added ranking
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tom.hempel
197
analysis_medium_ranking.py
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197
analysis_medium_ranking.py
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"""
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Friedman Test on medium preference rankings.
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Data format: each row = one participant; Rank1/Rank2/Rank3 hold the
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condition name (VR, Chat, Video) assigned to that rank position.
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We reshape so every participant has a numeric rank (1–3) for every
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condition, then run a Friedman test and save a summary plot.
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"""
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import numpy as np
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import pandas as pd
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import matplotlib.pyplot as plt
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import matplotlib.patches as mpatches
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import seaborn as sns
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from pathlib import Path
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from scipy import stats
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# ── 1. Load & reshape ─────────────────────────────────────────────────────────
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df_raw = pd.read_csv("Data/medium_order.csv")
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# Build a long table: (Participant, Condition, Rank)
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records = []
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for _, row in df_raw.iterrows():
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for rank_pos, col in enumerate(["Rank1", "Rank2", "Rank3"], start=1):
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records.append({
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"Participant": row["Participant"],
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"Condition": row[col],
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"Rank": rank_pos,
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})
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df_long = pd.DataFrame(records)
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# Pivot to wide: rows = participants, columns = conditions
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df_wide = df_long.pivot(index="Participant", columns="Condition", values="Rank")
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df_wide = df_wide[["VR", "Chat", "Video"]] # fix column order
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print("=" * 55)
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print("Reshaped ranking matrix (numeric ranks per condition)")
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print("=" * 55)
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print(df_wide.to_string())
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print()
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# ── 2. Descriptive statistics ─────────────────────────────────────────────────
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desc = df_wide.agg(["mean", "median", "std"]).T
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desc.index.name = "Condition"
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desc.columns = ["Mean rank", "Median rank", "SD"]
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print("=" * 55)
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print("Descriptive statistics (lower rank = more preferred)")
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print("=" * 55)
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print(desc.round(3).to_string())
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print()
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# ── 3. Friedman test ──────────────────────────────────────────────────────────
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# scipy expects one array per group (condition), each of length n_participants
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statistic, p_value = stats.friedmanchisquare(
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df_wide["VR"],
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df_wide["Chat"],
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df_wide["Video"],
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)
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n = len(df_wide)
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k = 3 # number of conditions
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df_friedman = k - 1 # degrees of freedom
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# Kendall's W (effect size)
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W = statistic / (n * (k - 1))
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print("=" * 55)
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print("Friedman test")
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print("=" * 55)
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print(f" N (participants) : {n}")
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print(f" k (conditions) : {k}")
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print(f" chi2({df_friedman}) : {statistic:.4f}")
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print(f" p-value : {p_value:.4f}")
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print(f" Kendall's W : {W:.4f}")
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print()
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if p_value < 0.05:
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print(" --> Significant difference in rankings (p < .05).")
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else:
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print(" --> No significant difference in rankings (p >= .05).")
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print()
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# ── 4. Post-hoc: Wilcoxon signed-rank tests (Bonferroni-corrected) ────────────
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from itertools import combinations
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pairs = list(combinations(["VR", "Chat", "Video"], 2))
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n_pairs = len(pairs)
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alpha_corr = 0.05 / n_pairs # Bonferroni threshold
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print("=" * 55)
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print(f"Post-hoc: Wilcoxon signed-rank tests")
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print(f"(Bonferroni-corrected alpha = {alpha_corr:.4f})")
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print("=" * 55)
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posthoc_rows = []
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for a, b in pairs:
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stat_w, p_w = stats.wilcoxon(df_wide[a], df_wide[b])
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sig = "*" if p_w < alpha_corr else ""
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posthoc_rows.append({
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"Pair": f"{a} vs {b}",
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"W statistic": round(stat_w, 4),
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"p (raw)": round(p_w, 4),
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"p (x3)": round(min(p_w * n_pairs, 1.0), 4),
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"Sig.": sig,
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})
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df_posthoc = pd.DataFrame(posthoc_rows).set_index("Pair")
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print(df_posthoc.to_string())
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print(f"\n * Significant after Bonferroni correction (alpha = {alpha_corr:.4f})")
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# ── 5. Plot ───────────────────────────────────────────────────────────────────
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CONDITIONS = ["VR", "Chat", "Video"]
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MED_COLORS = {"Chat": "#42A5F5", "Video": "#FFA726", "VR": "#66BB6A"}
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RANK_COLORS = ["#4CAF50", "#FFC107", "#F44336"] # 1st, 2nd, 3rd
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sns.set_theme(style="whitegrid", font_scale=1.05)
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plt.rcParams["figure.dpi"] = 150
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plt.rcParams["savefig.bbox"] = "tight"
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fig, axes = plt.subplots(1, 2, figsize=(13, 5))
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# ── Left panel: mean rank + individual jitter ─────────────────────────────────
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ax = axes[0]
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x_pos = np.arange(len(CONDITIONS))
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for i, cond in enumerate(CONDITIONS):
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vals = df_wide[cond].values
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jitter = np.random.default_rng(42).uniform(-0.12, 0.12, size=len(vals))
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ax.scatter(np.full(len(vals), i) + jitter, vals,
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color=MED_COLORS[cond], alpha=0.55, s=40, zorder=3)
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means = [df_wide[c].mean() for c in CONDITIONS]
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sems = [df_wide[c].sem() for c in CONDITIONS]
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bars = ax.bar(x_pos, means, yerr=sems, capsize=5,
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color=[MED_COLORS[c] for c in CONDITIONS],
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edgecolor="gray", linewidth=0.6, alpha=0.75, width=0.5, zorder=2)
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for i, (m, s) in enumerate(zip(means, sems)):
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ax.text(i, m + s + 0.08, f"M={m:.2f}", ha="center", fontsize=10, fontweight="bold")
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ax.set_xticks(x_pos)
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ax.set_xticklabels(CONDITIONS, fontsize=12)
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ax.set_ylim(0.5, 3.8)
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ax.set_yticks([1, 2, 3])
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ax.set_yticklabels(["1st\n(most preferred)", "2nd", "3rd\n(least preferred)"], fontsize=9)
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ax.set_ylabel("Rank (lower = more preferred)", fontsize=11)
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ax.set_title("Mean Rank per Condition\n(individual observations + SEM)", fontsize=11, fontweight="bold")
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stat_label = (
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f"Friedman: chi2({df_friedman}) = {statistic:.2f}, "
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f"p = {p_value:.3f}, W = {W:.2f}"
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)
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ax.text(0.5, 0.03, stat_label, transform=ax.transAxes,
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ha="center", va="bottom", fontsize=8.5, color="dimgray",
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bbox=dict(boxstyle="round,pad=0.3", fc="white", ec="lightgray", alpha=0.8))
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# ── Right panel: stacked rank-distribution bars ───────────────────────────────
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ax = axes[1]
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n_participants = len(df_wide)
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rank_counts = {
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cond: [(df_wide[cond] == r).sum() / n_participants * 100 for r in [1, 2, 3]]
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for cond in CONDITIONS
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}
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bottoms = np.zeros(len(CONDITIONS))
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for rank_idx, (rank_label, color) in enumerate(
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zip(["1st choice", "2nd choice", "3rd choice"], RANK_COLORS)
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):
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heights = [rank_counts[c][rank_idx] for c in CONDITIONS]
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bars = ax.bar(x_pos, heights, bottom=bottoms,
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color=color, edgecolor="white", linewidth=0.8,
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width=0.55, label=rank_label)
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for xi, (h, b) in enumerate(zip(heights, bottoms)):
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if h >= 8:
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ax.text(xi, b + h / 2, f"{h:.0f}%",
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ha="center", va="center", fontsize=10,
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fontweight="bold", color="white")
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bottoms += np.array(heights)
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ax.set_xticks(x_pos)
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ax.set_xticklabels(CONDITIONS, fontsize=12)
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ax.set_ylim(0, 105)
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ax.set_ylabel("Percentage of participants (%)", fontsize=11)
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ax.set_title("Rank Distribution per Condition\n(% participants assigning each rank)", fontsize=11, fontweight="bold")
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ax.legend(loc="upper right", fontsize=9,
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handles=[mpatches.Patch(color=c, label=l)
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for c, l in zip(RANK_COLORS, ["1st choice", "2nd choice", "3rd choice"])])
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fig.suptitle("Medium Preference Rankings (N=18, within-subjects)", fontsize=13, fontweight="bold")
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fig.tight_layout()
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out_path = Path("Data/plots_questionnaires/Q14_medium_ranking.png")
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fig.savefig(out_path)
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plt.close(fig)
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print(f"\nPlot saved: {out_path}")
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