Meterstick Documentation

The meterstick package provides a concise syntax to describe and execute routine data analysis tasks. Please see meterstick_demo.ipynb for examples.

Disclaimer

This is not an officially supported Google product.

tl;dr

Modify the demo colab notebook and adapt it to your needs.

Building up an analysis

Every analysis starts with a Metric or a MetricList. A full list of Metrics can be found below.

A Metric may be modified by one or more Operations. For example, we might want to calculate a confidence interval for the metric, a treatment-control comparison, or both.

Once we have specified the analysis, we pass in the data to compute the analysis on, as well as variables to slice by.

Here is an example of a full analysis:

# define metrics
cvr = Ratio("Conversions", "Visits")
bounce_rate = Ratio("Bounces", "Visits")

(MetricList((cvr, bounce_rate))
 | PercentChange("Experiment", "Control")
 | Jackknife("Cookie", confidence=.95)
 | compute_on(data, ["Country", "Device"]))

This calculates the percent change in conversion rate and bounce rate, relative to the control arm, for each country and device, together with 95% confidence intervals based on jackknife standard errors.

Building Blocks of an Analysis Object

Metrics

A Meterstick analysis begins with one or more metrics.

Currently built-in metrics include:

• Count(variable): calculates the number of (non-null) entries of the variable column.
• Sum(variable) : calculates the sum of the variable column.
• Dot(variable1, variable2, normalize=False): calculates the dot product between the variable1 column and the variable2 column; normalize determines whether to normalize the dot product using the length.
• Max(variable): calculates the max of the variable column.
• Min(variable): calculates the min of the variable column.
• Ratio(numerator, denominator) : calculates Sum(numerator) / Sum(denominator).
• Nth(variable, n, sort_by, ascending=True, dropna=True) computes the nth value (0-based indexing) in the variable column after sorting by the sort_by column.
• Variance(variable, unbiased=True): calculates the variance of the variable column unbiased determines whether the unbiased (sample) or population estimate is used.
• StandardDeviation(variable, unbiased=True): calculates the standard deviations of variable; unbiased determines whether the unbiased or MLE estimate is used.
• CV(variable, unbiased=True): calculates the coefficient of variation of the variable column; unbiased determines whether the unbiased or MLE estimate of the standard deviation is used.
• Correlation(variable1, variable2): calculates the Pearson correlation between variable1 and variable2.
• Cov(variable1, variable2): calculates the covariance between variable1 and variable2.

All metrics have an optional name argument which determines the column name in the output. If not specified, a default name will be provided. For instance, the metric Sum("Clicks") will have the default name sum(Clicks).

Metrics such as Mean and Quantile have an optional weight argument that specifies a weighting column. The resulting metric is a weighted mean or weighted quantile.

To calculate multiple metrics at once, create a MetricList of the individual Metrics. For example, to calculate both total visits and conversion rate, we would write:

sum_visits = Sum("Visits")
MetricList([sum_visits, Sum("Conversions") / sum_visits])

When computing analyses involving multiple metrics, Meterstick will try to cache redundant computations. For example, both metrics above require calculating Sum("Visits"); Meterstick will only calculate this once.

You can also define custom metrics. See section Custom Metric below for instructions.

Composite Metrics

Metrics are also composable. For example, you can:

• Add metrics: Sum("X") + Sum("Y") or Sum("X") + 1.
• Subtract metrics: Sum("X") - Sum("Y") or Sum("X") - 1.
• Multiply metrics: Sum("X") * Sum("Y") or 100 * Sum("X").
• Divide metrics: Sum("X") / Sum("Y") or Sum("X") / 2. (Note that the first is equivalent to Ratio("X", "Y").)
• Raise metrics to a power: Sum("X") ** 2 or 2 ** Sum("X") or Sum("X") ** Sum("Y").
• …or any combination of these: 100 * (Sum("X") / Sum("Y") - 1).

Common metrics can be implemented as follows:

• Click-through rate: Ratio('Clicks', 'Impressions', 'CTR')
• Conversion rate: Ratio('Conversions', 'Visits', 'CvR')
• Bounce rate: Ratio('Bounce', 'Visits', 'BounceRate')
• Cost per click (CPC): Ratio('Cost', 'Clicks', 'CPC')

Operations

Operations are defined on top of metrics. Operations include comparisons, standard errors, and distributions.

Comparisons

A comparison operation calculates the change in a metric between various conditions and a baseline. In A/B testing, the “condition” is typically a treatment and the “baseline” a control.

Built-in comparisons include:

• PercentChange(condition_column, baseline) : Computes the percent change (other - baseline) / baseline.
• AbsoluteChange(condition_column, baseline) : Computes the absolute change (other - baseline).
• MH(condition_column, baseline, stratified_by) : Computes the Mantel-Haenszel estimator. The metric being computed must be a Ratio or a MetricList of Ratios. The stratified_by argument specifies the strata over which the MH estimator is computed.
• CUPED(condition_column, baseline, covariates, stratified_by) : Computes the absolute change that has been adjusted using the CUPED approach. See the demo for details.
• PrePostChange(condition_column, baseline, covariates, stratified_by) : Computes the percent change that has been adjusted using the PrePost approach. See the demo for details.

Example Usage: ... | PercentChange("Experiment", "Control")

Note that condition_column can be a list of columns, in which case baseline should be a tuple of baselines, one for each condition variable.

Standard Errors

A standard error operation adds the standard error of the metric (or confidence interval) to the point estimate.

Built-in standard errors include:

• Jackknife(unit, confidence) : Computes a leave-one-out jackknife estimate of the standard error of the child Metric.

  unit is a string for the variable whose unique values will be resampled.

  confidence in (0,1) represents the level of the confidence interval; optional

• Bootstrap(unit, n_replicates, confidence, ci_method) : Computes a bootstrap estimate of the standard error or percentiles.

  n_replicates is the number of bootstrap replicates, default is 10000.

  unit is a string for the variable whose unique values will be resampled; if unit is not supplied the rows will be the unit.

  ci_method specifies the confidence interval method. Defaults to 'std', which computes bounds using standard error and normal approximation. If set to 'percentile', it computes the confidence interval using empirical percentiles from the bootstrap distribution and also returns the median.

  confidence in (0,1) represents the level of the confidence interval; optional if ci_method is 'std', but required if ci_method is 'percentile' (because standard error is not well defined for percentile bootstrapping).

• PoissonBootstrap(unit, n_replicates, confidence, ci_method) : Computes a Poisson bootstrap estimate of the standard error or percentiles. It’s identical to Bootstrap except that we use Poisson(1) instead of multinomial distribution in sampling. It’s faster than Bootstrap on large data when computing in SQL. See the post on The Unofficial Google Data Science Blog for a good introduction.

Example Usage: ... | Jackknife('CookieBucket', confidence=.95)

Transformations

Transformations are functions that can be applied to metrics to perform element-wise operations on their results.

Currently supported transformations include:

• ExponentialTransform(metric): Applies an exponential transformation to the metric result.

• LogTransform(metric, base='ln'): Applies a logarithmic transformation to the metric result. The base can be ln or log10.

• ExponentialPercentTransform(metric, base='ln'): Computes 100 * (base^metric - 1). If base='log10', it computes 100 * (10^metric - 1). It’s useful for converting log-transformed metrics back to a percent scale. For example, when PercentChange(.., Sum(x)) is skewed, applying the transformation sequence:

  (Sum(x)
   | LogTransform()
   | AbsoluteChange(...)
   | Jackknife(...)
   | ExponentialPercentTransform())

  computes the same percent change, while the confidence interval is calculated in the log-transformed space, which often results in less skewness.

Distributions

A distribution operation produces the distribution of the metric over a variable.

• Distribution(over): calculates the distribution of the metric over the variables in over; the values are normalized so that they sum to 1. It has an alias Normalize.
• CumulativeDistribution(over, order=None, ascending=True, sort_by_values=False): calculates the cumulative distribution of the metric over the variables in over. Before computing the cumulative sum, we sort by the values if sort_by_values=True else by the over column(s). If sort_by_values=False, you can pass in a list of values as a custom order. ascending determines the direction of the sort.

Example Usage: Sum("Queries") | Distribution("Device") calculates the proportion of queries that come from each device.

Diversity

A diversity operation measures how diverse the child metric values are.

• HHI(over): calculates the Herfindahl–Hirschman index of the metric values over the variables in over. The metric values are first normalized over over then the HHI is computed.
• Entropy(over): calculates the entropy of the metric values over the variables in over. The metric values are first normalized over over then the entropy is computed.
• TopK(over, k): calculates the total share of the top k contributors. The metric values are first normalized over over then largest k values are summed.
• Nxx(over, x): calculates the minimum number of contributors to achieve x total share. The metric values are first normalized over over then we count the largest n contributors that make up x total share.

Models

A Meterstick Model fits a model on data computed by children Metrics.

Model(y, x, groupby).compute_on(data) is equivalent to

1. Computes y.compute_on(data, groupby) and x.compute_on(data, groupby).
2. Fits the underlying model on the results from #1.

We have built-in support for LinearRegression, Ridge, Lasso, ElasticNet and LogisticRegression. Example Usage: LinearRegression(Sum('Y'), Sum('X'), 'country') calculates the sum of Y and X by country respectively, then fits a linear regression between them.

Note that x, the 2nd arg, can be a Metric, a MetricList, or a list of Metrics.

Filtering

We can restrict our metrics to subsets of the data. For instance to calculate metrics for non-spam clicks you can add a where clause to the Metric or MetricList. This clause is a boolean expression which can be passed to pandas’ query() method.

sum_non_spam_clicks = Sum("Clicks", where="~IsSpam")
MetricList([Sum("Clicks"), Sum("Conversions")], where="~IsSpam")

Data and Slicing

Once we have specified the metric(s) and operation(s), it is time to compute the analysis on some data. The final step is to pass in the data, along with any variables we want to slice by. The analysis will be carried out for each slice separately.

The data can be supplied in two forms:

• a pandas DataFrame
• a string representing a SQL table or subquery.

Example Usage: compute_on(df, ["Country", "Device"])

Example Usage:

compute_on_sql("SELECT * FROM table WHERE date = '20200101'", "Country")

Customizing the Output Format

When calculating multiple metrics, Meterstick will store each metric as a separate column by default. However, it is sometimes more convenient to store the data in a different shape: with one column storing the metric values and another column storing the metric names. This makes it easier to facet by metric in packages like ggplot2 and altair. This is known as the “melted” representation of the data. To return the output in melted form, simply add the argument melted=True in compute_on() or compute_on_sql().

Visualization

If the last operation applied to the metric is Jackknife or Bootstrap with confidence, the output can be displayed in a way that highlights significant changes by calling .display().

You can customize the display. It takes the same arguments as the underlying visualization library. Arguments return_pre_agg_df and return_formatted_df, are particularly valuable for advanced use cases. They offer nearly unlimited customization of the output.

You can visualize the Metric tree by calling visualize_metric_tree(rendering_fn), where rendering_fn is a function that can render a string of DOT representation. It can help you to sanity check complex Metrics.

SQL

You can get the SQL query for all built-in Metrics and Operations by calling to_sql(sql_data_source, split_by) on the Metric. sql_data_source could be a table or a subquery. For example,

MetricList((Sum('X', where='Y > 0'), Sum('X'))).to_sql('table', 'grp')

gives

SELECT
  grp,
  SUM(IF(Y > 0, X, NULL)) AS sum_X,
  SUM(X) AS sum_X_1
FROM table
GROUP BY grp

Very often what you need is the execution of the SQL query, then you can call

compute_on_sql(sql_data_source, split_by=None, execute=None, melted=False, mode=None)

directly, which will give you a output similar to compute_on(). execute is a function that can execute SQL query. The mode can be None or 'mixed'. The former is recommended and computes things in SQL whenever possible while the latter only computes the leaf Metrics in SQL.

The default dialect it uses is GoogleSQL. You can use set_dialect() to choose other dialects. Currently we support

• PostgreSQL
• MySQL and MariaDB
• SQLite
• Oracle
• Microsoft SQL Server
• Trino SQL

For other dialects, you can manually overwrite the default string templates at the top of sql.py file.

Apache Beam

There is also a

compute_on_beam(pcol, split_by=None, execute=None, melted=False, mode=None, dialect=None)

method which takes an PCollection with a schema as input. The args are similar to those of compute_on_sql except that execute now should evaluate a PCollection. Under the hood, we generate SQL queries and pass them to SqlTransform. As a result,

• You need to choose a Beam runner that supports SqlTransform. For example, the InteractiveRunner does NOT.
• The config of the pipeline that carries the PCollection is set up by you. For example, your setup decides if the pipeline will be ran in process or in Cloud.

Custom Metric

You can write your own Metric and Operation. Below is a Metric taken from the demo colab. The Metric fits a LOWESS model.

import statsmodels.api as sm
lowess = sm.nonparametric.lowess

class Lowess(Metric):
 def __init__(self, x, y, name=None, where=None):
   self.x = x
   self.y = y
   name = name or 'LOWESS(%s ~ %s)' % (y, x)
   super(Lowess, self).__init__(name, where=where)

 def compute(self, data):
   lowess_fit = pd.DataFrame(
       lowess(data[self.y], data[self.x]), columns=[self.x, self.y])
   return lowess_fit.drop_duplicates().reset_index(drop=True)

As long as the Metric obeys some rules, it will work with all built-in Metrics and Operations. For example, we can pass it to Jackknife to get a confidence interval.

jk = Lowess('x', 'y') | Jackknife('cookie', confidence=0.9) | compute_on(df)
point_est = jk[('y', 'Value')]
ci_lower = jk[('y', 'Jackknife CI-lower')]
ci_upper = jk[('y', 'Jackknife CI-upper')]

plt.scatter(df.x, df.y)
plt.plot(x, point_est, c='g')
plt.fill_between(x, ci_lower, ci_upper, color='g', alpha=0.5)
plt.show()

Further Reading

• Paper