Belonging Pilot 2 Analyses
Samantha Grayson
2026-05-21
Load packages and data
library(qualtRics)
library(tidyverse)## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ dplyr 1.1.4 ✔ readr 2.1.5
## ✔ forcats 1.0.0 ✔ stringr 1.5.1
## ✔ ggplot2 3.5.1 ✔ tibble 3.2.1
## ✔ lubridate 1.9.4 ✔ tidyr 1.3.1
## ✔ purrr 1.0.4
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errorslibrary(psych) # for reliability##
## Attaching package: 'psych'
##
## The following objects are masked from 'package:ggplot2':
##
## %+%, alphalibrary(broom) # for tidy model outputs
df <- read_survey("~/Google drive/My Drive/YEAR 3/PROJECTS/DANIEL/Belonging/belonging_pilot2.csv")##
## ── Column specification ────────────────────────────────────────────────────────
## cols(
## .default = col_double(),
## StartDate = col_character(),
## EndDate = col_character(),
## IPAddress = col_character(),
## RecordedDate = col_character(),
## ResponseId = col_character(),
## RecipientLastName = col_logical(),
## RecipientFirstName = col_logical(),
## RecipientEmail = col_logical(),
## ExternalReference = col_logical(),
## DistributionChannel = col_character(),
## UserLanguage = col_character(),
## open_1 = col_character(),
## open_2 = col_character(),
## open_3 = col_character(),
## industry = col_character(),
## attn = col_character(),
## attn_bots = col_character(),
## gender_4_TEXT = col_logical(),
## race = col_number(),
## race_8_TEXT = col_logical()
## # ... with 17 more columns
## )
## ℹ Use `spec()` for the full column specifications.df_clean <- df %>%
filter(attn == 24)Demographic overview
Sample
table(df_clean$gender)##
## 1 2
## 64 35table(df_clean$race)##
## 1 2 3 4 5 8 9 14 15 17 23 156
## 63 12 5 1 6 1 2 1 4 2 1 1table(df_clean$ses)##
## 1 2 3 4 5 6
## 2 10 47 13 25 2table(df_clean$income_now)##
## 1 2 3 4 5 6 7
## 1 8 16 30 16 21 7table(df_clean$employment)##
## 1 2
## 98 1mean(df_clean$age, na.rm = T)## [1] 40.09091Team info
table(df_clean$team_info)##
## 1 2
## 94 51 = current team 2 = past team
Current
mean(df_clean$team_size_current, na.rm = T)## [1] 9.606383Former
mean(df_clean$team_size_former, na.rm = T)## [1] 7.8Clean data
Reverse coding
df_clean <- df_clean %>%
mutate(across(ends_with("R"),
~ 8 - .)) # overwrite directly (simpler)Create composites
df_scales <- df_clean %>%
mutate(
interactional_justice = rowMeans(select(., starts_with("colquitt_")), na.rm = TRUE),
personal_treatment = rowMeans(select(., starts_with("treat_")), na.rm = TRUE),
idea_inclusion = rowMeans(select(., starts_with("idea_")), na.rm = TRUE),
belonging = rowMeans(select(., starts_with("belong_")), na.rm = TRUE),
intellectual_humility = rowMeans(select(., starts_with("hum_")), na.rm = TRUE),
needtobelong = rowMeans(select(., starts_with("ntb_")), na.rm = TRUE),
needforaffiliation = rowMeans(select(., starts_with("IOS_")), na.rm = TRUE)
)Check reliability
psych::alpha(df_scales %>% select(starts_with("colquitt_")))##
## Reliability analysis
## Call: psych::alpha(x = df_scales %>% select(starts_with("colquitt_")))
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.86 0.87 0.86 0.63 6.8 0.023 5.8 0.97 0.63
##
## 95% confidence boundaries
## lower alpha upper
## Feldt 0.81 0.86 0.9
## Duhachek 0.81 0.86 0.9
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## colquitt_1 0.85 0.86 0.85 0.68 6.3 0.028 0.029 0.61
## colquitt_2 0.78 0.79 0.74 0.56 3.9 0.037 0.014 0.61
## colquitt_3 0.76 0.79 0.73 0.55 3.7 0.040 0.015 0.55
## colquitt_4 0.89 0.89 0.87 0.73 8.1 0.018 0.015 0.67
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## colquitt_1 99 0.77 0.81 0.70 0.65 6.1 0.9
## colquitt_2 99 0.90 0.91 0.91 0.81 5.9 1.1
## colquitt_3 99 0.92 0.92 0.92 0.85 5.9 1.1
## colquitt_4 99 0.80 0.76 0.62 0.59 5.6 1.4
##
## Non missing response frequency for each item
## 1 2 3 4 5 6 7 miss
## colquitt_1 0.01 0.00 0.00 0.02 0.16 0.51 0.30 0
## colquitt_2 0.01 0.02 0.00 0.07 0.15 0.44 0.30 0
## colquitt_3 0.01 0.01 0.03 0.03 0.17 0.46 0.28 0
## colquitt_4 0.02 0.04 0.04 0.04 0.23 0.37 0.25 0psych::alpha(df_scales %>% select(starts_with("treat_")))##
## Reliability analysis
## Call: psych::alpha(x = df_scales %>% select(starts_with("treat_")))
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.89 0.9 0.92 0.56 8.9 0.017 5.6 0.98 0.54
##
## 95% confidence boundaries
## lower alpha upper
## Feldt 0.85 0.89 0.92
## Duhachek 0.85 0.89 0.92
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## treat_1 0.88 0.90 0.91 0.59 8.7 0.017 0.0083 0.57
## treat_2 0.86 0.88 0.89 0.55 7.3 0.020 0.0120 0.54
## treat_3 0.86 0.88 0.89 0.55 7.2 0.022 0.0149 0.53
## treat_4 0.86 0.88 0.89 0.55 7.3 0.020 0.0125 0.54
## treat_5 0.87 0.88 0.90 0.55 7.5 0.019 0.0111 0.53
## treat_6 0.87 0.88 0.90 0.56 7.7 0.019 0.0157 0.54
## treat_7 0.87 0.89 0.91 0.56 7.7 0.019 0.0128 0.57
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## treat_1 99 0.75 0.70 0.65 0.62 5.1 1.63
## treat_2 99 0.81 0.81 0.80 0.73 5.6 1.31
## treat_3 99 0.86 0.83 0.80 0.77 5.2 1.60
## treat_4 99 0.82 0.81 0.79 0.74 5.6 1.24
## treat_5 99 0.75 0.80 0.78 0.69 6.1 0.81
## treat_6 99 0.76 0.78 0.75 0.68 6.1 1.04
## treat_7 99 0.74 0.78 0.74 0.66 5.8 1.05
##
## Non missing response frequency for each item
## 1 2 3 4 5 6 7 miss
## treat_1 0.04 0.07 0.03 0.17 0.22 0.26 0.20 0
## treat_2 0.01 0.05 0.01 0.03 0.29 0.34 0.26 0
## treat_3 0.04 0.05 0.06 0.13 0.16 0.37 0.18 0
## treat_4 0.01 0.03 0.02 0.07 0.22 0.41 0.23 0
## treat_5 0.00 0.00 0.00 0.06 0.10 0.53 0.31 0
## treat_6 0.01 0.01 0.00 0.04 0.13 0.44 0.36 0
## treat_7 0.00 0.02 0.02 0.05 0.16 0.49 0.25 0psych::alpha(df_scales %>% select(starts_with("idea_")))## Number of categories should be increased in order to count frequencies.## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was done## In smc, smcs < 0 were set to .0## In smc, smcs < 0 were set to .0##
## Reliability analysis
## Call: psych::alpha(x = df_scales %>% select(starts_with("idea_")))
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.93 0.94 0.93 0.64 16 0.011 5.6 1 0.68
##
## 95% confidence boundaries
## lower alpha upper
## Feldt 0.91 0.93 0.95
## Duhachek 0.91 0.93 0.95
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## idea_1 0.91 0.93 0.98 0.62 13 0.0137 0.033 0.66
## idea_2 0.92 0.94 0.97 0.65 15 0.0126 0.037 0.69
## idea_3 0.92 0.93 0.98 0.63 13 0.0133 0.037 0.67
## idea_4 0.92 0.93 0.98 0.63 14 0.0131 0.038 0.67
## idea_5 0.92 0.93 0.98 0.63 14 0.0131 0.035 0.67
## idea_6 0.92 0.93 0.98 0.63 14 0.0133 0.035 0.67
## idea_7 0.93 0.94 0.98 0.66 15 0.0122 0.037 0.70
## idea_8R 0.95 0.95 0.96 0.72 21 0.0074 0.010 0.71
## idea_inclusion 0.91 0.92 0.93 0.59 12 0.0143 0.030 0.66
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## idea_1 99 0.89 0.90 0.91 0.86 5.6 1.2
## idea_2 99 0.80 0.80 0.77 0.74 5.6 1.3
## idea_3 99 0.86 0.87 0.87 0.82 5.7 1.2
## idea_4 99 0.84 0.85 0.84 0.80 5.6 1.1
## idea_5 99 0.85 0.86 0.86 0.81 5.6 1.2
## idea_6 99 0.86 0.86 0.86 0.81 5.6 1.3
## idea_7 99 0.75 0.76 0.73 0.69 5.5 1.1
## idea_8R 99 0.55 0.52 0.42 0.40 5.3 1.7
## idea_inclusion 99 1.00 1.00 0.90 1.00 5.6 1.0psych::alpha(df_scales %>% select(starts_with("belong_")))##
## Reliability analysis
## Call: psych::alpha(x = df_scales %>% select(starts_with("belong_")))
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.97 0.97 0.97 0.81 35 0.0043 5.5 1.3 0.81
##
## 95% confidence boundaries
## lower alpha upper
## Feldt 0.96 0.97 0.98
## Duhachek 0.96 0.97 0.98
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## belong_1 0.97 0.97 0.97 0.81 29 0.0052 0.0036 0.79
## belong_2R 0.97 0.97 0.97 0.83 34 0.0045 0.0033 0.84
## belong_3 0.97 0.97 0.97 0.81 31 0.0049 0.0040 0.83
## belong_4R 0.97 0.97 0.97 0.83 35 0.0044 0.0031 0.84
## belong_5 0.97 0.97 0.97 0.80 28 0.0053 0.0033 0.79
## belong_6R 0.97 0.97 0.97 0.81 29 0.0052 0.0038 0.79
## belong_7 0.97 0.97 0.97 0.81 29 0.0052 0.0030 0.79
## belong_8R 0.97 0.97 0.97 0.81 29 0.0053 0.0039 0.78
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## belong_1 99 0.93 0.94 0.93 0.91 5.4 1.5
## belong_2R 99 0.87 0.87 0.84 0.83 5.6 1.5
## belong_3 99 0.90 0.91 0.89 0.88 5.7 1.3
## belong_4R 99 0.86 0.86 0.83 0.82 5.7 1.4
## belong_5 99 0.94 0.95 0.94 0.93 5.5 1.4
## belong_6R 99 0.93 0.93 0.93 0.91 5.4 1.5
## belong_7 99 0.93 0.93 0.93 0.91 5.4 1.4
## belong_8R 99 0.94 0.93 0.93 0.92 5.4 1.6
##
## Non missing response frequency for each item
## 1 2 3 4 5 6 7 miss
## belong_1 0.03 0.04 0.04 0.07 0.23 0.35 0.23 0
## belong_2R 0.03 0.02 0.09 0.03 0.12 0.43 0.27 0
## belong_3 0.02 0.02 0.03 0.05 0.20 0.43 0.24 0
## belong_4R 0.03 0.01 0.07 0.04 0.15 0.39 0.30 0
## belong_5 0.02 0.03 0.06 0.03 0.29 0.33 0.23 0
## belong_6R 0.03 0.02 0.10 0.06 0.19 0.34 0.25 0
## belong_7 0.02 0.04 0.06 0.05 0.22 0.39 0.21 0
## belong_8R 0.03 0.05 0.07 0.06 0.12 0.41 0.25 0psych::alpha(df_scales %>% select(starts_with("hum_")))##
## Reliability analysis
## Call: psych::alpha(x = df_scales %>% select(starts_with("hum_")))
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.83 0.84 0.85 0.47 5.3 0.026 5.8 0.72 0.47
##
## 95% confidence boundaries
## lower alpha upper
## Feldt 0.77 0.83 0.88
## Duhachek 0.78 0.83 0.88
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## hum_1 0.80 0.81 0.80 0.46 4.3 0.033 0.0219 0.51
## hum_2 0.81 0.81 0.79 0.46 4.3 0.030 0.0128 0.46
## hum_3 0.81 0.82 0.81 0.47 4.4 0.030 0.0180 0.46
## hum_4 0.78 0.80 0.79 0.45 4.0 0.034 0.0200 0.43
## hum_5 0.79 0.80 0.80 0.45 4.0 0.033 0.0222 0.43
## hum_6 0.84 0.85 0.84 0.54 5.8 0.025 0.0095 0.53
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## hum_1 99 0.79 0.76 0.71 0.65 5.6 1.17
## hum_2 99 0.73 0.77 0.73 0.63 6.1 0.77
## hum_3 99 0.71 0.75 0.69 0.60 6.1 0.77
## hum_4 99 0.81 0.80 0.76 0.70 5.7 1.03
## hum_5 99 0.79 0.80 0.75 0.68 6.0 0.97
## hum_6 99 0.64 0.60 0.48 0.45 5.5 1.12
##
## Non missing response frequency for each item
## 2 3 4 5 6 7 miss
## hum_1 0.03 0.03 0.07 0.24 0.41 0.21 0
## hum_2 0.00 0.00 0.02 0.19 0.47 0.31 0
## hum_3 0.00 0.00 0.02 0.18 0.45 0.34 0
## hum_4 0.02 0.00 0.08 0.25 0.42 0.22 0
## hum_5 0.02 0.01 0.01 0.17 0.48 0.30 0
## hum_6 0.03 0.01 0.13 0.24 0.43 0.15 0psych::alpha(df_scales %>% select(starts_with("ntb_")))##
## Reliability analysis
## Call: psych::alpha(x = df_scales %>% select(starts_with("ntb_")))
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.85 0.86 0.88 0.37 5.9 0.022 4 1.1 0.35
##
## 95% confidence boundaries
## lower alpha upper
## Feldt 0.81 0.85 0.89
## Duhachek 0.81 0.85 0.90
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## ntb_1R 0.84 0.84 0.86 0.37 5.2 0.024 0.019 0.34
## ntb_2 0.84 0.84 0.87 0.38 5.4 0.024 0.024 0.34
## ntb_3R 0.85 0.85 0.87 0.39 5.8 0.022 0.019 0.38
## ntb_4 0.85 0.85 0.86 0.38 5.5 0.023 0.020 0.38
## ntb_5 0.85 0.85 0.87 0.39 5.7 0.023 0.021 0.36
## ntb_6 0.84 0.84 0.86 0.38 5.4 0.024 0.022 0.38
## ntb_7R 0.85 0.85 0.87 0.39 5.9 0.022 0.021 0.39
## ntb_8 0.83 0.83 0.85 0.35 4.8 0.026 0.019 0.33
## ntb_9 0.82 0.83 0.85 0.34 4.7 0.027 0.017 0.32
## ntb_10 0.83 0.83 0.85 0.36 5.0 0.025 0.018 0.34
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## ntb_1R 99 0.69 0.69 0.66 0.60 3.5 1.6
## ntb_2 99 0.64 0.64 0.58 0.54 4.6 1.7
## ntb_3R 99 0.57 0.56 0.49 0.45 3.8 1.7
## ntb_4 99 0.61 0.61 0.57 0.50 5.2 1.6
## ntb_5 99 0.55 0.58 0.52 0.46 5.2 1.2
## ntb_6 99 0.65 0.64 0.59 0.54 3.3 1.7
## ntb_7R 99 0.55 0.54 0.46 0.42 3.6 1.8
## ntb_8 99 0.78 0.78 0.77 0.71 3.6 1.6
## ntb_9 99 0.81 0.81 0.81 0.75 3.7 1.7
## ntb_10 99 0.73 0.74 0.72 0.65 3.5 1.7
##
## Non missing response frequency for each item
## 1 2 3 4 5 6 7 miss
## ntb_1R 0.09 0.20 0.29 0.15 0.14 0.08 0.04 0
## ntb_2 0.06 0.07 0.11 0.19 0.20 0.25 0.11 0
## ntb_3R 0.07 0.19 0.21 0.17 0.16 0.12 0.07 0
## ntb_4 0.05 0.04 0.07 0.11 0.15 0.38 0.19 0
## ntb_5 0.02 0.01 0.05 0.14 0.29 0.37 0.11 0
## ntb_6 0.13 0.27 0.19 0.13 0.12 0.10 0.05 0
## ntb_7R 0.14 0.20 0.16 0.12 0.15 0.20 0.02 0
## ntb_8 0.09 0.17 0.24 0.19 0.16 0.08 0.06 0
## ntb_9 0.08 0.22 0.19 0.19 0.14 0.11 0.06 0
## ntb_10 0.12 0.17 0.25 0.15 0.19 0.04 0.07 0psych::alpha(df_scales %>% select(starts_with("IOS_")))##
## Reliability analysis
## Call: psych::alpha(x = df_scales %>% select(starts_with("IOS_")))
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.84 0.84 0.88 0.39 5.1 0.025 4.2 1.2 0.38
##
## 95% confidence boundaries
## lower alpha upper
## Feldt 0.78 0.84 0.88
## Duhachek 0.79 0.84 0.89
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## IOS_emo_1 0.82 0.82 0.86 0.39 4.4 0.029 0.036 0.38
## IOS_emo_2 0.80 0.80 0.84 0.36 4.0 0.031 0.036 0.33
## IOS_attn_1 0.80 0.80 0.85 0.36 3.9 0.032 0.036 0.37
## IOS_attn_2 0.82 0.82 0.87 0.39 4.5 0.028 0.037 0.38
## IOS_pos_1 0.83 0.83 0.85 0.41 5.0 0.026 0.024 0.41
## IOS_pos_2 0.83 0.82 0.85 0.40 4.7 0.027 0.032 0.38
## IOS_compare_1 0.82 0.82 0.87 0.39 4.6 0.028 0.036 0.38
## IOS_compare_2 0.83 0.83 0.86 0.40 4.7 0.027 0.027 0.38
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## IOS_emo_1 99 0.71 0.69 0.65 0.58 4.1 1.9
## IOS_emo_2 99 0.79 0.78 0.76 0.70 3.8 1.8
## IOS_attn_1 99 0.80 0.80 0.78 0.72 3.8 1.8
## IOS_attn_2 99 0.67 0.67 0.62 0.55 4.4 1.6
## IOS_pos_1 99 0.57 0.58 0.55 0.44 4.9 1.6
## IOS_pos_2 99 0.63 0.64 0.61 0.51 4.6 1.6
## IOS_compare_1 99 0.66 0.66 0.60 0.54 3.8 1.7
## IOS_compare_2 99 0.63 0.63 0.58 0.50 4.1 1.7
##
## Non missing response frequency for each item
## 1 2 3 4 5 6 7 miss
## IOS_emo_1 0.12 0.15 0.10 0.17 0.20 0.12 0.13 0
## IOS_emo_2 0.15 0.14 0.14 0.17 0.19 0.14 0.06 0
## IOS_attn_1 0.12 0.20 0.09 0.15 0.24 0.15 0.04 0
## IOS_attn_2 0.07 0.10 0.06 0.22 0.23 0.25 0.06 0
## IOS_pos_1 0.05 0.07 0.07 0.12 0.27 0.28 0.13 0
## IOS_pos_2 0.07 0.07 0.09 0.16 0.29 0.23 0.08 0
## IOS_compare_1 0.13 0.17 0.10 0.19 0.25 0.11 0.04 0
## IOS_compare_2 0.09 0.12 0.18 0.13 0.26 0.13 0.08 0All alphas are above 0.80. Looks good to me!
Summary stats
df_scales %>%
summarise(
across(c(interactional_justice,
personal_treatment,
idea_inclusion,
belonging,
intellectual_humility,
needtobelong,
needforaffiliation),
list(mean = ~mean(.x, na.rm = TRUE),
sd = ~sd(.x, na.rm = TRUE)))
)## # A tibble: 1 × 14
## interactional_justice_mean interactional_justice_sd personal_treatment_mean
## <dbl> <dbl> <dbl>
## 1 5.84 0.970 5.64
## # ℹ 11 more variables: personal_treatment_sd <dbl>, idea_inclusion_mean <dbl>,
## # idea_inclusion_sd <dbl>, belonging_mean <dbl>, belonging_sd <dbl>,
## # intellectual_humility_mean <dbl>, intellectual_humility_sd <dbl>,
## # needtobelong_mean <dbl>, needtobelong_sd <dbl>,
## # needforaffiliation_mean <dbl>, needforaffiliation_sd <dbl>Correl matrix
df_scales %>%
select(interactional_justice,
personal_treatment,
idea_inclusion,
belonging,
intellectual_humility,
needtobelong,
needforaffiliation
) %>%
cor(use = "pairwise.complete.obs")## interactional_justice personal_treatment idea_inclusion
## interactional_justice 1.00000000 0.69440223 0.72573686
## personal_treatment 0.69440223 1.00000000 0.80359876
## idea_inclusion 0.72573686 0.80359876 1.00000000
## belonging 0.62771833 0.82079792 0.69866017
## intellectual_humility 0.05601992 0.20639112 0.14192196
## needtobelong 0.07353745 0.01681903 0.02358824
## needforaffiliation 0.25004916 0.30477319 0.26119501
## belonging intellectual_humility needtobelong
## interactional_justice 0.62771833 0.05601992 0.07353745
## personal_treatment 0.82079792 0.20639112 0.01681903
## idea_inclusion 0.69866017 0.14192196 0.02358824
## belonging 1.00000000 0.10849534 -0.02775247
## intellectual_humility 0.10849534 1.00000000 -0.04171387
## needtobelong -0.02775247 -0.04171387 1.00000000
## needforaffiliation 0.28073499 -0.07640614 0.51223861
## needforaffiliation
## interactional_justice 0.25004916
## personal_treatment 0.30477319
## idea_inclusion 0.26119501
## belonging 0.28073499
## intellectual_humility -0.07640614
## needtobelong 0.51223861
## needforaffiliation 1.00000000Testing our model
Path 1: Personal treatment → Belonging
model1 <- lm(belonging ~ interactional_justice + personal_treatment,
data = df_scales)
summary(model1)##
## Call:
## lm(formula = belonging ~ interactional_justice + personal_treatment,
## data = df_scales)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.2370 -0.1752 0.0997 0.4509 1.8965
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.0827 0.4985 -2.172 0.0323 *
## interactional_justice 0.1532 0.1102 1.390 0.1676
## personal_treatment 1.0107 0.1091 9.267 5.59e-15 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7616 on 96 degrees of freedom
## Multiple R-squared: 0.6802, Adjusted R-squared: 0.6735
## F-statistic: 102.1 on 2 and 96 DF, p-value: < 2.2e-16library(ggplot2)
ggplot(df_scales, aes(x = personal_treatment, y = belonging)) +
geom_point(alpha = .6) +
geom_smooth(method = "lm", se = TRUE) +
labs(
x = "Personal Treatment",
y = "Belonging",
title = "Path 1: Personal Treatment → Belonging"
) +
theme_minimal()## `geom_smooth()` using formula = 'y ~ x'
ggplot(df_scales, aes(x = interactional_justice, y = belonging)) +
geom_point(alpha = .6) +
geom_smooth(method = "lm", se = TRUE) +
labs(
x = "Interactional Justice",
y = "Belonging",
title = "Interactional Justice → Belonging"
) +
theme_minimal()## `geom_smooth()` using formula = 'y ~ x'
Path 2: Felt idea inclusion → Belonging
model2 <- lm(belonging ~ idea_inclusion,
data = df_scales)
summary(model2)##
## Call:
## lm(formula = belonging ~ idea_inclusion, data = df_scales)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.7567 -0.3120 0.0814 0.4841 4.0366
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.36088 0.54438 0.663 0.509
## idea_inclusion 0.92628 0.09631 9.618 8.98e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9585 on 97 degrees of freedom
## Multiple R-squared: 0.4881, Adjusted R-squared: 0.4828
## F-statistic: 92.5 on 1 and 97 DF, p-value: 8.976e-16ggplot(df_scales, aes(x = idea_inclusion, y = belonging)) +
geom_point(alpha = .6) +
geom_smooth(method = "lm", se = TRUE) +
labs(
x = "Felt Idea Inclusion",
y = "Belonging",
title = "Path 2: Idea Inclusion → Belonging"
) +
theme_minimal()## `geom_smooth()` using formula = 'y ~ x'
What about both personal treatment and idea inclusion in the same model?
model_full <- lm(belonging ~ interactional_justice +
personal_treatment +
idea_inclusion,
data = df_scales)
summary(model_full)##
## Call:
## lm(formula = belonging ~ interactional_justice + personal_treatment +
## idea_inclusion, data = df_scales)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.3049 -0.2150 0.0956 0.4301 2.0821
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.10577 0.50136 -2.206 0.0298 *
## interactional_justice 0.12299 0.12010 1.024 0.3084
## personal_treatment 0.95724 0.13743 6.965 4.25e-10 ***
## idea_inclusion 0.09001 0.14017 0.642 0.5223
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7639 on 95 degrees of freedom
## Multiple R-squared: 0.6815, Adjusted R-squared: 0.6715
## F-statistic: 67.77 on 3 and 95 DF, p-value: < 2.2e-16Personal treatment is a stronger predictor of belonging. In our first pilot, both came out as significant…
Moderation analyses
Intellectual humility
model3 <- lm(belonging ~ idea_inclusion * intellectual_humility,
data = df_scales)
summary(model3)##
## Call:
## lm(formula = belonging ~ idea_inclusion * intellectual_humility,
## data = df_scales)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.6951 -0.3601 0.0997 0.5663 3.1666
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -8.5720 4.5305 -1.892 0.06153 .
## idea_inclusion 2.5251 0.8101 3.117 0.00242 **
## intellectual_humility 1.4670 0.7406 1.981 0.05050 .
## idea_inclusion:intellectual_humility -0.2617 0.1315 -1.990 0.04948 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9489 on 95 degrees of freedom
## Multiple R-squared: 0.5087, Adjusted R-squared: 0.4932
## F-statistic: 32.79 on 3 and 95 DF, p-value: 1.233e-14library(interactions)
model3 <- lm(belonging ~ idea_inclusion * intellectual_humility, data = df_scales)interact_plot(model3,
pred = idea_inclusion,
modx = intellectual_humility,
modx.values = c(-1, 1), # ±1 SD
plot.points = TRUE)
Need to belong
model4 <- lm(belonging ~ idea_inclusion * needtobelong,
data = df_scales)
summary(model4)##
## Call:
## lm(formula = belonging ~ idea_inclusion * needtobelong, data = df_scales)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.7370 -0.3586 0.0981 0.4766 4.0250
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.84719 1.87383 1.519 0.132
## idea_inclusion 0.52230 0.32787 1.593 0.114
## needtobelong -0.63347 0.45650 -1.388 0.168
## idea_inclusion:needtobelong 0.10304 0.07967 1.293 0.199
##
## Residual standard error: 0.9583 on 95 degrees of freedom
## Multiple R-squared: 0.4989, Adjusted R-squared: 0.4831
## F-statistic: 31.53 on 3 and 95 DF, p-value: 3.117e-14library(interactions)
model4 <- lm(belonging ~ idea_inclusion * needtobelong, data = df_scales)interact_plot(model4,
pred = idea_inclusion,
modx = needtobelong,
modx.values = c(-1, 1), # ±1 SD
plot.points = TRUE)
Need for affiliation
model5 <- lm(belonging ~ idea_inclusion * needforaffiliation,
data = df_scales)
summary(model5)##
## Call:
## lm(formula = belonging ~ idea_inclusion * needforaffiliation,
## data = df_scales)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.5394 -0.3790 0.0977 0.4979 3.8451
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.56795 1.42670 1.099 0.2745
## idea_inclusion 0.62449 0.25174 2.481 0.0149 *
## needforaffiliation -0.31768 0.38900 -0.817 0.4162
## idea_inclusion:needforaffiliation 0.07643 0.06667 1.146 0.2545
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9521 on 95 degrees of freedom
## Multiple R-squared: 0.5053, Adjusted R-squared: 0.4897
## F-statistic: 32.35 on 3 and 95 DF, p-value: 1.7e-14library(interactions)
model5 <- lm(belonging ~ idea_inclusion * needforaffiliation, data = df_scales)interact_plot(model5,
pred = idea_inclusion,
modx = needforaffiliation,
modx.values = c(-1, 1), # ±1 SD
plot.points = TRUE)