def METHOD_NAME(df):
    """
    Computes the ratio of responses indicating a great deal or very much worry about terrorist attacks
    to responses indicating not at all or not much worry.
    Args:
        df (DataFrame): The input DataFrame.
    Returns:
        DataFrame: A DataFrame with columns: "country", "year", and "great_deal_or_very_much_not_at_all_or_not_much_ratio".
    """
    dict_q1 = {1: "Very much", 2: "A great deal", 3: "Not much", 4: "Not at all", -1: "Don't know", -2: "No answer"}
    # Calculate percentage for worries about a terrorist attack
    counts_q1 = calculate_percentage(df, "worries__a_terrorist_attack", dict_q1)
    # Select relevant columns
    select_df = counts_q1[["country", "year", "percentage", "worries__a_terrorist_attack"]]
    # Pivot the DataFrame
    pivoted_df = pd.pivot(
        select_df, index=["country", "year"], columns="worries__a_terrorist_attack", values="percentage"
    )
    pivoted_df.reset_index(inplace=True)
    pivoted_df.columns.name = None
    # Compute the ratio of great deal or very much to not at all or not much
    pivoted_df["great_deal_or_very_much"] = pivoted_df["A great deal"] + pivoted_df["Very much"]
    pivoted_df["not_at_all_or_not_much"] = pivoted_df["Not at all"] + pivoted_df["Not much"]
    pivoted_df["great_deal_or_very_much_not_at_all_or_not_much_ratio"] = (
        pivoted_df["great_deal_or_very_much"] / pivoted_df["not_at_all_or_not_much"]
    )
    pivoted_df = pivoted_df[
        [
            "country",
            "year",
            "great_deal_or_very_much",
            "not_at_all_or_not_much",
            "great_deal_or_very_much_not_at_all_or_not_much_ratio",
        ]
    ]
    return pivoted_df