0.89 25 0.0049
## var.r med.r
## GENERALINTENT_POST_1 0.00021 0.88
## GENERALINTENT_POST_2 0.00001 0.90
## GENERALINTENT_POST_3 0.00031 0.90
## GENERALINTENT_POST_4 0.00055 0.89
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## GENERALINTENT_POST_1 196 0.97 0.97 0.95 0.94 3.8 1.1
## GENERALINTENT_POST_2 197 0.96 0.96 0.94 0.92 3.8 1.2
## GENERALINTENT_POST_3 197 0.95 0.95 0.93 0.92 3.7 1.2
## GENERALINTENT_POST_4 197 0.96 0.96 0.94 0.93 3.7 1.2
##
## Non missing response frequency for each item
## 1 2 3 4 5 miss
## GENERALINTENT_POST_1 0.03 0.15 0.16 0.35 0.32 0.01
## GENERALINTENT_POST_2 0.04 0.15 0.16 0.35 0.31 0.00
## GENERALINTENT_POST_3 0.04 0.15 0.17 0.34 0.31 0.00
## GENERALINTENT_POST_4 0.05 0.15 0.15 0.34 0.32 0.00## Warning in alpha(dplyr::select(df.clean, AOT_1:AOT_10), check.keys = T, : Some items were negatively correlated with total scale and were automatically reversed.
## This is indicated by a negative sign for the variable name.##
## Reliability analysis
## Call: alpha(x = dplyr::select(df.clean, AOT_1:AOT_10), na.rm = T, check.keys = T)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.75 0.76 0.78 0.24 3.2 0.026 19 0.48 0.25
##
## lower alpha upper 95% confidence boundaries
## 0.7 0.75 0.8
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## AOT_1 0.75 0.76 0.78 0.26 3.2 0.026 0.019 0.26
## AOT_2 0.73 0.73 0.74 0.23 2.7 0.029 0.019 0.24
## AOT_3- 0.73 0.75 0.76 0.25 2.9 0.028 0.018 0.25
## AOT_4 0.73 0.73 0.75 0.23 2.8 0.028 0.019 0.24
## AOT_5- 0.71 0.72 0.74 0.23 2.6 0.031 0.017 0.25
## AOT_6 0.76 0.77 0.78 0.27 3.3 0.025 0.018 0.26
## AOT_7- 0.72 0.73 0.75 0.23 2.7 0.030 0.019 0.25
## AOT_8- 0.71 0.73 0.74 0.23 2.7 0.031 0.017 0.25
## AOT_9 0.75 0.76 0.78 0.26 3.2 0.026 0.020 0.27
## AOT_10 0.73 0.73 0.75 0.24 2.8 0.029 0.022 0.25
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## AOT_1 197 0.40 0.45 0.34 0.26 19 0.74
## AOT_2 197 0.60 0.65 0.61 0.50 19 0.64
## AOT_3- 196 0.58 0.54 0.47 0.41 19 1.03
## AOT_4 197 0.57 0.62 0.57 0.46 19 0.71
## AOT_5- 197 0.69 0.67 0.64 0.57 19 0.84
## AOT_6 197 0.40 0.40 0.28 0.22 19 0.92
## AOT_7- 197 0.65 0.63 0.58 0.51 19 0.95
## AOT_8- 197 0.69 0.65 0.61 0.54 19 1.06
## AOT_9 197 0.45 0.44 0.33 0.29 19 0.88
## AOT_10 197 0.58 0.61 0.54 0.48 19 0.67
##
## Non missing response frequency for each item
## 16 17 18 19 20 miss
## AOT_1 0.00 0.05 0.16 0.60 0.18 0.00
## AOT_2 0.01 0.01 0.03 0.54 0.42 0.00
## AOT_3 0.18 0.46 0.19 0.14 0.03 0.01
## AOT_4 0.00 0.03 0.09 0.52 0.36 0.00
## AOT_5 0.59 0.32 0.03 0.05 0.01 0.00
## AOT_6 0.02 0.08 0.28 0.45 0.17 0.00
## AOT_7 0.41 0.35 0.16 0.07 0.01 0.00
## AOT_8 0.29 0.38 0.19 0.13 0.02 0.00
## AOT_9 0.01 0.10 0.15 0.56 0.18 0.00
## AOT_10 0.00 0.02 0.06 0.43 0.50 0.00##
## Reliability analysis
## Call: alpha(x = dplyr::select(df.clean, EXPERIENCE_1:EXPERIENCE_3),
## na.rm = T, check.keys = T)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.88 0.89 0.85 0.73 8.1 0.015 3.1 1 0.7
##
## lower alpha upper 95% confidence boundaries
## 0.85 0.88 0.91
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r
## EXPERIENCE_1 0.89 0.89 0.8 0.8 7.8 0.016 NA
## EXPERIENCE_2 0.81 0.82 0.7 0.7 4.6 0.026 NA
## EXPERIENCE_3 0.81 0.82 0.7 0.7 4.6 0.026 NA
## med.r
## EXPERIENCE_1 0.8
## EXPERIENCE_2 0.7
## EXPERIENCE_3 0.7
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## EXPERIENCE_1 197 0.90 0.88 0.77 0.74 3.3 1.3
## EXPERIENCE_2 197 0.91 0.92 0.87 0.80 2.9 1.0
## EXPERIENCE_3 197 0.91 0.92 0.86 0.80 3.0 1.0
##
## Non missing response frequency for each item
## 1 2 3 4 5 8 miss
## EXPERIENCE_1 0.07 0.14 0.40 0.25 0.12 0.03 0
## EXPERIENCE_2 0.09 0.20 0.45 0.23 0.03 0.01 0
## EXPERIENCE_3 0.08 0.20 0.43 0.22 0.07 0.00 03. Between Subject ANOVAs
2x2 ANOVA - Transportation
## Df Sum Sq Mean Sq F value Pr(>F)
## COND_SCRIPT 1 2.20 2.1997 7.178 0.00802 **
## COND_STAT 1 0.04 0.0436 0.142 0.70641
## COND_SCRIPT:COND_STAT 1 0.27 0.2694 0.879 0.34962
## Residuals 193 59.14 0.3064
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Warning: Converting "SUBJID" to factor for ANOVA.## Warning: "COND_SCRIPT" will be treated as numeric.## Warning: "COND_STAT" will be treated as numeric.## Warning: Data is unbalanced (unequal N per group). Make sure you specified
## a well-considered value for the type argument to ezANOVA().## Coefficient covariances computed by hccm()## Warning: At least one numeric between-Ss variable detected, therefore no
## assumption test will be returned.##
##
## ANOVA results
##
##
## Predictor df_num df_den SS_num SS_den F p ges
## COND_SCRIPT 1 193 2.22 59.14 7.26 .008 .04
## COND_STAT 1 193 0.04 59.14 0.14 .706 .00
## COND_SCRIPT x COND_STAT 1 193 0.27 59.14 0.88 .350 .00
##
## Note. df_num indicates degrees of freedom numerator. df_den indicates degrees of freedom denominator.
## SS_num indicates sum of squares numerator. SS_den indicates sum of squares denominator.
## ges indicates generalized eta-squared.
## ## # A tibble: 2 x 3
## COND_SCRIPT mean sdev
## <dbl> <dbl> <dbl>
## 1 0 3.32 0.570
## 2 1 3.53 0.5332x2 ANOVA - Counter arguing
## Df Sum Sq Mean Sq F value Pr(>F)
## COND_SCRIPT 1 13.39 13.391 14.249 0.000213 ***
## COND_STAT 1 0.49 0.489 0.520 0.471663
## COND_SCRIPT:COND_STAT 1 0.37 0.369 0.393 0.531602
## Residuals 193 181.38 0.940
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Warning: Converting "SUBJID" to factor for ANOVA.## Warning: "COND_SCRIPT" will be treated as numeric.## Warning: "COND_STAT" will be treated as numeric.## Warning: Data is unbalanced (unequal N per group). Make sure you specified
## a well-considered value for the type argument to ezANOVA().## Coefficient covariances computed by hccm()## Warning: At least one numeric between-Ss variable detected, therefore no
## assumption test will be returned.## $ANOVA
## Effect DFn DFd SSn SSd F
## 1 COND_SCRIPT 1 193 13.5976851 181.3766 14.4690871
## 2 COND_STAT 1 193 0.4887954 181.3766 0.5201196
## 3 COND_SCRIPT:COND_STAT 1 193 0.3690887 181.3766 0.3927416
## p p<.05 ges
## 1 0.0001911128 * 0.069740930
## 2 0.4716633770 0.002687677
## 3 0.5316023617 0.002030798##
##
## ANOVA results
##
##
## Predictor df_num df_den SS_num SS_den F p ges
## COND_SCRIPT 1 193 13.60 181.38 14.47 .000 .07
## COND_STAT 1 193 0.49 181.38 0.52 .472 .00
## COND_SCRIPT x COND_STAT 1 193 0.37 181.38 0.39 .532 .00
##
## Note. df_num indicates degrees of freedom numerator. df_den indicates degrees of freedom denominator.
## SS_num indicates sum of squares numerator. SS_den indicates sum of squares denominator.
## ges indicates generalized eta-squared.
## ## # A tibble: 2 x 3
## COND_SCRIPT mean sdev
## <dbl> <dbl> <dbl>
## 1 0 2.64 1.08
## 2 1 2.12 0.8342x2 ANOVA - General attitude change (post-pre)
## Df Sum Sq Mean Sq F value Pr(>F)
## COND_SCRIPT 1 3.98 3.983 5.162 0.0242 *
## COND_STAT 1 0.71 0.706 0.916 0.3398
## COND_SCRIPT:COND_STAT 1 0.15 0.147 0.190 0.6633
## Residuals 193 148.91 0.772
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 12x2 ANOVA - Hiring experience
# Same results in ez
ezModel.1 <- ezANOVA(
data = df.clean
, dv = M_HIREEXPERIENCE
, wid = SUBJID
, between = .(COND_SCRIPT, COND_STAT)
, detailed = T
)## Warning: Converting "SUBJID" to factor for ANOVA.## Warning: "COND_SCRIPT" will be treated as numeric.## Warning: "COND_STAT" will be treated as numeric.## Warning: Data is unbalanced (unequal N per group). Make sure you specified
## a well-considered value for the type argument to ezANOVA().## Coefficient covariances computed by hccm()## Warning: At least one numeric between-Ss variable detected, therefore no
## assumption test will be returned. print(ezModel.1)## $ANOVA
## Effect DFn DFd SSn SSd F p
## 1 COND_SCRIPT 1 193 0.1099841 190.8707 0.1112110 0.73913161
## 2 COND_STAT 1 193 3.9112306 190.8707 3.9548631 0.04814905
## 3 COND_SCRIPT:COND_STAT 1 193 0.8981033 190.8707 0.9081223 0.34180509
## p<.05 ges
## 1 0.0005758911
## 2 * 0.0200800482
## 3 0.0046832605t.test(M_HIREEXPERIENCE~COND_STAT, data = df.clean)##
## Welch Two Sample t-test
##
## data: M_HIREEXPERIENCE by COND_STAT
## t = 1.9788, df = 189.02, p-value = 0.04929
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 0.0008755983 0.5590089615
## sample estimates:
## mean in group 0 mean in group 1
## 3.232323 2.952381Table of Means Between Groups
jmv::descriptives(
formula = M_GENATT_PRE + M_TRANSPORT + M_COUNTER + M_CREDIBLE + M_GENATT_POST ~ COND_SCRIPT:COND_STAT,
data = df.clean,
sd = TRUE,
min = FALSE,
max = FALSE)##
## DESCRIPTIVES
##
## Descriptives
## ─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
## COND_SCRIPT COND_STAT M_GENATT_PRE M_TRANSPORT M_COUNTER M_CREDIBLE M_GENATT_POST
## ─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
## N 0 0 48 48 48 48 48
## 1 52 52 52 52 52
## 1 0 51 51 51 51 51
## 1 46 46 46 46 46
## Missing 0 0 0 0 0 0 0
## 1 0 0 0 0 0
## 1 0 0 0 0 0 0
## 1 0 0 0 0 0
## Mean 0 0 3.24 3.34 2.65 3.55 3.57
## 1 3.03 3.29 2.63 3.59 3.42
## 1 0 3.35 3.48 2.21 3.77 3.91
## 1 3.39 3.58 2.02 3.80 4.13
## Median 0 0 3.25 3.33 2.67 3.60 3.75
## 1 3.00 3.33 2.67 3.60 3.88
## 1 0 3.75 3.44 2.00 3.80 4.00
## 1 3.75 3.56 2.00 3.80 4.12
## Standard deviation 0 0 1.29 0.577 1.04 0.433 1.15
## 1 1.27 0.569 1.13 0.524 1.27
## 1 0 1.28 0.548 0.832 0.391 0.930
## 1 1.25 0.516 0.835 0.356 0.916
## ─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────4. Repeated Measures ANOVA
##
## REPEATED MEASURES ANOVA
##
## Within Subjects Effects
## ─────────────────────────────────────────────────────────────────────────────────────────────
## Sum of Squares df Mean Square F p
## ─────────────────────────────────────────────────────────────────────────────────────────────
## PREPOST 25.1900 1 25.1900 65.295 < .001
## PREPOST:COND_SCRIPT 2.0696 1 2.0696 5.365 0.022
## PREPOST:COND_STAT 0.3582 1 0.3582 0.929 0.336
## PREPOST:COND_SCRIPT:COND_STAT 0.0734 1 0.0734 0.190 0.663
## Residual 74.4564 193 0.3858
## ─────────────────────────────────────────────────────────────────────────────────────────────
## Note. Type 3 Sums of Squares
##
##
## Between Subjects Effects
## ────────────────────────────────────────────────────────────────────────────────────
## Sum of Squares df Mean Square F p
## ────────────────────────────────────────────────────────────────────────────────────
## COND_SCRIPT 14.0391 1 14.0391 5.8517 0.016
## COND_STAT 0.0662 1 0.0662 0.0276 0.868
## COND_SCRIPT:COND_STAT 2.4200 1 2.4200 1.0087 0.316
## Residual 463.0353 193 2.3991
## ────────────────────────────────────────────────────────────────────────────────────
## Note. Type 3 Sums of Squares
##
##
## ESTIMATED MARGINAL MEANS
##
## COND_SCRIPT:COND_STAT:PREPOST
##
## Estimated Marginal Means - COND_SCRIPT:COND_STAT:PREPOST
## ───────────────────────────────────────────────────────────────────────────
## PREPOST COND_STAT COND_SCRIPT Mean SE Lower Upper
## ───────────────────────────────────────────────────────────────────────────
## PRETEST 0 0 3.24 0.169 2.90 3.57
## 1 3.34 0.167 3.01 3.67
## 1 0 3.02 0.166 2.70 3.35
## 1 3.38 0.172 3.05 3.72
## POSTTEST 0 0 3.57 0.169 3.23 3.90
## 1 3.91 0.167 3.58 4.23
## 1 0 3.42 0.166 3.09 3.74
## 1 4.12 0.172 3.79 4.46
## ───────────────────────────────────────────────────────────────────────────
## [1] 3.248731## [1] 3.751269## [1] 1.27062## [1] 1.10671## # A tibble: 2 x 6
## COND_SCRIPT pre.mean pre.sd post.mean post.sd n
## <dbl> <dbl> <dbl> <dbl> <dbl> <int>
## 1 0 3.13 1.28 3.50 1.21 100
## 2 1 3.37 1.26 4.02 0.925 97# Becker 1988Using ezAnova
library(ez)
library(lsr)
### Transform wide data
wide.df <- df.clean %>%
gather("treatment", "attitude", 129, 123) %>%
arrange(desc(treatment))
wide.df$FACT_SCRIPT <- as.factor(wide.df$COND_SCRIPT)
wide.df$FACT_STAT <- as.factor(wide.df$COND_STAT)
### ANOVA
mixed_anova <- ezANOVA(data = wide.df,
dv = attitude,
wid = SUBJID,
between = .(COND_SCRIPT, COND_STAT),
#between_covariates = M_HIREEXPERIENCE,
within = .(treatment), #within subjects variables to include in the model
detailed = T) ## Warning: Converting "SUBJID" to factor for ANOVA.## Warning: Converting "treatment" to factor for ANOVA.## Warning: "COND_SCRIPT" will be treated as numeric.## Warning: "COND_STAT" will be treated as numeric.## Warning: Data is unbalanced (unequal N per group). Make sure you specified
## a well-considered value for the type argument to ezANOVA(). print(mixed_anova)## $ANOVA
## Effect DFn DFd SSn SSd
## 1 (Intercept) 1 193 4826.5000000 463.03531
## 2 COND_SCRIPT 1 193 13.9640830 463.03531
## 3 COND_STAT 1 193 0.0794755 463.03531
## 5 treatment 1 193 24.8756345 74.45638
## 4 COND_SCRIPT:COND_STAT 1 193 2.4200207 463.03531
## 6 COND_SCRIPT:treatment 1 193 2.0646514 74.45638
## 7 COND_STAT:treatment 1 193 0.3532244 74.45638
## 8 COND_SCRIPT:COND_STAT:treatment 1 193 0.0733703 74.45638
## F p p<.05 ges
## 1 2.011757e+03 5.014744e-104 * 0.8997963238
## 2 5.820437e+00 1.677658e-02 * 0.0253222176
## 3 3.312657e-02 8.557682e-01 0.0001478418
## 5 6.448067e+01 9.380993e-14 * 0.0442337839
## 4 1.008701e+00 3.164719e-01 0.0044822527
## 6 5.351828e+00 2.175414e-02 * 0.0038265724
## 7 9.156005e-01 3.398298e-01 0.0006567402
## 8 1.901847e-01 6.632503e-01 0.0001364864 apaTables::apa.ezANOVA.table(mixed_anova, filename = "outResults/anovaTable.rtf")##
##
## ANOVA results
##
##
## Predictor df_num df_den SS_num SS_den F
## (Intercept) 1 193 4826.50 463.04 2011.76
## COND_SCRIPT 1 193 13.96 463.04 5.82
## COND_STAT 1 193 0.08 463.04 0.03
## treatment 1 193 24.88 74.46 64.48
## COND_SCRIPT x COND_STAT 1 193 2.42 463.04 1.01
## COND_SCRIPT x treatment 1 193 2.06 74.46 5.35
## COND_STAT x treatment 1 193 0.35 74.46 0.92
## COND_SCRIPT x COND_STAT x treatment 1 193 0.07 74.46 0.19
## p ges
## .000 .90
## .017 .03
## .856 .00
## .000 .04
## .316 .00
## .022 .00
## .340 .00
## .663 .00
##
## Note. df_num indicates degrees of freedom numerator. df_den indicates degrees of freedom denominator.
## SS_num indicates sum of squares numerator. SS_den indicates sum of squares denominator.
## ges indicates generalized eta-squared.
## apaTables::apa.ezANOVA.table(mixed_anova)##
##
## ANOVA results
##
##
## Predictor df_num df_den SS_num SS_den F
## (Intercept) 1 193 4826.50 463.04 2011.76
## COND_SCRIPT 1 193 13.96 463.04 5.82
## COND_STAT 1 193 0.08 463.04 0.03
## treatment 1 193 24.88 74.46 64.48
## COND_SCRIPT x COND_STAT 1 193 2.42 463.04 1.01
## COND_SCRIPT x treatment 1 193 2.06 74.46 5.35
## COND_STAT x treatment 1 193 0.35 74.46 0.92
## COND_SCRIPT x COND_STAT x treatment 1 193 0.07 74.46 0.19
## p ges
## .000 .90
## .017 .03
## .856 .00
## .000 .04
## .316 .00
## .022 .00
## .340 .00
## .663 .00
##
## Note. df_num indicates degrees of freedom numerator. df_den indicates degrees of freedom denominator.
## SS_num indicates sum of squares numerator. SS_den indicates sum of squares denominator.
## ges indicates generalized eta-squared.
## ## Plot
temp <- ezPlot(
data = wide.df
, dv = .(attitude)
, wid = .(SUBJID)
, within = .(treatment)
, between = .(FACT_SCRIPT, FACT_STAT)
, x = .(FACT_STAT)
, split = .(FACT_SCRIPT)
, col = .(treatment)
, x_lab = 'Stats'
, y_lab = 'Attitudes'
, split_lab = 'Treatment'
, print_code = T
)## Warning: Converting "SUBJID" to factor for ANOVA.## Warning: Converting "treatment" to factor for ANOVA.## Warning: Data is unbalanced (unequal N per group). Make sure you specified
## a well-considered value for the type argument to ezANOVA().## Warning in ezStats(data = data, dv = dv, wid = wid, within = within,
## within_full = within_full, : Unbalanced groups. Mean N will be used in
## computation of FLSD## ggplot(
## data = stats
## , mapping = aes(
## y = Mean
## , x = FACT_STAT
## )
## )+
## geom_point(
## mapping = aes(
## colour = FACT_SCRIPT
## , shape = FACT_SCRIPT
## )
## , alpha = .8
## )+
## geom_line(
## mapping = aes(
## colour = FACT_SCRIPT
## , linetype = FACT_SCRIPT
## , x = I(as.numeric(FACT_STAT))
## )
## , alpha = .8
## )+
## geom_errorbar(
## mapping = aes(
## colour = FACT_SCRIPT
## , ymin = lo
## , ymax = hi
## )
## , linetype = 1
## , show.legend = FALSE
## , width = 0.25
## , alpha = .5
## )+
## facet_grid(
## facets = . ~ treatment
## , scales = 'free_y'
## )+
## labs(
## x = 'Stats'
## , y = 'Attitudes'
## , colour = 'Treatment'
## , shape = 'Treatment'
## , linetype = 'Treatment'
## ) levels(temp$FACT_SCRIPT) <- list("Advice" = 0, "Story" = 1)
levels(temp$FACT_STAT) <- list("Control" = 0, "Stats" = 1)
levels(temp$treatment) <- list("Pretest" = "M_GENATT_PRE", "Posttest" = "M_GENATT_POST")figure1 <- ggplot(
data = temp
, mapping = aes(
y = Mean
, x = FACT_STAT
)
)+
geom_point(
mapping = aes(
#colour = FACT_SCRIPT
, shape = FACT_SCRIPT
)
, alpha = 1
)+
geom_line(
mapping = aes(
#colour = FACT_SCRIPT
, linetype = FACT_SCRIPT
, x = I(as.numeric(FACT_STAT))
)
, alpha = .8
, size = .75
)+
geom_errorbar(
mapping = aes(
#colour = FACT_SCRIPT
, ymin = lo
, ymax = hi
)
, linetype = 1
, show.legend = FALSE
, width = 0.25
, alpha = .5
)+
facet_grid(
facets = . ~ treatment
, scales = 'free_y'
)+
labs(
x = 'Statistical Evidence'
, y = 'Preference for Structured Interviews'
, colour = 'Script'
, shape = 'Script'
, linetype = 'Script'
) + ylim(2.5,4.5)
#+ theme_apa(legend.use.title = FALSE, legend.font.size = 14, x.font.size = 14, y.font.size = 14, facet.title.size = 14)
# ggsave(filename = "outResults/anovaFigure.pdf", figure1, device = "pdf", width = 6, height = 4)5. Mediation Analysis with Lavaan
Model 1 - Counter argue and transportation as simultaneous mediators
## lavaan 0.6-3 ended normally after 18 iterations
##
## Optimization method NLMINB
## Number of free parameters 8
##
## Number of observations 197
##
## Estimator ML
## Model Fit Test Statistic 69.962
## Degrees of freedom 1
## P-value (Chi-square) 0.000
##
## Parameter Estimates:
##
## Information Expected
## Information saturated (h1) model Structured
## Standard Errors Standard
##
## Regressions:
## Estimate Std.Err z-value P(>|z|)
## M_TRANSPORT ~
## COND_SCRI (a1) 0.211 0.078 2.700 0.007
## M_COUNTER ~
## COND_SCRI (a2) -0.521 0.137 -3.805 0.000
## CHANGE_GENATTITDE ~
## M_TRANSPO (b1) 0.130 0.109 1.185 0.236
## M_COUNTER (b2) -0.180 0.062 -2.876 0.004
## COND_SCRI (c) 0.163 0.127 1.289 0.198
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .M_TRANSPORT 0.302 0.030 9.925 0.000
## .M_COUNTER 0.925 0.093 9.925 0.000
## .CHANGE_GENATTI 0.712 0.072 9.925 0.000
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|)
## ind_transport 0.027 0.025 1.085 0.278
## ind_counter 0.094 0.041 2.294 0.022
## totaleffect 0.284 0.123 2.309 0.021Model 2 - Script -> Transportation -> Counterargue -> Attitude change
pathModel.2 <- '
# Direct Paths
M_TRANSPORT ~ a*COND_SCRIPT
M_COUNTER ~ b*M_TRANSPORT
CHANGE_GENATTITDE ~ c*M_COUNTER + d*COND_SCRIPT
# Indirect Paths
ind_total := a*b*c
'
pathFit.2 <- sem(pathModel.2, data = df.clean, se = "bootstrap", bootstrap = 1000)
boot.fit.2<-parameterEstimates(pathFit.2, ci=TRUE,level=.95,boot.ci.type="bca.simple")
#pathFit.2 <- sem(pathModel.2, data = df.clean)
summary(pathFit.2)## lavaan 0.6-3 ended normally after 16 iterations
##
## Optimization method NLMINB
## Number of free parameters 7
##
## Number of observations 197
##
## Estimator ML
## Model Fit Test Statistic 8.304
## Degrees of freedom 2
## P-value (Chi-square) 0.016
##
## Parameter Estimates:
##
## Standard Errors Bootstrap
## Number of requested bootstrap draws 1000
## Number of successful bootstrap draws 1000
##
## Regressions:
## Estimate Std.Err z-value P(>|z|)
## M_TRANSPORT ~
## COND_SCRIP (a) 0.211 0.081 2.604 0.009
## M_COUNTER ~
## M_TRANSPOR (b) -1.011 0.091 -11.141 0.000
## CHANGE_GENATTITDE ~
## M_COUNTER (c) -0.220 0.061 -3.618 0.000
## COND_SCRIP (d) 0.170 0.125 1.355 0.176
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .M_TRANSPORT 0.302 0.030 10.143 0.000
## .M_COUNTER 0.673 0.067 10.065 0.000
## .CHANGE_GENATTI 0.715 0.081 8.815 0.000
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|)
## ind_total 0.047 0.023 2.034 0.042print(boot.fit.2)## lhs op rhs label est se z
## 1 M_TRANSPORT ~ COND_SCRIPT a 0.211 0.081 2.604
## 2 M_COUNTER ~ M_TRANSPORT b -1.011 0.091 -11.141
## 3 CHANGE_GENATTITDE ~ M_COUNTER c -0.220 0.061 -3.618
## 4 CHANGE_GENATTITDE ~ COND_SCRIPT d 0.170 0.125 1.355
## 5 M_TRANSPORT ~~ M_TRANSPORT 0.302 0.030 10.143
## 6 M_COUNTER ~~ M_COUNTER 0.673 0.067 10.065
## 7 CHANGE_GENATTITDE ~~ CHANGE_GENATTITDE 0.715 0.081 8.815
## 8 COND_SCRIPT ~~ COND_SCRIPT 0.250 0.000 NA
## 9 ind_total := a*b*c ind_total 0.047 0.023 2.034
## pvalue ci.lower ci.upper
## 1 0.009 0.049 0.375
## 2 0.000 -1.192 -0.839
## 3 0.000 -0.342 -0.105
## 4 0.176 -0.070 0.430
## 5 0.000 0.250 0.371
## 6 0.000 0.559 0.832
## 7 0.000 0.566 0.887
## 8 NA 0.250 0.250
## 9 0.042 0.011 0.111Model 3 - Script -> Transportation -> Counterargue
pathModel.3 <- '
# Direct Paths
M_TRANSPORT ~ a*COND_SCRIPT
M_COUNTER ~ b*M_TRANSPORT + c*M_TRANSPORT
# Indirect Paths
ind_total := a*b
'
pathFit.3 <- sem(pathModel.3, data = df.clean, se = "bootstrap", bootstrap = 1000)
boot.fit.3<-parameterEstimates(pathFit.3, ci=TRUE,level=.95,boot.ci.type="bca.simple")
#pathFit.3 <- sem(pathModel.3, data = df.clean)
summary(pathFit.3)## lavaan 0.6-3 ended normally after 15 iterations
##
## Optimization method NLMINB
## Number of free parameters 4
##
## Number of observations 197
##
## Estimator ML
## Model Fit Test Statistic 7.321
## Degrees of freedom 1
## P-value (Chi-square) 0.007
##
## Parameter Estimates:
##
## Standard Errors Bootstrap
## Number of requested bootstrap draws 1000
## Number of successful bootstrap draws 1000
##
## Regressions:
## Estimate Std.Err z-value P(>|z|)
## M_TRANSPORT ~
## COND_SCRIP (a) 0.211 0.078 2.694 0.007
## M_COUNTER ~
## M_TRANSPOR (b) -1.011 0.089 -11.321 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .M_TRANSPORT 0.302 0.030 10.190 0.000
## .M_COUNTER 0.673 0.064 10.524 0.000
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|)
## ind_total -0.214 0.083 -2.588 0.010print(boot.fit.3)## lhs op rhs label est se z pvalue
## 1 M_TRANSPORT ~ COND_SCRIPT a 0.211 0.078 2.694 0.007
## 2 M_COUNTER ~ M_TRANSPORT b -1.011 0.089 -11.321 0.000
## 3 M_TRANSPORT ~~ M_TRANSPORT 0.302 0.030 10.190 0.000
## 4 M_COUNTER ~~ M_COUNTER 0.673 0.064 10.524 0.000
## 5 COND_SCRIPT ~~ COND_SCRIPT 0.250 0.000 NA NA
## 6 ind_total := a*b ind_total -0.214 0.083 -2.588 0.010
## ci.lower ci.upper
## 1 0.055 0.370
## 2 -1.192 -0.827
## 3 0.250 0.373
## 4 0.554 0.810
## 5 0.250 0.250
## 6 -0.388 -0.0595. Exploratory Analysis
Hiring experience moderating persuasion effects?
lm1.0 <- lm(CHANGE_GENATTITDE~M_HIREEXPERIENCE+CURRHIRE, data = df.clean)
lm1.0 <- lm(CHANGE_GENATTITDE~M_HIREEXPERIENCE*COND_SCRIPT+CURRHIRE*COND_SCRIPT, data = df.clean)
apa.reg.table(lm1.0)##
##
## Regression results using CHANGE_GENATTITDE as the criterion
##
##
## Predictor b b_95%_CI sr2 sr2_95%_CI
## (Intercept) 0.89** [0.28, 1.50]
## M_HIREEXPERIENCE -0.09 [-0.26, 0.08] .00 [-.01, .02]
## COND_SCRIPT 0.39 [-0.48, 1.26] .00 [-.01, .02]
## CURRHIRE -0.08 [-0.21, 0.05] .01 [-.01, .03]
## M_HIREEXPERIENCE:COND_SCRIPT 0.20 [-0.03, 0.44] .01 [-.02, .04]
## COND_SCRIPT:CURRHIRE -0.23* [-0.41, -0.05] .03 [-.01, .07]
##
##
##
## Fit
##
##
##
##
##
##
## R2 = .151**
## 95% CI[.05,.22]
##
##
## Note. A significant b-weight indicates the semi-partial correlation is also significant.
## b represents unstandardized regression weights.
## sr2 represents the semi-partial correlation squared.
## Square brackets are used to enclose the lower and upper limits of a confidence interval.
## * indicates p < .05. ** indicates p < .01.
##