<PAGE>   1

                                  UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                              WASHINGTON, DC 20549

                                    FORM 10-K

[X]  ANNUAL REPORT PURSUANT TO SECTION 13 OR 15(D) OF THE SECURITIES EXCHANGE
     ACT OF 1934

                   FOR THE FISCAL YEAR ENDED DECEMBER 31, 1998

                                       OR

[ ]  TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(D) OF THE SECURITIES
     EXCHANGE ACT OF 1934

                   FOR THE TRANSITION PERIOD FROM N/A TO N/A 

                         COMMISSION FILE NUMBER 0-16540

                              UNITED BANCORP, INC.
             -------------------------------------------------------
             (Exact name of registrant as specified in its Charter.)

               OHIO                                        34-1405357 
-------------------------------               ----------------------------------
(State or other jurisdiction of               (IRS) Employer Identification No.)
incorporation or organization)               

    201 SOUTH FOURTH STREET, MARTINS FERRY, OHIO                 43935 
---------------------------------------------------         --------------
    (Address of principal executive offices)                  (ZIP Code)

REGISTRANT'S TELEPHONE NUMBER, INCLUDING AREA CODE:  (740) 633-0445
                                                   -------------------

           SECURITIES REGISTERED PURSUANT TO SECTION 12(B) OF THE ACT:
<TABLE>
<S>                                          <C>                                                      
COMMON STOCK, PAR VALUE $1.00 A SHARE            NASDAQ REGULAR MARKET (SMALLCAP)
-------------------------------------            --------------------------------
           (Title of class)                  (Name of each exchange on which registered)
</TABLE>

           SECURITIES REGISTERED PURSUANT TO SECTION 12(G) OF THE ACT:

                      COMMON STOCK, PAR VALUE $1.00 A SHARE
                      -------------------------------------
                                (Title of class)

INDICATE BY CHECK MARK WHETHER THE REGISTRANT (1) HAS FILED ALL REPORTS REQUIRED
TO BE FILED BY SECTION 13 OR 15(D) OF THE SECURITIES EXCHANGE ACT OF 1934 DURING
THE PRECEDING 12 MONTHS (OR FOR SUCH SHORTER PERIOD THAT THE REGISTRANT WAS
REQUIRED TO FILE SUCH REPORTS), AND (2) HAS BEEN SUBJECT TO SUCH FILING
REQUIREMENTS FOR THE PAST 90 DAYS.    YES  X  NO
                                          ---    ---

INDICATE BY CHECK MARK IF DISCLOSURE OF DELINQUENT FILERS PURSUANT TO ITEM 405
OF REGULATION S-K IS NOT CONTAINED HEREIN, AND WILL NOT BE CONTAINED TO THE BEST
OF REGISTRANT'S KNOWLEDGE, IN DEFINITIVE PROXY OR INFORMATION STATEMENTS
INCORPORATED BY REFERENCE IN PART III OF THIS FORM 10-K OR ANY AMENDMENT TO THIS
FORM 10-K. {X }

THE AGGREGATE MARKET VALUE OF THE VOTING STOCK HELD BY NON-AFFILIATES OF THE
REGISTRANT AS OF MARCH 15, 1999.

                   COMMON STOCK, $1.00 PAR VALUE: $54,171,390

THE NUMBER OF SHARES OUTSTANDING OF THE REGISTRANT'S CLASSES OF COMMON STOCK AS
OF MARCH 15, 1999.

                 COMMON STOCK, $1.00 PAR VALUE: 2,800,298 SHARES

DOCUMENTS INCORPORATED BY REFERENCE
PORTIONS OF THE ANNUAL SHAREHOLDERS REPORT FOR THE YEAR ENDED DECEMBER 31, 1998
ARE INCORPORATED BY REFERENCE INTO PARTS I AND II, (INDEX ON PAGE 2)

PORTIONS OF THE PROXY STATEMENT FOR THE ANNUAL SHAREHOLDERS MEETING TO BE HELD
APRIL 21, 1999 ARE INCORPORATED BY REFERENCE INTO PART III (INDEX ON PAGE 2).


<PAGE>   2

                         UNITED BANCORP, INC. FORM 10-K

            INDEX OF ITEMS INCORPORATED BY REFERENCE WITHIN FORM 10-K

<TABLE>
<CAPTION>
                       FORM 10-K
PAGE #            ITEM DESCRIPTION                                              REFERENCE DESCRIPTION                           
--------------------------------------------------------------------------------------------------------------------------------
<S>        <C>                                   <C>
     3     Part I, Item 1, (a)                   Incorporated by reference to Pages 4 - 5 of the Annual Report To Shareholders.

     3     Part I, Item 1, (b)                   Incorporated by reference to Page 24, Note 1 of the Annual Report To Shareholders.

     4     Part I, Item 1, I                     Incorporated by reference to Pages 16 - 17 of the Annual Report To Shareholders.

     5     Part I, Item 1, II, B                 Incorporated by reference to Page 28, Note 2 of the Annual Report To Shareholders.

     7     Part I, Item 1, III, C, 4             Incorporated by reference to Page 36, Note 11 of the Annual Report To Shareholders.

     7     Part I, Item 1, IV                    Incorporated  by  reference  to Page 10 and Pages 24 - 25,  Note 1 the  Annual 
                                                 Report To Shareholders.

     10    Part I, Item 1, V, A                  Incorporated by reference to Page 16 of the Annual Report To Shareholders.

     11    Part I, Item 2                        Incorporated by reference to Pages 4 - 5 of the Annual Report To Shareholders.

     11    Part I, Item 3                        Incorporated by reference to Page 35, Note 10 of the Annual Report To Shareholders.

     11    Part II, Item 5                       Incorporated by reference to Page 7 of the Annual Report To Shareholders.

     11    Part II, Item 6                       Incorporated by reference to Inside Back Cover of the Annual Report To
                                                 Shareholders.

     11    Part II, Item 7                       Incorporated  by  reference  to  Pages  9 -  18,  43 - 44  of  the  Annual  Report 
                                                 To Shareholders.

     12    Part II, Item 7A                      Incorporated by reference to Pages 13 - 14 of the Annual Report To Shareholders.

     12    Part II, Item 8                       Incorporated  by  reference  to  Pages  15  and  19 -  40  of  the  Annual  Report 
                                                 To Shareholders.

     12    Part III, Item 10                     Incorporated by reference to Pages 4 - 8 of the Proxy Statement.

     13    Part III, Item 11                     Incorporated by reference to Pages 10 - 15 of the Proxy Statement.

     13    Part III, Item 12                     Incorporated by reference to Pages 4 - 8 of the Proxy Statement.

     13    Part III, Item 13                     Incorporated by reference to Page 15 of the Proxy Statement.

     14    Part IV, Item 14, (a), 1              Incorporated by reference to Pages 19 - 40 of the Annual Report To Shareholders.

     14    Part IV, Item 14, (a), 2              Incorporated by reference to Page 15 of the Annual Report To Shareholders.

     14    Part IV, Item 14, (a), 3, Exhibit 10  Incorporated by reference to Page 14 of the Proxy Statement.

     14    Part IV, Item 14, (a), 3, Exhibit 11  Incorporated by reference to Page 26 of the Annual Report To Shareholders.
</TABLE>


                                       2
<PAGE>   3
                         UNITED BANCORP, INC. FORM 10-K


PART I

ITEM 1   DESCRIPTION OF BUSINESS

         (A)  GENERAL DEVELOPMENT OF BUSINESS

              United Bancorp, Inc. (Company) is a multi-bank holding company
              headquartered in Martins Ferry, Ohio. The Company has three
              wholly owned subsidiary banks, The Citizens Savings Bank, Martins
              Ferry, Ohio (CITIZENS), The Citizens-State Bank of Strasburg,
              Strasburg, Ohio (CITIZENS-STATE), and The Community Bank,
              Glouster, Ohio (COMMUNITY), collectively "banks". For additional
              information about the Company's location and description of
              business, refer to Pages 4 - 5, Corporate Profile, in the Annual
              Report To Shareholders for the year ended December 31, 1998.

         (B)  FINANCIAL INFORMATION ABOUT INDUSTRY SEGMENTS

              Refer to Page 24, Note 1 of the Annual Report To Shareholders.

         (C)  NARRATIVE DESCRIPTION OF BUSINESS

              The Company is a multi-bank holding company as defined under the
              Bank Holding Company Act of 1956, as amended (the "BHC Act"). The
              BHC Act regulates acquisitions by the Company of voting shares or
              assets of any bank or other company. The Company is subject to the
              reporting requirements of, and examination and regulation by, the
              Board of Governors of the Federal Reserve System, as well as
              reporting requirements under the Securities and Exchange
              Commission Act of 1934.

              The Company's Banks are located in northeastern, eastern, and
              southeastern Ohio and are engaged in the business of commercial
              and retail banking in Belmont, Harrison, Jefferson, Tuscarawas,
              Carroll, Athens, Hocking, and Fairfield counties and the
              surrounding localities. The Banks provide a broad range of banking
              and financial services, which include accepting demand, savings
              and time deposits and granting commercial, real estate and
              consumer loans. CITIZENS conducts its business through its main
              office in Martins Ferry, Ohio and four branches located in
              Bridgeport, Colerain, Jewett, and St. Clairsville, Ohio.
              CITIZENS-STATE conducts its business through its main office in
              Strasburg, Ohio and its four branches located in Dover, New
              Philadelphia, Sherrodsville and Dellroy, Ohio. COMMUNITY conducts
              its business through its offices in Glouster, Amesville and
              Nelsonsville, Ohio.

              The banking markets in which the Company's subsidiaries operate
              continue to be highly competitive. CITIZENS competes for loans and
              deposits with other retail commercial banks, savings and loan
              associations, finance companies, credit unions and other types of
              financial institutions within the Mid-Ohio valley geographic area
              along the eastern border of Ohio, extending into the northern
              panhandle of West Virginia. CITIZENS-STATE, encounters similar
              competition for loans and deposits throughout the Tuscarawas and
              Carroll County geographic areas of northeastern Ohio. COMMUNITY
              also encounters similar competition for loans and deposits
              throughout Athens, Hocking, and Fairfield County geographic areas
              of southeastern Ohio.

                                       3

<PAGE>   4
                         UNITED BANCORP, INC. FORM 10-K

ITEM 1 DESCRIPTION OF BUSINESS (CONTINUED)

         (C)  NARRATIVE DESCRIPTION OF BUSINESS (CONTINUED)

              The Company's three subsidiary banks are subject to regulation by
              the Ohio Division of Financial Institutions and the Federal
              Deposit Insurance Corporation ("FDIC"). The regulations and
              restrictions affecting the Banks pertain to, among other things,
              allowable loans, guidelines for allowance for loan losses,
              accountability for fair and accurate disclosures to customers and
              regulatory agencies, permissible investments and limitations of
              risk and regulation of capital requirements for safe and sound
              operation of the financial institution.

              The Banks have no single customer or related group of customers
              whose banking activities, whether through deposits or lending,
              would have a material impact on the continued earnings
              capabilities if those activities were removed.

              The Company itself, as a shell holding company, has no compensated
              employees. CITIZENS has 54 full time employees, with 17 of these
              serving in a management capacity and 23 part time employees.
              CITIZENS-STATE has 23 full time employees, with 8 serving in a
              management capacity and 13 part time employees. COMMUNITY has 33
              full time employees, with 8 serving in a management capacity and
              10 part time employees. The Company considers employee relations
              to be good at all subsidiary locations.

         (D)  FINANCIAL INFORMATION ABOUT FOREIGN AND DOMESTIC OPERATIONS

              Not applicable.

     I        DISTRIBUTION OF ASSETS, LIABILITIES AND STOCKHOLDERS EQUITY; 
              INTEREST RATES AND INTEREST DIFFERENTIAL

              A   Refer to Page 16 of the Annual Report To Shareholders

              B   Refer to Page 16 of the Annual Report To Shareholders

              C   Refer to Page 17 of the Annual Report To Shareholders


                                       4
<PAGE>   5
                         UNITED BANCORP, INC. FORM 10-K

ITEM 1   DESCRIPTION OF BUSINESS (CONTINUED)

         II   INVESTMENT PORTFOLIO

              A    The following table sets forth the carrying amount of
                   securities at December 31, 1998, 1997 and 1996:
<TABLE>
<CAPTION>

                                                       DECEMBER 31,
                                         -------------------------------------
          (In thousands)                  1998            1997           1996
                                         -------        -------        -------
AVAILABLE FOR SALE
<S>                                      <C>            <C>            <C>    
  US Treasury obligations                $ 1,509        $ 3,308        $ 3,799
  US Agency obligations                   67,506         37,199         30,488
  State and municipal obligations          2,197            577            476
  Mortgage-backed obligations              3,028          3,785            784
  Other securities                         1,552          1,134            876
                                         -------        -------        -------
                                         $75,792        $46,003        $36,423
                                         =======        =======        =======

         (In thousands)
HELD TO MATURITY
  US Agency obligations                  $    --        $ 7,501        $11,535
  State and municipal obligations         21,848         21,559         22,272
  Other securities                            46             --             --
                                         -------        -------        -------
                                         $21,894        $29,060        $33,807
                                         =======        =======        =======
</TABLE>

              B    Refer to Page 28, Note 2 of the Annual Report To
                   Shareholders.

              C    Excluding holdings of U.S. Treasury and U.S. Agency, there
                   were no investments in securities of any one issuer
                   exceedi8ng 10% of the Corporation's consolidated
                   shareholders' equity at December 31, 1998.

         III  LOAN PORTFOLIO

              A    TYPES OF LOANS

                   The amounts of gross loans outstanding at December 31, 1998,
                   1997, 1996, 1995 and 1994 are shown in the following table
                   according to types of loans:


<TABLE>
<CAPTION>
                                                                   DECEMBER 31,
                                    ------------------------------------------------------------------------
                                      1998            1997            1996            1995            1994
                                    --------        --------        --------        --------        --------
          (In thousands)
<S>                                 <C>             <C>             <C>             <C>             <C>     
Commercial loans                    $ 12,912        $ 16,636        $ 15,065        $ 13,606        $ 10,449

Commercial real estate loans          54,195          49,189          41,565          35,926          28,651

Real estate loans                     49,438          49,857          52,955          51,042          49,731

Installment loans                     47,676          55,795          56,931          56,795          52,245
                                    --------        --------        --------        --------        --------

  Total loans                       $164,221        $171,477        $166,516        $157,369        $141,076
                                    ========        ========        ========        ========        ========
</TABLE>

                                       5


<PAGE>   6


                         UNITED BANCORP, INC. FORM 10-K

ITEM 1   DESCRIPTION OF BUSINESS (CONTINUED)

     III LOAN PORTFOLIO (CONTINUED)

         B    MATURITIES AND SENSITIVITIES OF LOANS TO CHANGES IN INTEREST
              RATES

              The following is a schedule of commercial and commercial real
              estate loans at December 31, 1998 maturing within the various
              time frames indicated:

<TABLE>
<CAPTION>
                                      ONE YEAR        ONE THROUGH        AFTER
          (In thousands)               OR LESS       FIVE YEARS        FIVE YEARS         TOTAL
                                    --------------  --------------  ----------------  -------------
<S>                                    <C>              <C>            <C>               <C>      
  Commercial loans                     $   11,504       $   1,267      $        141      $  12,912
  Commercial real estate loans             24,454          13,529            16,212         54,195
                                    --------------  --------------  ----------------  -------------
    Total                              $   35,958       $  14,796      $     16,353      $  67,107
                                    ==============  ==============  ================  =============
</TABLE>



              The following is a schedule of fixed rate and variable rate
              commercial and commercial real estate loans at December 31,
              1998 due to mature after one year:

<TABLE>
<CAPTION>
            (In thousands)               FIXED RATE          VARIABLE RATE         TOTAL > ONE YEAR
                                       --------------      -----------------      ------------------
<S>                                     <C>                 <C>                    <C>  
  Commercial loans                          $  1,408               $      -               $    1,408
  Commercial real estate loans                                                     
                                              10,827                 18,914                   29,741
                                       --------------      -----------------      -------------------
    Total                                   $ 12,235              $  18,914               $   31,149
                                       ==============      =================      ===================
</TABLE>

                                                                            
              Variable rate loans are those loans with floating or
              adjustable interest rates.

         C    RISK ELEMENTS

              1.   NONACCRUAL, PAST DUE, RESTRUCTURED AND IMPAIRED LOANS

              The following schedule summarizes nonaccrual loans, accruing loans
              which are contractually 90 days or more past due, troubled debt
              restructurings and impaired loans at December 31, 1998, 1997,
              1996, 1995 and 1994:

<TABLE>
<CAPTION>
                                                                DECEMBER 31,
                                             ------------------------------------------------------------
               (In thousands)                   1998        1997        1996        1995         1994
                                             -----------  ----------  ----------  ----------  -----------
<S>                                          <C>          <C>         <C>         <C>         <C>  
Nonaccrual basis                                 $  399      $  480      $  667      $  622       $  114

Accruing loans 90 days or greater past due          150         319         256         544          419

Troubled debt restructuring                         N/A         N/A         N/A         N/A            -

Impaired loans                                       (1)         (1)         (1)         (1)         N/A
</TABLE>

              (1) Loans considered impaired under the provisions of SFAS No. 114
              and interest recognized on a cash received basis were not
              considered material during any of the periods presented.


                                       6
<PAGE>   7
                         UNITED BANCORP, INC. FORM 10-K

ITEM 1   DESCRIPTION OF BUSINESS (CONTINUED)

     III LOAN PORTFOLIO (CONTINUED)

         1.   Interest income is not reported when full loan repayment is
              doubtful, typically when the loan is impaired or payments are past
              due over 90 days. Payments received on such loans are reported as
              principal reductions.

              A loan is impaired when full payment under the loan terms is not
              expected. Impairment is evaluated in total for smaller-balance
              loans of similar nature such as residential mortgage, consumer,
              and credit card loans, and on an individual loan basis for other
              loans. If a loan is impaired, a portion of the allowance is
              allocated so that the loan is reported, net, at the present value
              of estimated future cash flows using the loan's existing rate or
              at the fair value of collateral if repayment is expected solely
              from the collateral.

         2.   POTENTIAL PROBLEM LOANS

              The Company had no potential problem loans as of December 31, 1998
              which have not been disclosed in Table C 1., but where known
              information about possible credit problems of borrowers causes
              management to have serious doubts as to the ability of such
              borrowers to comply with the present loan repayment terms and
              which may result in disclosure of such loans into one of the
              problem loan categories.

         3.   FOREIGN OUTSTANDING

              Not applicable.

         4.   LOAN CONCENTRATIONS

              Refer to Page 36, Note 11 of the Annual Report To Shareholders.

         D.   OTHER INTEREST-BEARING ASSETS

              Not applicable.


     IV SUMMARY OF LOAN LOSS EXPERIENCE

         For additional explanation of factors which influence management's
         judgment in determining amounts charged to expense, refer to Page 10,
         "Management Discussion and Analysis" and Pages 24 - 25, Note 1 of the
         Annual Report To Shareholders.

                                       7

<PAGE>   8
                         UNITED BANCORP, INC. FORM 10-K

ITEM 1  DESCRIPTION OF BUSINESS (CONTINUED)

     IV SUMMARY OF LOAN LOSS EXPERIENCE (CONTINUED)

         A    ANALYSIS OF THE ALLOWANCE FOR LOAN LOSSES

              The following schedule presents an analysis of the allowance for
              loan losses, average loan data and related ratios for the years
              ended December 31, 1998, 1997, 1996, 1995 and 1994:


<TABLE>
<CAPTION>
          (In thousands)                1998          1997           1996           1995          1994
                                    -------------  ------------  -------------- -------------  ------------
<S>                                    <C>            <C>            <C>           <C>            <C>     
LOANS
Loans outstanding                      $ 164,221      $171,477       $ 166,516     $ 157,369      $141,076
Average loans outstanding              $ 168,626      $169,066       $ 160,409     $ 150,429      $130,221

          (In thousands)
ALLOWANCE FOR LOAN LOSSES
Balance at beginning of year           $   3,039      $  2,756       $   2,593     $   1,693      $  1,520
Loan charge-offs:
     Commercial                              139           125             467            69            34
     Commercial real estate                    -             -               -             -             -
     Real estate                              51            20              40             9            27
     Installment                             861           661             583           308           220
                                    -------------  ------------  -------------- -------------  ------------
Total loan charge-offs                     1,051           806           1,090           386           281
                                    -------------  ------------  -------------- -------------  ------------


Loan recoveries
     Commercial                               87            32              13             6             7
     Commercial real estate                    -             -               -             -             -
     Real estate                               9             3               5             1             -
     Installment                             151           122              70            75            36
                                    -------------  ------------  -------------- -------------  ------------
Total loan recoveries                        247           157              88            82            43
                                    -------------  ------------  -------------- -------------  ------------

Net loan charge-offs                         804           649           1,002           304           238

Provision for loan losses                    798           932           1,165         1,204           411
                                    -------------  ------------  -------------- -------------  ------------

Balance at end of year                  $  3,033      $  3,039       $   2,756     $   2,593      $  1,693
                                    =============  ============  ============== =============  ============

Ratio of net charge-offs to average
  loans outstanding for the year           0.48%         0.38%           0.62%         0.20%         0.18%
                                    =============  ============  ============== =============  ============

</TABLE>

                                       8
<PAGE>   9
                         UNITED BANCORP, INC. FORM 10-K

ITEM 1   DESCRIPTION OF BUSINESS (CONTINUED)

    IV SUMMARY OF LOAN LOSS EXPERIENCE (CONTINUED)

         B    ALLOCATION OF THE ALLOWANCE FOR LOAN LOSSES

              The following table allocates the allowance for possible loan
              losses at December 31, 1998, 1997, 1996, 1995 and 1994. The
              allowance has been allocated according to the amount deemed to be
              reasonably necessary to provide for the possibility of losses
              being incurred within the following categories of loans at the
              dates indicated:

<TABLE>
<CAPTION>
                                        1998                                                    1997
                            ---------------------------                             --------------------------
                                           % OF LOANS                                              % OF LOANS
       (In thousands)        ALLOWANCE      TO TOTAL            (In thousands)        ALLOWANCE     TO TOTAL
Loan type                      AMOUNT        LOANS       Loan type                      AMOUNT        LOANS
                            ----------- ---------------                             ------------ -------------
<S>                         <C>                 <C>                                      <C>         <C>
    Commercial                   $  215           7.87%       Commercial                 $   403         9.70%
    Commercial real estate          432          33.00%       Commercial real estate         322        28.69%
    Real estate                     567          30.10%       Real estate                    606        29.07%
    Installment                     818          29.03%       Installment                  1,200        32.54%
    Unallocated                   1,001             N/A       Unallocated                    508           N/A
                             ----------- ---------------                             ------------ -------------
Total                           $ 3,033         100.00%   Total                          $ 3,039       100.00%
                             =========== ===============                             ============ =============
<CAPTION>

                                        1996                                                    1995
                             ---------------------------                             --------------------------
                                           % OF LOANS                                              % OF LOANS
       (In thousands)        ALLOWANCE      TO TOTAL            (In thousands)        ALLOWANCE     TO TOTAL
Loan type                      AMOUNT        LOANS        Loan type                    AMOUNT        LOANS
                             ----------- ---------------                             ------------ -------------
<S>                         <C>                 <C>                                      <C>         <C>
    Commercial                   $  320           9.05%       Commercial                 $   551         8.65%
    Commercial real estate          292          24.96%       Commercial real estate         348        22.83%
    Real estate                     601          31.80%       Real estate                    416        32.43%
    Installment                     841          34.19%       Installment                    694        36.09%
    Unallocated                     702             N/A       Unallocated                    584           N/A
                             ----------- ---------------                             ------------ -------------
Total                           $ 2,756         100.00%   Total                          $ 2,593       100.00%
                             =========== ===============                             ============ =============

<CAPTION>
                                        1994
                             ---------------------------
                                           % OF LOANS
       (In thousands)        ALLOWANCE      TO TOTAL
Loan type                      AMOUNT        LOANS
                             ----------- ---------------
<S>                         <C>                 <C>                                      
    Commercial                   $   71           7.41%
    Commercial real estate          258          20.31%
    Real estate                     218          35.25%
    Installment                     584          37.03%
    Unallocated                     562             N/A
                             ----------- ---------------
Total                           $ 1,693         100.00%
                             =========== ===============
</TABLE>


                                       9
<PAGE>   10

                         UNITED BANCORP, INC. FORM 10-K

ITEM 1   DESCRIPTION OF BUSINESS (CONTINUED)

    V    DEPOSITS

      A  SCHEDULE OF AVERAGE DEPOSIT AMOUNTS AND RATES

              (1)  Refer to Page 16 of the Annual Report To Shareholders.
              (2)  Refer to Page 16 of the Annual Report To Shareholders.
              (3)  Refer to Page 16 of the Annual Report To Shareholders.
              (4)  Refer to Page 16 of the Annual Report To Shareholders.
              (5)  - (8) Not applicable.

      B  OTHER CATEGORIES

         Not applicable.

      C  FOREIGN DEPOSITS

         Not applicable.

      D  MATURITY ANALYSIS OF TIME DEPOSITS GREATER THAN $100,000.

         The following schedule details the maturities of time certificates of
         deposit in amounts of $100,000 or more for the year ended December 31,
         1998:

<TABLE>
<CAPTION>
         (In thousands)
<S>                                    <C>         
Three months or less                   $      5,655
Over three through six months                 4,122
Over six through twelve months                3,800
Over twelve months                            8,387
                                       ------------
Total                                  $     21,964
                                       ============
</TABLE>


      E  TIME DEPOSITS GREATER THAN $100,000 ISSUED BY FOREIGN
         OFFICES.

         Not applicable.

    VI   RETURN ON EQUITY AND ASSETS

         The ratio of net income to daily average total assets and average
         shareholders' equity, and certain other ratios, are as follows:

<TABLE>
<CAPTION>
                                                                    DECEMBER 31,
                                                   --------------------------------------------
                                                       1998           1997           1996
                                                   -------------  -------------- --------------
<S>                                                     <C>             <C>            <C>  
Percentage of net income to:

     Average total assets                                 1.17%           1.10%          1.06%
     Average shareholders' equity                        11.80%          11.48%         11.44%

Percentage of dividends declared to net income           39.76%          36.38%         35.10%
Percentage of average shareholders' equity
  to average total assets                                 9.83%           9.55%          9.30%
</TABLE>


                                       10
<PAGE>   11

                         UNITED BANCORP, INC. FORM 10-K

ITEM 1   DESCRIPTION OF BUSINESS (CONTINUED)

    VII  SHORT-TERM BORROWINGS

         Information concerning securities sold under agreements to
         repurchase is summarized as follows:

<TABLE>
<CAPTION>
                (In thousands)                      1998            1997           1996
                                                --------------  -------------- --------------
<S>                                                 <C>             <C>            <C>      
Balance at December 31,                             $   7,733       $   8,391      $   8,642
Weighted average interest rate at December 31,          4.44%           4.90%          4.63%
Average daily balance during the year               $   7,817       $   8,211      $   6,318
Average interest rate during the year                   4.66%           4.81%          4.67%
Maximum month-end balance during the year           $   9,109       $   9,316      $   8,667
</TABLE>

         Securities sold under agreements to repurchase are financing
         arrangements whereby the Company sells securities and agrees to
         repurchase the identical securities at the maturities of the agreements
         at specified prices


         Information concerning the cash management line of credit from the
         Federal Home Loan Bank of Cincinnati, Ohio is summarized as follows:

<TABLE>
<CAPTION>
                (In thousands)                      1998            1997           1996
                                                --------------  -------------- --------------
<S>                                               <C>             <C>          <C>      
Balance at December 31,                           $    9,175      $        -   $       200
Weighted average interest rate at December 31,          5.02%              -          7.15%
Average daily balance during the year             $    2,085      $      608   $       242
Average interest rate during the year                   5.95%           6.06%         5.92%
Maximum month-end balance during the year         $    9,175      $    1,845   $     1,000
</TABLE>

         No other individual component of the borrowed funds total comprised
         more than 30% of shareholders' equity and accordingly are not disclosed
         in detail.

ITEM 2   PROPERTIES

         Refer to Pages 4 - 5, "Corporate Profile" in the Annual Report To
Shareholders.

ITEM 3   LEGAL PROCEEDINGS

         Refer to Page 35, Note 10 of the Annual Report To Shareholders.

ITEM 4   SUBMISSION OF MATTERS TO A VOTE OF SECURITY HOLDERS

         No motions were submitted to shareholders for a vote during the fourth
quarter of 1998.

PART II

ITEM 5   MARKET FOR REGISTRANT'S COMMON EQUITY AND RELATED STOCKHOLDER MATTERS

         Refer to Page 7, "Shareholder Information" of the Annual Report To
Shareholders.

ITEM 6   SELECTED FINANCIAL DATA

         Refer to inside back cover, "Five Year Performance Summary" of the
Annual Report To Shareholders.

ITEM 7   MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND RESULTS
         OF OPERATIONS 

         Refer to Pages 9 - 18, 43 and 44, "Management's Discussion and
Analysis" of the Annual Report To Shareholders.


                                       11

<PAGE>   12

ITEM 7A  QUANTITATIVE AND QUALITATIVE DISCLOSURES ABOUT MARKET RISK

         Refer to Pages 13 - 14, "Asset/Liability Management and Sensitivity to
Market Risks" of the Annual Report To Shareholders.

ITEM 8   FINANCIAL STATEMENTS AND SUPPLEMENTARY DATA

         Refer to Pages 15 and 19 - 40 of the Annual Report To Shareholders.

ITEM 9   CHANGES IN AND DISAGREEMENTS WITH ACCOUNTANTS

         There were no changes in or disagreements with accountants.


                                       12


<PAGE>   13
                         UNITED BANCORP, INC. FORM 10-K

PART III

ITEM 10  DIRECTORS AND EXECUTIVE OFFICERS OF THE REGISTRANT

         (a)  Refer to Pages 4 - 8 of the Proxy Statement.

         (b)  Executive Officers of the Registrant:

<TABLE>
<S>                                                  <C>      <C>                                               
                  James W. Everson                   60       Chairman, President and Chief Executive Officer

                  Norman F. Assenza, Jr.             53       Vice President - Operations and Secretary

                  Randall M. Greenwood               35       Vice President - Chief Financial Officer, Treasurer

                  Alan M.  Hooker                    48       Vice President - Administration

                  James A. Lodes                     53       Vice President - Lending

                  Harold W. Price                    53       Vice President - Administration
</TABLE>


         (1)  Each individual has held the position noted during the past five
              years, except for the following:

              Randall M. Greenwood served as a Business Assurance Manager of
              Coopers and Lybrand LLP of Columbus, Ohio from 1993 to November of
              1997. He served as a Manager for BankOne Corporation in Columbus,
              Ohio from February 1991 to August 1993 and as a Supervisor at
              Coopers and Lybrand LLP in Columbus, Ohio from September 1986
              through February 1991. He has served as Vice President - Chief
              Financial Officer of United Bancorp, Inc. and as Senior Vice
              President - Chief Financial Officer of The Citizens Savings Bank,
              Martins Ferry, Ohio since December 1997.

              Alan M. Hooker served as President of Fairfield National Division
              of the Park National Bank where he also served on their Advisory
              Board. He has held senior level banking positions with financial
              institutions in Washington, D.C., and Baltimore, Maryland. He has
              served as President and Chief Executive Officer of The Community
              Bank, Glouster, Ohio and as Vice President - Administration of
              United Bancorp, Inc. since October 26, 1998.

              James A. Lodes, served as Vice President - Commercial Lending
              since December 1992 and as Senior Vice President Lending since
              1994 with The Citizens Savings Bank, Martins Ferry, Ohio and Vice
              President - Lending for United Bancorp, Inc. since 1995.

              Harold W. Price has previously served as President and Chief
              Executive Officer of the Exchange Bank of Canal Fulton from 1979
              until 1984 when it was acquired by the First National Bank of
              Akron, an affiliate of First Bancorp, Inc. of Ohio. From 1985 to
              1992, he served as Executive Vice President and a member of the
              Board of Directors of The Old Phoenix National Bank of Medina.
              From 1992 to 1993, he served as Executive Vice President and
              Senior Loan Officer of the Elyria Savings and Trust Company in
              Elyria, Ohio. He has served as President and Chief Executive
              Officer of The Citizens-State Bank of Strasburg, Strasburg, Ohio
              and as Vice President of United Bancorp, Inc. since April 1, 1993.
              He has served as Vice President - Administration of United
              Bancorp, Inc. since April 19, 1995.

ITEM 11       EXECUTIVE COMPENSATION

              Refer to Pages 10 - 15 of the Proxy Statement.

ITEM 12       SECURITY OWNERSHIP OF CERTAIN BENEFICIAL OWNERS AND MANAGEMENT

              Refer to Pages 4 - 8 of the Proxy Statement.

ITEM 13       CERTAIN RELATIONSHIPS AND RELATED TRANSACTIONS

              Refer to Page 15 of the Proxy Statement.


                                       13
<PAGE>   14


PART IV

ITEM 14    EXHIBITS, FINANCIAL STATEMENTS, SCHEDULES AND REPORTS ON FORM 8-K

    (a)  DOCUMENTS FILED AS PART OF FORM 10-K

         1.   The following consolidated financial statements appear in the 1998
              Annual Report To Shareholders and are incorporated by reference:

<TABLE>
<S>                                                                       <C>
              Report of Independent Auditors                              Page     19
              Consolidated Balance Sheets                                 Page     20
              Consolidated Statements of Income                           Page     21
              Consolidated Statements of Shareholders' Equity             Page     22
              Consolidated Statements of Cash Flow                        Page     23
              Notes to the Consolidated Financial Statements              Pages    24 - 40
</TABLE>

         2.   The summary of selected quarterly results of operations appears on
              Page 15 in the 1998 Annual Report To Shareholders and is
              incorporated by reference.

         3.   Exhibits

              2    Not Applicable
              3    (i)(ii) Articles of Incorporation of United Bancorp, Inc.
                   including amendments and By Laws, previously filed with the
                   Securities and Exchange Commission on November 16, 1983.
              4    Not applicable.
              9    Not applicable.
              10   Reference to special severance agreement on Page 14 of the
                   Proxy Statement
              11   Statement regarding computation of per share earnings
                   (included in Note 1 to the consolidated financial statements
                   on page 26 of the Annual Report To Shareholders.)
              12   Not applicable.
              13   Reference to the Annual Report To Shareholders for the fiscal
                   year ended December 31, 1998. 16 Not applicable.
              18   Not applicable.

              21.1 Reference to The Citizens Savings Bank, Martins Ferry, Ohio,
                   incorporated on December 31, 1902, previously filed with the
                   Securities and Exchange Commission.
              21.2 Reference to The Citizens-State Bank of Strasburg, Strasburg,
                   Ohio, incorporated on December 31, 1924, previously filed
                   with the Securities and Exchange Commission.
              21.3 Reference to The Glouster Community Bank, Glouster, Ohio,
                   incorporated on August 1, 1949, previously filed with the
                   Securities and Exchange Commission.
              22   Not applicable.
              23   Consents of Experts and Council.
              24   Not applicable.
              27   Financial Data Schedule
              28   Not applicable.
              99   Not applicable.

     (b)  The Company filed no reports on SEC Form 8-K during the last quarter
          of the period covered by this report.


                                       14

<PAGE>   15
                         UNITED BANCORP, INC. FORM 10-K

                                                                            
     Pursuant to the requirements of Section 13 or 15(d) of the Securities
     Exchange Act of 1934, the registrant has duly caused this report to be
     signed on its behalf by the undersigned, thereunto duly authorized.

     (Registrant) United Bancorp, Inc.

     By:   /s/ James W. Everson                                  March 24, 1999
           -------------------------------------
           James W. Everson, Chairman, President & CEO


     By:   /s/ Randall M. Greenwood                              March 24, 1999
           -------------------------------------
           Randall M. Greenwood, CFO


     By:   /s/ Michael J. Arciello                               March 24, 1999
           -------------------------------------
           Michael J. Arciello


     By:   /s/ Herman E. Borkoski                                March 24, 1999
           -------------------------------------
           Herman E. Borkoski


     By:   /s/ John H. Clark, Jr.                                March 24, 1999
           -------------------------------------
           John H. Clark, Jr.


     By:   /s/ Dr. Leon F. Favede                                March 24, 1999
           -------------------------------------
           Dr. Leon F. Favede


     By:   /s/ John M. Hoopingarner                              March 24, 1999
           -------------------------------------
           John M. Hoopingarner


     By:   /s/ Richard L. Riesbeck                               March 24, 1999
           -------------------------------------
           Richard L. Riesbeck


     By:   /s/ L.E. Richardson, Jr.                              March 24, 1999
           -------------------------------------
           L.E. Richardson, Jr.


     By:   /s/ Errol C. Sambuco                                  March 24, 1999
           -------------------------------------
           Errol C. Sambuco


     By:   /s/ Matthew C. Thomas                                 March 24, 1999
           -------------------------------------
           Matthew C. Thomas


                                       15
<PAGE>   16
                         UNITED BANCORP, INC. FORM 10-K

                                 EXHIBIT INDEX

Exhibit No.                        Description                   SK Item 601 No.

 13                      Annual Report To Shareholders
 23.1                    Consent Crowe, Chizek, and Company LLP
 23.2                    Consent of Robb, Dixon, Francis, Davis, Oneson 
                         & Company
                         Onison and Company 
 27.1998                 Financial Data Schedule
 27.1997                 Financial Data Schedule (Restated)
 27.1996                 Financial Data Schedule (Restated)
 27.1998-1Q              Financial Data Schedule (Restated)
 27.1998-2Q              Financial Data Schedule (Restated)
 27.1997-1Q              Financial Data Schedule (Restated)
 27.1997-2Q              Financial Data Schedule (Restated)
               




                                       16