<PAGE>

                                                                    EXHIBIT 31.2

                                 CERTIFICATIONS

I, Randall M. Greenwood, Chief Financial Officer of United Bancorp, Inc.,
certify that:

1. I have reviewed Form 10-Q of United Bancorp, Inc.;

2. Based on my knowledge, this report does not contain any untrue statement of a
material fact or omit to state a material fact necessary to make the statements
made, in light of the circumstances under which such statements were made, not
misleading with respect to the period covered by this report;

3. Based on my knowledge, the financial statements, and other financial
information included in this report, fairly present in all material respects the
financial condition, results of operations and cash flows of the registrant as
of, and for, the periods presented in this report;

4. The registrant's other certifying officer and I are responsible for
establishing and maintaining disclosure controls and procedures (as defined in
Exchange Act Rules 13a-15(e) and 15d-15(e)) and internal control over financial
reporting (as defined in Exchange Act Rules 13a-15(f) and 15d-15(f)) for the
registrant and have:

     (a) Designed such disclosure controls and procedures, or caused such
     disclosure controls and procedures to be designed under our supervision, to
     ensure that material information relating to the registrant, including its
     consolidated subsidiaries, is made known to us by others within those
     entities, particularly during the period in which this report is being
     prepared;

     (b) Designed such internal control over financial reporting, or caused such
     internal control over financial reporting to be designed under our
     supervision, to provide reasonable assurance regarding the reliability of
     financial reporting and the preparation of financial statements for
     external purposes in accordance with generally accepted accounting
     principles;

     (c) Evaluated the effectiveness of the registrant's disclosure controls and
     procedures and presented in this report our conclusions about the
     effectiveness of the disclosure controls and procedures, as of the end of
     the period covered by this report based on such evaluation; and

     (d) Disclosed in this report any change in the registrant's internal
     control over financial reporting that occurred during the registrant's most
     recent fiscal quarter (the registrant's fourth fiscal quarter in the case
     of an annual report) that has materially affected, or is reasonably likely
     to materially affect, the registrant's internal control over financial
     reporting; and

5. The registrant's other certifying officer and I have disclosed, based on our
most recent evaluation of internal control over financial reporting, to the
registrant's auditors and the audit committee of the registrant's board of
directors (or persons performing the equivalent functions):

     (a) All significant deficiencies and material weaknesses in the design or
     operation of internal control over financial reporting which are reasonably
     likely to adversely affect the registrant's ability to record, process,
     summarize and report financial information; and

     (b) Any fraud, whether or not material, that involves management or other
     employees who have a significant role in the registrant's internal control
     over financial reporting.


     Date: August 12, 2008              /s/ Randall M. Greenwood
                                        ----------------------------------------
                                        Randall M. Greenwood, CFO