Data analysis code

Question 1

What does axis=1 do in a DataFrame operation?

Answer 1

It moves along rows (horizontally)

Question 2

What does axis=0 do in a DataFrame operation?

Answer 2

It moves down columns (vertically).

Question 3

What is the purpose of the Shapiro-Wilk test?

Answer 3

It tests whether the data is normally distributed.

Question 4

What is the interpretation of a p-value greater than 0.05 in the Shapiro-Wilk test?

Answer 4

Data is normally distributed; fail to reject the null hypothesis.

Question 5

What does df.shape return?

Answer 5

A tuple with the number of rows and columns: (number of rows, number of columns).

Question 6

What statistics does df.describe() provide?

Answer 6

It provides summary statistics: Count, Mean, Standard Deviation, Minimum, Quartiles (25%, 50%, 75%), and Maximum.

Question 7

What does df.mean() do in a DataFrame?

Answer 7

It computes the mean of each column.

Question 8

How do you access a specific column in a DataFrame?

Answer 8

Use the column name: df[‘column_name’].

Question 9

What does the code df[‘column_name’].max() do?

Answer 9

It returns the maximum value in the specified column.

Question 10

What assumptions does the paired t-test make?

Answer 10

It assumes no major outliers, independent observations, continuous dependent variable, and normally distributed dependent variable.

Question 11

How do you read a CSV file into a DataFrame in Python?

Answer 11

df = pd.read_csv(‘../folder/name.filetype’)

Question 12

How do you read an Excel file into a DataFrame in Python?

Answer 12

df = pd.read_excel(‘file_path’)

Question 13

How do you read a tab-separated file into a DataFrame?

Answer 13

Use the sep=’\t’ parameter in pd.read_csv().

Question 14

How do you handle missing data when reading a file?

Answer 14

Use na_values=’’ to replace ‘’ with NaN.

Question 15

How do you specify the data type for integer columns in a DataFrame?

Answer 15

Use dtype=pd.Int64Dtype() to convert float to integers.

Question 16

How do you rename columns when reading a file into a DataFrame?

Answer 16

Use header=None, names=[‘column1’, ‘column2’, …] when reading the file.

Question 17

How do you skip rows from the top when reading a file?

Answer 17

Use the skiprows=… parameter.

Question 18

How do you skip rows from the bottom when reading a file?

Answer 18

Use the skipfooter=… parameter.

Question 19

How do you set a specific column as the index when reading a file?

Answer 19

Use index_col=1 to set the second column as the index

Question 20

How do you update a specific value in a DataFrame?

Answer 20

Use df.at[‘row_name’, ‘column_name’] = new_value.

Question 21

What does df.info() display?

Answer 21

It displays the number of entries, index range, columns, and non-null count per column.

Question 22

What does the data type float64 represent?

Answer 22

It represents decimal numbers.

Question 23

What does the data type int64 represent?

Answer 23

It represents whole numbers (integers).

Question 24

What does the data type object represent?

Answer 24

It represents strings or words.

Question 25

How do you display the last 5 rows of a DataFrame?

Answer 25

Use df.tail().

Question 26

How do you sort the values in a DataFrame by a specific column?

Answer 26

Use df.sort_values(by=[‘column_name’], ascending=False).

Question 27

How do you drop rows with missing values from a DataFrame?

Answer 27

Use df.dropna(inplace=True).

Question 28

What is the effect of using inplace=True in df.dropna()?

Answer 28

It modifies the original DataFrame.

Question 29

What is the effect of using inplace=False in df.dropna()?

Answer 29

It creates a new DataFrame and leaves the original unchanged.

Question 30

How do you drop columns with missing values from a DataFrame?

Answer 30

Use df.dropna(axis=’columns’, inplace=True)

Question 31

How do you drop rows that have less than 2 non-missing values?

Answer 31

Use df.dropna(thresh=2, inplace=True).

Question 32

How do you drop rows based on missing values in specific columns?

Answer 32

Use df.dropna(subset=[‘column1’, ‘column2’], inplace=True).

Question 33

How do you save a DataFrame as a CSV file?

Answer 33

Use df.to_csv(‘data_name.filetype’, index=False).

Question 34

How do you save a DataFrame as an Excel file?

Answer 34

Use df.to_excel(‘data_name.filetype’, index=False).

Question 35

How do you exclude the index when saving a DataFrame to a file?

Answer 35

Use index=False in the to_csv() or to_excel() methods.

Question 36

How do you add a new column to a DataFrame?

Answer 36

df[‘Column name’] = [‘column contents’, ‘next value’, …]

Question 37

How do you forward-fill NaN values in a column?

Answer 37

df[‘Column name’] = df[‘Column name’].fillna(method=”ffill”)

Question 38

How do you remove a single column from a DataFrame?

Answer 38

df = df.drop(columns=’column name’)

Question 39

How do you remove multiple columns from a DataFrame?

Answer 39

df = df.drop(columns=[‘name 1’, ‘name 2’])

Question 40

How do you remove a specific row by its index?

Answer 40

df = df.drop(row_number)

Question 41

How do you rearrange columns into a custom order?

Answer 41

cols = df.columns.tolist()
cols_new = [cols[1], cols[3], cols[2], cols[0]]
df = df[cols_new]

Question 42

How do you sort the columns alphabetically?

Answer 42

cols_new = sorted(cols) then df = df[cols_new]

Question 43

How do you sort the columns in reverse alphabetical order?

Answer 43

cols_new = sorted(cols, reverse=True) then df = df[cols_new]

Question 44

How do you sort values by multiple columns in descending order?

Answer 44

df = df.sort_values(by=[col1, col2], ascending=False)

Question 45

How do you create a new column by multiplying an existing column by a scalar?

Answer 45

df[‘new column’] = df[‘old column’] * 50

Question 46

How do you apply a logarithmic transformation to a column?

Answer 46

df[‘new column’] = np.log(df[‘old column’])

Question 47

How do you apply a square root transformation to a column?

Answer 47

df[‘new column’] = np.sqrt(df[‘old column’])

Question 48

How do you concatenate two string columns in a DataFrame?

Answer 48

df[‘Soil_Drainage’] = df[‘Soil’] + ‘_’ + df[‘Drainage’]

Question 49

How do you convert numerical data to strings before concatenating?

Answer 49

df[‘new_column’] = df[‘old col’] + ‘_’ + df[‘old col’].astype(str)

Question 50

How do you split a column into multiple columns based on a delimiter?

Answer 50

df[[‘new col1’, ‘new col2’]] = df[‘old_column’].str.split(‘_’, expand=True)

Question 51

How do you limit the number of splits to just once when splitting a column?

Answer 51

df[[‘new col1’, ‘new col2’]] = df[‘old_column’].str.split(‘_’, n=1, expand=True)

Question 52

How do you use a specific substring for splitting a column?

Answer 52

df[[‘new col1’, ‘new col2’]] = df[‘old_column’].str.split(‘_20’, expand=True)

Question 53

How do you remove duplicate rows from a DataFrame?

Answer 53

data = data.drop_duplicates()

Question 54

How do you reset the index after dropping duplicates from a DataFrame?

Answer 54

data = data.drop_duplicates().reset_index(drop=True)

Question 55

How do you transpose a DataFrame to swap rows and columns?

Answer 55

df = df.T (This makes the index the column headers and the column headers the index).

Question 56

How do you reset the index and move it to a column in a DataFrame?

Answer 56

Use df.reset_index(inplace=True) to reset the index, then df = df.drop(columns=’index’) to remove the newly created index column.

Question 57

How do you select a range of rows using iloc in a DataFrame?

Answer 57

f.iloc[1:2] selects rows from position 1 up to but not including position 2.

Question 58

How do you check the data types of each column in a DataFrame?

Answer 58

Use df.dtypes to check the data types of each column.

Question 59

How do you change the data type of a column in a DataFrame?

Answer 59

Use df[‘col number’].astype(type you want) to cast a column to a different type.

Question 60

What is the purpose of melting a DataFrame, and how do you do it?

Answer 60

Melting transforms data from wide form into long form, which is useful for certain types of analysis and visualization. Use pd.melt(dataframe, id_vars, value_vars, var_name=’new_var_name’, value_name=’new_value_name’).

Question 61

What parameters do you need to specify when melting a DataFrame?

Answer 61

id_vars: Columns to keep as is (typically identifiers).
value_vars: Columns containing the values to melt.
var_name: The name for the new variable column.
value_name: The name for the new value column.

Question 62

What is the benefit of melting a DataFrame?

Answer 62

Melting makes the dataset more suitable for graphing and further analysis, especially for visualizing or performing operations on variables in a consistent, long format.

Question 63

What is casting (pivoting) in DataFrame manipulation, and how do you do it?

Answer 63

Pivoting (casting) reverses melting, converting a long-form DataFrame into a wide-form DataFrame by spreading values into new columns. Use pd.pivot(dataframe, columns=’column header’, index=[‘index header,…], values=’data column’).

Question 64

What parameters do you need to specify when pivoting a DataFrame?

Answer 64

columns: The column whose unique values become the new column headers.
index: The column(s) that become the index of the DataFrame.
values: The column containing the data to populate the new table.

Question 65

How do you reset the index after pivoting a DataFrame?

Answer 65

Use df_cast.reset_index(inplace=True) to convert any multi-level index back into regular columns.

Question 66

How do you create a relational plot to show the relationship between two numerical variables?

Answer 66

Use sns.relplot(x=’sepal_length’, y=’petal_length’, data=iris).

Question 67

How do you turn a relational plot into a line plot with a confidence interval?

Answer 67

Add kind=’line’ to the sns.relplot function. The shaded area represents the 95% confidence interval.

Question 68

How do you differentiate points in a relational plot by a categorical variable using color?

Answer 68

Add hue=’column_name’ to the plot, where ‘column_name’ is the categorical variable

Question 69

What does sns.lmplot do?

Answer 69

It creates a scatter plot with a linear regression line and a shaded 95% confidence interval.

Question 70

How do you create a composite plot with both categorical and numerical variables?

Answer 70

Use sns.jointplot(x=’sepal_length’, y=’petal_length’, data=iris) or sns.pairplot(data=iris).

Question 71

How do you create a heatmap in Seaborn?

Answer 71

Use sns.heatmap(data, annot=True, fmt=”.2f”, cmap=”viridis”, cbar=True).

Question 72

How do you create multiple plots side by side?

Answer 72

Use fig, axes = plt.subplots(1, 2, figsize=(10, 5)) for two plots in one row

Question 73

How do you create a distribution plot (histogram) for numerical variables?

Answer 73

Use sns.displot(x=’sepal_length’, data=iris). Add hue or col=’column_name’ for splitting based on a categorical variable.

Question 74

How do you explore relationships between categorical variables using a categorical plot?

Answer 74

Use sns.catplot(x=’Species’, y=’petal_length’, data=iris). You can add swarm or strip for different plot styles.

Question 75

How do you customize violin plots to display both categories of a variable on the same plot?

Answer 75

Add split=True to sns.violinplot to show both categories of the variable in the same plot.

Question 76

How do you set different Seaborn plot styles?

Answer 76

Use sns.set_style(‘style’). Options:

whitegrid: White background with grid
darkgrid: Grey background with grid
dark: Grey background without grid
white: White background without grid

Question 77

How do you suppress the top text on a Seaborn plot?

Answer 77

Always add a semicolon ; at the end of the Seaborn plotting code to suppress text like <seaborn.axisgrid.JointGrid at 0x7fa572bf5b50>.

Question 78

How do you set the context for a Seaborn plot?

Answer 78

Use sns.set_context(‘context’). Options:

paper: Smaller text for publication
notebook: Default for notebooks
talk: Larger for presentations
poster: Largest for posters

Question 79

How do you view and set color palettes in Seaborn?

Answer 79

To view: sns.color_palette(‘color name’)
To set: sns.set_palette(‘color name’) (e.g., sns.set_palette(‘tab10’) for the default color set)

Question 80

How do you reset Seaborn’s default settings?

Answer 80

Use sns.reset_defaults() to reset color and figure size to Seaborn’s default settings

Question 81

How do you control the size of figure-level plots (e.g., relplot, displot)?

Answer 81

Use sns.relplot(x=’’, y=’’, data=…, hue=’’, height=6, aspect=1.5).

height: Plot height in inches
aspect: Aspect ratio (width/height)

Question 82

How do you control the size of axes-level plots (e.g., scatterplot, boxplot)?

Answer 82

Use plt.figure(figsize=(width, height)). Example: plt.figure(figsize=(9, 6)) for 9x6 inches.

Question 83

How do you customize titles and axis labels for multiple plots in Seaborn?

Answer 83

Title: g.fig.suptitle(‘Title’, fontsize=…, y=…)
Axis labels: g.set_axis_labels(‘x label’, ‘y label’, fontsize=…)
Set y-axis limits: g.set(ylim=(0, 8))

Question 84

How do you customize individual plots and legends in Seaborn and Matplotlib?

Answer 84

Title: plt.title(‘Title’, fontsize=…)
Remove legend: plt.legend(False)
Axis labels: plt.xlabel(‘x label’, fontsize=…), plt.ylabel(‘y label’, fontsize=…)
Customize legend: plt.legend(loc=’’, title=’’, frameon=False)

Question 85

How do you save a plot as an image?

Answer 85

Use plt.savefig(‘filename.png’) to save the plot as an image (you can specify other formats like .jpg, .svg, etc.).

Question 86

What are the four types of joins in Pandas?

Answer 86

Outer Join: Combines all rows from both dataframes, including non-overlapping rows.
Inner Join: Includes only rows common to both dataframes.
Left Join: Includes all rows from the left dataframe and matching rows from the right.
Right Join: Includes all rows from the right dataframe and matching rows from the left.

Question 87

How do you combine multiple merge() commands in a single line?

Answer 87

df = dataframe1.merge(dataframe2).merge(dataframe3)

Question 88

How do you specify custom keys for merging dataframes in Pandas?

Answer 88

df = df1.merge(df2, on=’column_name’).merge(df3, left_on=’df1_column’, right_on=’df2_column’)

Question 89

What does pd.concat() do, and what are its key parameters?

Answer 89

Combines multiple datasets into one structure.
Key Parameters:
axis: 0 (vertical) or 1 (horizontal).
join: Type of join (default = outer).
keys: Labels to identify data sources.

Question 90

What is the syntax for a vertical concatenation of dataframes?

Answer 90

df = pd.concat([df1, df2], axis=0)

Question 91

How do you concatenate dataframes horizontally with an inner join?

Answer 91

df = pd.concat([df1.set_index(‘col_name’), df2.set_index(‘col_name’)], join=’inner’, axis=1)

Question 92

How do you merge two dataframes on a common column?

Answer 92

df = dataframe1.merge(dataframe2, how=’join_type’, on=’common_column’)
Join types: inner, outer, left, right.

Question 93

How do you merge dataframes with custom join columns?

Answer 93

df = df1.merge(df2, left_on=’col_df1’, right_on=’col_df2’, suffixes=[‘_df1’, ‘_df2’])

Question 94

What happens when matching columns overlap during merging?

Answer 94

Pandas appends _x (from dataframe1) and _y (from dataframe2) to differentiate. Use suffixes to customize labels.

Question 95

What is the difference between merge() and join() in Pandas?

Answer 95

merge(): Combines dataframes based on common columns.
join(): Combines dataframes on their indexes.

Question 96

What is the default behavior of pd.concat() when the axis parameter is not specified?

Answer 96

By default, pd.concat() stacks dataframes vertically (axis=0).

Question 97

How do you add labels to identify the source of data in concatenation?

Answer 97

Use the keys parameter:
df = pd.concat([df1, df2], keys=[‘data1’, ‘data2’], axis=0)

Question 98

What is the syntax for an outer merge?

Answer 98

df = df1.merge(df2, how=’outer’, on=’common_column’)

Question 99

How do you combine dataframes using join()?

Answer 99

df = dataframe1.join(dataframe2, how=’join_type’, lsuffix=’_left’, rsuffix=’_right’)
Default join type: Left join.

Question 100

How do you merge dataframes when they share no common column?

Answer 100

Use left_on and right_on parameters:
df = df1.merge(df2, left_on=’col1_df1’, right_on=’col2_df2’)

Question 101

How do you differentiate overlapping columns from merged dataframes?

Answer 101

Use the suffixes parameter:
suffixes=[‘_df1’, ‘_df2’]

Question 102

What happens when concatenating dataframes with different indexes or columns?

Answer 102

Outer join (default): Includes all indexes or columns.
Inner join: Keeps only matching indexes or columns.

Question 103

How do you align dataframes by their column names for concatenation?

Answer 103

Set indexes with .set_index() before concatenation:
df = pd.concat([df1.set_index(‘col’), df2.set_index(‘col’)], axis=1)

Question 104

What is a key advantage of chaining merge() commands?

Answer 104

Efficiency and clarity when combining multiple datasets in a single line:
df = df1.merge(df2).merge(df3)

Question 105

What is the difference between axis=0 and axis=1 in concatenation?

Answer 105

axis=0: Stacks dataframes vertically (rows).
axis=1: Stacks dataframes horizontally (columns).

Question 107

What does the len() function do in Python when applied to a DataFrame or list?

Answer 107

It returns the total number of rows or items in the structure, excluding the zeroth index.

Question 108

How do you access a column’s values in a DataFrame by its name?

Answer 108

Use count[‘column_name’].

Question 109

How can you isolate specific columns in a DataFrame?

Answer 109

Use double square brackets, e.g., df[[‘column1’, ‘column2’]]. The columns will appear in the order specified.

Question 110

How do you create a subset of rows from rows 1 to 4 using indexing?

Answer 110

Use count[1:5] (row 5 is excluded).

Question 111

How would you display the first 7 rows of a DataFrame?

Answer 111

Use count[:7].

Question 112

How would you display only the last row of a DataFrame?

Answer 112

Use count[-1:].

Question 113

How do you access a specific value in a DataFrame using iloc?

Answer 113

Use integer positions, e.g., df.iloc[2, 3] for the value at row 2, column 3.

Question 114

How do you select all rows but only the last column using iloc?

Answer 114

Use df.iloc[:, -1].

Question 115

How does loc differ from iloc?

Answer 115

loc uses labels (row/column names), while iloc uses integer positions.

Question 116

How do you retrieve a specific value at row 2 and column ‘field’ using loc?

Answer 116

Use df.loc[2, ‘field’].

Question 117

How can you filter rows based on a column value being greater than 10?

Answer 117

Use df[df[‘column_name’] > 10].

Question 118

How do you extract rows with specific values in a column using .isin()?

Answer 118

Use df[df[‘column_name’].isin([‘value1’, ‘value2’])]

Question 119

How do you filter rows based on a string condition using .query()?

Answer 119

Use syntax like df.query(‘Column == “Value”’).

Question 120

What is the purpose of the groupby function in Pandas?

Answer 120

It splits a DataFrame into groups based on column(s) and performs operations on each group (e.g., grouping rows by soil types or drainage levels).

Question 121

What are some common aggregation functions used with groupby?

Answer 121

mean: Calculates the average for each group.
max: Finds the maximum value for each group.
min: Finds the minimum value for each group.
sum: Adds up values for each group.

Question 122

How do you avoid warnings when using groupby on columns with mixed data types?

Answer 122

Use numeric_only=True to limit operations to numeric columns.

Question 123

How can you calculate the mean of grouped data using groupby?

Answer 123

Syntax: df.groupby([‘set’]).mean()
Example: Groups by the “set” column and calculates the mean, producing a matrix with rows for “control” and “experiment.”

Question 124

How do you count the occurrences of unique values in a column using groupby?

Answer 124

Use df.groupby(‘col_name’).size() to get a list of unique values and their counts.

Question 125

What is the purpose of splitting columns in a DataFrame?

Answer 125

To split values in a column into multiple new columns based on a delimiter or character.

Question 126

What is the syntax for splitting a column into multiple columns?

Answer 126

df[[‘new_col1’, ‘new_col2’]] = df[‘original_col’].str.split(‘delimiter’, n=number_of_splits, expand=True)
delimiter: Character where the split occurs.
n: Number of splits to perform.
expand=True: Ensures output is split into separate columns.

Question 127

How do you split the string “coding” at the letter d?

Answer 127

df[[‘col1’, ‘col2’]] = df[‘coding’].str.split(‘d’, n=1, expand=True)
Result:
col1: “co”
col2: “ding”

Question 128

What are two key notes about splitting columns?

Answer 128

Always use expand=True to create multiple columns.
Use the n parameter to control how many splits occur if the delimiter appears multiple times.

Question 129

What is the purpose of increasing sample size in correlation analysis?

Answer 129

Increasing the sample size improves the precision of the correlation estimate, reduces uncertainty in the p-value, and makes the results more reliable.

Question 130

How do you calculate the Pearson correlation coefficient in Python?

Answer 130

result = pearsonr(df[‘col1’], df[‘col2’])
print(f’r = {result.statistic:.2f}’)

Question 131

What does a Pearson correlation coefficient r value of 0.46 and a p-value of 0.03 indicate?

Answer 131

The p-value of 0.03 indicates there is a 3% chance that the correlation occurred by random chance, assuming there is no real correlation (null hypothesis). Since the p-value is low (< 0.05), we may reject the null hypothesis and consider the correlation statistically significant.

Question 132

What is the difference between a statistic and a parameter?

Answer 132

Statistic: A numerical property of a sample (e.g., sample correlation coefficient r).
Parameter: A numerical property of the population (e.g., population correlation coefficient ρ).

Question 133

What is the purpose of the p-value in hypothesis testing?

Answer 133

The p-value helps assess the significance of the observed correlation. It represents the probability of observing a test statistic as extreme as the observed one, assuming the null hypothesis is true.

Question 134

How do you interpret a p-value in correlation analysis?

Answer 134

If the p-value < 0.05, we reject the null hypothesis (no correlation) and consider the correlation significant.
If the p-value > 0.05, the correlation might be due to random chance and we fail to reject the null hypothesis.

Question 135

How can you calculate a 95% confidence interval for a Pearson correlation?

Answer 135

ci = result.confidence_interval()
ci.low, ci.high

Question 136

What is the purpose of the Shapiro-Wilk test?

Answer 136

The Shapiro-Wilk test assesses if the data follows a normal distribution. The null hypothesis is that the data comes from a normally distributed population.

Question 137

How do you apply the Shapiro-Wilk test in Python?

Answer 137

result = Shapiro(df[‘col_name’])

Question 138

How do you handle non-normally distributed data in Python?

Answer 138

to transform non-normally distributed data, apply a log transformation:

df[‘log-variable’] = np.log10(df[‘col_name’])

Question 139

What is the purpose of a t-test for independent samples?

Answer 139

A t-test for independent samples tests whether two independent samples have different means

Question 140

How do you perform a t-test for independent samples in Python?

Answer 140

result = ttest_ind(subset[‘col1’], subset[‘col2’])

Question 141

How do you modify the y-axis scale for large values in a scatter plot?

Answer 141

ax.set_yscale(‘log’)

Question 142

What is the probability of observing a correlation of at least 0.46, assuming no real correlation exists?

Answer 142

The p-value gives the probability of observing a correlation of at least 0.46 by chance. If the p-value is small (e.g., < 0.05), it suggests that the observed correlation is statistically significant.

Question 143

What is the purpose of a swarm plot?

Answer 143

Swarm plots are used to compare a numerical variable with two categories, allowing us to visually assess the difference in means between those categories.

Question 144

What is the best use of a scatterplot (lmplot)?

Answer 144

Scatterplots (lmplot) are ideal for visualizing the relationship between two numerical variables. It combines a scatter plot with a regression line to show the relationship.

Question 145

What is an explanatory variable in regression?

Answer 145

The explanatory variable is the independent variable (cause). It is expected to explain the variation in the response variable.

Question 146

What is a response variable in regression?

Answer 146

The response variable is the dependent variable (effect). It is expected to change in response to the explanatory variable.

Question 147

What is the model formula for regression?

Answer 147

The relationship between the response and explanatory variables is expressed as:
response_variable ~ explanatory_variable

Question 148

What does the t-value represent in regression?

Answer 148

The t-value measures how many standard errors the coefficient is away from zero.
Example: t-value = 0.79.

Question 149

What does the p-value indicate in regression?

Answer 149

The p-value indicates the probability that the coefficient is zero in the population.
Example: p-value = 0.433. Since p > 0.05, we accept the null hypothesis (no significant effect).

Question 150

What is a 95% Confidence Interval (CI) in regression?

Answer 150

The 95% CI is a range within which the true population parameter is likely to fall.
Example: CI = (-0.25, 0.109). Since the CI does not contain 0, we cannot reject the null hypothesis.

Question 151

How do you interpret the relationship between the y-axis and x-axis in linear models?

Answer 151

The mean of the y-axis is given by the equation:
Mean of y = intercept + slope * x

Question 152

What must be mentioned in the conclusion when interpreting relationships?

Answer 152

It is important to mention whether the relationship is linear or logarithmic and state if there is a statistically significant relationship.