Run a One Sample T Test - Platform For AI - Alibaba Cloud - Platform For AI

The one-sample t-test determines whether the sample mean is statistically significantly different from a known or hypothesized population mean.

Null hypothesis (H0): The sample mean equals the hypothesized mean.

The test computes a t-statistic and compares it against a t-distribution with the appropriate degrees of freedom. It assumes normally distributed data—this assumption is especially important when the sample size is small.

If the p-value is less than alpha (1 - confidence level), reject the null hypothesis and conclude that the sample mean differs significantly from the hypothesized mean.

Configure the component

Method 1: Configure in Machine Learning Designer

Add a One Sample T Test component on the pipeline page and configure the following parameters.

Fields setting

Parameter	Description
Sample 1 Column	The column that contains the sample data.

Parameters setting

Parameter	Default	Description
Alternative Hypothesis Type	`two.sided`	The direction of the alternative hypothesis. See Choose an alternative hypothesis type.
Confidence Level	`0.95`	The confidence level of the test. Valid values: `0.8`, `0.9`, `0.95`, `0.99`, `0.995`, `0.999`.
Hypothesized Mean	`0`	The population mean to test against.
Core number	—	The number of cores. Must be a positive integer.
Memory Size per Core	—	The memory size per core. Valid values: 1–65536. Unit: MB.

Choose an alternative hypothesis type

Select the alternative hypothesis type based on what you want to test:

Value	Meaning	When to use
`two.sided`	The sample mean is different from the hypothesized mean (two-tailed test).	No prior expectation of direction.
`less`	The sample mean is less than the hypothesized mean (left-tailed test).	Expecting the sample mean to be lower.
`greater`	The sample mean is greater than the hypothesized mean (right-tailed test).	Expecting the sample mean to be higher.

Method 2: Use PAI commands

Use PAI commands to configure and run the one-sample t-test. For more information about command syntax, see SQL Script.

pai -name t_test -project algo_public
    -DxTableName=pai_t_test_all_type
    -DxColName=col1_double
    -DoutputTableName=pai_t_test_out
    -DxTablePartitions=ds=2010/dt=1
    -Dalternative=less
    -Dmu=47
    -DconfidenceLevel=0.95

Parameter	Required	Default	Description
`xTableName`	Yes	—	The name of the input table.
`xColName`	Yes	—	The column to test.
`outputTableName`	Yes	—	The name of the output table.
`xTablePartitions`	No	`null`	The partitions to select from the input table.
`alternative`	No	`two.sided`	The alternative hypothesis type. Valid values: `two.sided`, `less`, `greater`.
`mu`	No	`0`	The hypothesized mean.
`confidenceLevel`	No	`0.95`	The confidence level. Valid values: `0.8`, `0.9`, `0.95`, `0.99`, `0.995`, `0.999`.

Sample output

{
    "AlternativeHypthesis": "mean not equals to 0",
    "ConfidenceInterval": "(44.72234194006504, 46.27765805993496)",
    "ConfidenceLevel": 0.95,
    "alpha": 0.05,
    "df": 99,
    "mean": 45.5,
    "p": 0,
    "stdDeviation": 3.919647479510927,
    "t": 116.081867662439
}

Output fields

Field	Description
`AlternativeHypthesis`	The alternative hypothesis tested, stated in plain language.
`ConfidenceInterval`	The range in which the true population mean is expected to fall at the specified confidence level.
`ConfidenceLevel`	The confidence level configured (for example, `0.95`).
`alpha`	The significance level (1 - confidence level). Reject the null hypothesis if `p` < `alpha`.
`df`	Degrees of freedom (sample size minus 1).
`mean`	The sample mean.
`p`	The p-value. A value near `0` indicates strong evidence against the null hypothesis. A displayed value of `0` means the p-value is below the floating-point precision of the output, not exactly zero.
`stdDeviation`	The sample standard deviation.
`t`	The t-statistic. A large absolute value indicates the sample mean is far from the hypothesized mean.

How to interpret the results

Compare p against alpha (1 - confidence level):

If p < alpha: reject the null hypothesis. The sample mean is statistically significantly different from the hypothesized mean.
If p >= alpha: do not reject the null hypothesis. The data does not provide sufficient evidence of a difference.

Reading the example above: The p-value is approximately 0 (far below alpha = 0.05), and the t-statistic is 116.08. This is strong evidence to reject the null hypothesis—the sample mean of 45.5 is statistically significantly different from 0.