query regarding hypothesis interpretation

[Prachi Agarwal]

Dear members

I have a methodological query regarding hypothesis interpretation in SEM/PLS-SEM.

Suppose a hypothesis is proposed as a **negative relationship** between two constructs. The statistical results show that the **p-value is < 0.05 (significant)**, but the **standardized beta coefficient is positive**.

In this case, should the hypothesis be considered **supported** because the relationship is statistically significant, or **not supported** because the direction of the relationship is opposite to the hypothesized direction?

Should both conditions be fulfilled p value and beta or only p value.

I would appreciate your guidance. Thank you.

Best Regards,
PRACHI AGARWAL
Doctoral Scholar

LinkedIn

[Niti kp]

Dear Prachi and Members,

Thank you for raising this important methodological question.

In PLS-SEM, both conditions must be fulfilled for a hypothesis to be considered supported — statistical significance (p < 0.05) AND the beta coefficient aligning with the hypothesized direction.

In the scenario described, the hypothesis should be considered NOT supported. A significant p-value confirms the relationship exists, but the positive beta contradicts the hypothesized negative direction. Direction is an integral part of the hypothesis itself.

The recommended way to report this would be:

"The hypothesis was not supported. Although a statistically significant relationship was found (β = +0.XX, p < 0.05), the direction was positive, contrary to the hypothesized negative relationship."

This finding is still valuable and should be discussed in the results section as an unexpected outcome.

Hope this helps!

Warm regards,

Nitika Kashyap

PhD Scholar, Commerce

Banasthali Vidyapith

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[Prachi Agarwal]

Thankyou so much for the clarification ma'am

Best Regards,
PRACHI AGARWAL
Doctoral Scholar

LinkedIn

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[Kannan R]

Hi,

In SEM / PLS-SEM, hypothesis testing is not based on significance alone. It is jointly based on two conditions:

1. Statistical significance (p-value / t-value)

2. Direction consistency (sign of the path coefficient vs hypothesized direction)

Your case:

• Hypothesis: Negative relationship (β < 0 expected)

• Result: β is positive

• p-value: < 0.05 (significant)

Interpretation:

This hypothesis is NOT supported.

Why:

A significant p-value only tells you that a relationship exists.
It does not validate the direction you proposed.

So you have:

• Evidence of a relationship ✔

• But evidence contradicts your theoretical claim about direction ✖

Standard SEM/PLS reporting rule (widely accepted in Q1 journals):

A hypothesis is supported only when:

• p-value < 0.05 (or t-value threshold met), AND

• The coefficient sign matches the hypothesized direction

If either condition fails, the hypothesis is rejected or not supported.

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In your specific situation:

You would report something like the following:

The relationship was statistically significant (β = +0.xx, p < 0.05), however the direction was opposite to the hypothesized negative effect; therefore, Hx is not supported.

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Conceptual implication (important, often overlooked):

A sign reversal typically signals one of these issues:

• misspecified theory (wrong assumed direction)

• suppression effects or multicollinearity

• mediation not modeled correctly

• inconsistent measurement coding (especially reverse-coded items)

• sample-specific behavioral pattern

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[Prachi Agarwal]

Thank you for the clarification sir

Best Regards,
PRACHI AGARWAL
Doctoral Scholar

LinkedIn

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4. Never write Open-ended queries. This group intends to help research scholars, NOT TO WORK FOR THEM.
5. Never write words like URGENT in your posts. People will help when they are free.
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[Kannan R]

Anytime, Anytime!

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Cheers,
Kannan

[Muhammad R Siregar]

Dear Prachi,

A directional hypothesis is supported when the bootstrap confidence interval excludes zero, and the estimated coefficient has the hypothesised sign.

Regarding Kannan R’s mention of the t-value, bootstrap confidence interval is preferred. The PLS-SEM t-value is a Wald statistic that relies only on the bootstrap-estimated standard error, whereas bootstrap confidence interval provides a more informative basis for statistical inference. BCa confidence interval is generally preferred because it also adjusts for bias and skewness.

Best,

MRS

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